diff --git "a/CdE0T4oBgHgl3EQfyQI7/content/tmp_files/load_file.txt" "b/CdE0T4oBgHgl3EQfyQI7/content/tmp_files/load_file.txt" new file mode 100644--- /dev/null +++ "b/CdE0T4oBgHgl3EQfyQI7/content/tmp_files/load_file.txt" @@ -0,0 +1,2118 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf,len=2117 +page_content='Astronomy & Astrophysics manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' ms ©ESO 2023 January 9, 2023 TDCOSMO XIII.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Improved Hubble constant measurement from lensing time delays using spatially resolved stellar kinematics of the lens galaxy Anowar J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Shajib,1, 2,⋆ Pritom Mozumdar,3 Geoff C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='-F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Chen,4 Tommaso Treu,4 Michele Cappellari,5 Shawn Knabel,4 Sherry H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Suyu,6, 7, 8 Vardha N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Bennert,9 Joshua A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Frieman,1, 2, 10 Dominique Sluse,11 Simon Birrer,12, 13, 14 Frederic Courbin,15 Christopher D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Fassnacht,3 Lizvette Villafaña,4 Peter R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Williams4 (Affiliations can be found after the references) Received xxx, xxxx;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' accepted xxx, xxxx ABSTRACT Strong-lensing time delays enable measurement of the Hubble constant (H0) independently of other traditional methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The main limitation to the precision of time-delay cosmography is mass-sheet degeneracy (MSD).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Some of the previous TDCOSMO analyses broke the MSD by making standard assumptions about the mass density profile of the lens galaxy, reaching 2% precision from seven lenses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' However, this approach could potentially bias the H0 measurement or underestimate the errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' In this work, for the first time, we break the MSD using spatially resolved kinematics of the lens galaxy in RXJ1131−1231 obtained from the Keck Cosmic Web Imager spectroscopy, in combination with previously published time delay and lens models derived from Hubble Space Telescope imaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' This approach allows us to robustly estimate H0, effectively implementing a maximally flexible mass model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Following a blind analysis, we estimate the angular diameter distance to the lens galaxy Dd = 865+85 −81 Mpc and the time-delay distance D∆t = 2180+472 −271 Mpc, giving H0 = 77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1+7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='3 −7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1 km s−1 Mpc−1 – for a flat Λ cold dark matter cosmology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The error budget accounts for all uncertainties, including the MSD inherent to the lens mass profile and the line-of-sight effects, and those related to the mass–anisotropy degeneracy and projection effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Our new measurement is in excellent agreement with those obtained in the past using standard simply parametrized mass profiles for this single system (H0 = 78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='3+3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='4 −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='3 km s−1 Mpc−1) and for seven lenses (H0 = 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='2+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='6 −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='6 km s−1 Mpc−1), or for seven lenses using single-aperture kinematics and the same maximally flexible models used by us (H0 = 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='3+5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='8 −5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='8 km s−1 Mpc−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' This agreement corroborates the methodology of time-delay cosmography.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Key words.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' cosmology: distance scale – gravitational lensing: strong – Galaxy: kinematics and dynamics – Galaxies: elliptical and lenticular, cD – Galaxies: individual: RXJ1131−1231 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Introduction The Hubble constant, H0, the current value of the Universe’s ex- pansion rate, is a crucial cosmological parameter that also sets the extragalactic distance scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Recently, tension has emerged between early- and late-Universe estimates of H0 (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Freed- man 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Abdalla et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The temperature and polarisa- tion fluctuations in the cosmic microwave background (CMB) provide an estimate of the Hubble parameter at the last scatter- ing surface H(z ≈ 1100), which can be extrapolated to the cur- rent epoch using the Λ cold dark matter (ΛCDM) cosmology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The CMB measurements from Planck give H0 = 67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='4 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5 km s−1 Mpc−1 (Planck Collaboration 2020) and H0 = 67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='6 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1 km s−1 Mpc−1(Aiola et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' In the local Universe, H0 can be estimated using the cosmic distance ladder, which uses luminos- ity distances of type Ia supernovae (SNe Ia) with their absolute brightness calibrated using different classes of stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The Super- nova H0 for the Equation of State of the dark energy (SH0ES) team uses Cepheids and parallax distances for this calibration, and they find H0 = 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='04 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='04 km s−1 Mpc−1 (Riess et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' This value is in 5σ tension with the Planck CMB-based measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' If this difference is not due to systematic errors in either of these measurements (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Efstathiou 2021), then this tension could point to new physics beyond the ΛCDM cosmo- logical model (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Knox & Millea 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' ⋆ NFHP Einstein Fellow To determine whether this “Hubble tension” is due to sys- tematics or new physics, multiple independent methods to mea- sure H0 are needed (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Verde et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Di Valentino et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Freedman 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The Carnegie–Chicago Hubble Project uses the tip of the red giant branch (TRGB) to calibrate the SNe Ia absolute brightness and measures H0 = 69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='6 ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='9 km s−1 Mpc−1 (Freedman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2019, 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' This TRGB-calibrated measurement is statistically consistent with both the SH0ES measurement and the CMB-based measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' However, sev- eral independent local probes strengthen the “H0 tension” by measuring values consistent with the SH0ES value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' For exam- ple, the Megamaser Cosmology Project (MCP) estimates H0 = 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='9 ± 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='0 km s−1 Mpc−1(Pesce et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2020), the surface bright- ness fluctuation (SBF) method measures H0 = 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='7 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='7 ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='4 km s−1 Mpc−1 (Blakeslee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2021), and the Tully–Fisher- relation-based method calibrated with Cepheids measures H0 = 75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='2 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='3 km s−1 Mpc−1 (Kourkchi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Strong-lensing time delays provide an independent measure- ment of H0 (Refsdal 1964;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' for an up-to-date review, see Bir- rer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2022b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Treu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2022, for a historical perspective, see Treu & Marshall 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' In strong lensing, a background source appears as multiple images due to the gravitational de- flection of photons by a massive foreground galaxy or galaxy cluster.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The photons that were emitted at the same time from the background source arrive in different images with a rela- tive time delay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' This time delay carries cosmological informa- Article number, page 1 of 21 arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='02656v1 [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='CO] 6 Jan 2023 A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' ms tion through a combination of angular diameter distances in- volved in the lensing system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' This combination is referred to as the “time-delay distance", which is inversely proportional to H0 (Refsdal 1964;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Schneider et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 1992;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Suyu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2010).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The Time-Delay COSMOgraphy (TDCOSMO) collaboration has an- alyzed seven time-delay lenses to measure H0 with 2% error, H0 = 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='2±1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='6 km s−1 Mpc−1 assuming a power-law or compos- ite (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', stars and Navarro–Frenk–White (NFW) halo;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Navarro et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 1996, 1997) mass profile for the lensing galaxies (Mil- lon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2020b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The TDCOSMO collaboration encompasses the COSmological MOnitoring of GRAvItational Lenses (COS- MOGRAIL;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Courbin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2005;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Millon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2020a), the H0 Lenses in COSMOGRAIL’s Wellspring (H0LiCOW;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Suyu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2010, 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Bonvin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Birrer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Rusu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Wong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2020), the Strong-lensing High Angular Reso- lution Programme (SHARP;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2019), and the STRong- lensing Insights into the Dark Energy Survey (STRIDES;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Treu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Shajib et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2020) collaborations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The simple parametric lens models, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', the power law, adopted in the TDCOSMO analyses are “industry standard” con- sistent with non-lensing measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The TDCOSMO collab- oration has performed various systematic checks on the adopted lens modeling procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' These checks find potential system- atic biases to be lower than the acceptable limit (∼1%) from the choice of mass model parametrization (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', power law or composite, Millon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2020b), from ignoring dark substruc- tures in the lens galaxy’s halo (Gilman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2020), from ig- noring disky or boxy-ness in the baryonic distribution (Van de Vyvere et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2022a), from using different lens modeling soft- ware (Shajib et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2022a), and from ignoring potential isoden- sity twists and ellipticity gradients in the lens galaxy (Van de Vyvere et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2022b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' However, a significant source of potential systematics could arise due to the relatively simple parametriza- tion of the lens mass profile (Kochanek 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The well-known mass-sheet degeneracy (MSD) does not allow one to constrain the mass profile shape of the deflector galaxy from lens imaging observables alone (Falco et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 1985;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Schneider & Sluse 2013, 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Non-lensing observables, such as the deflector galaxy’s velocity dispersion or the source’s unlensed intrinsic brightness, are required to break the mass-sheet degeneracy and simultane- ously constrain H0 and the mass profile shape (Treu & Koop- mans 2002;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Shajib et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Yıldırım et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2020, 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Birrer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2020, 2022a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The TDCOSMO collaboration has redesigned the experi- ment to mitigate this systematic by relaxing the simple paramet- ric assumptions in the mass profile and constraining the profile shape solely from stellar velocity dispersion measurements of the lensing galaxies (Birrer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Relaxing the assump- tion on the mass profile leads to an increase in the H0 uncer- tainty from 2 to 8% – which is dominated by the uncertainty of the measured velocity dispersion – giving H0 = 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5+5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='6 −6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1 km s−1 Mpc−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' One approach to improving the precision is to incorpo- rate prior information on the mass profile shape from the mea- sured velocity dispersions of a larger sample of external lenses without measured time delays.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Assuming that the Sloan Lens ACS (SLACS) survey’s lens galaxies are drawn from the same population as the TDCOSMO lens galaxies and using their ve- locity dispersions to constrain the mass profile shape, the un- certainty on H0 improves to 5%, giving H0 = 67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='4+4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1 −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='2 km s−1 Mpc−1(Birrer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Note that this estimate is statistically consistent within 1σ with the larger 8% H0 measurement above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' However, the shift could also arise from systematic differences, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', a difference between the parent populations of time-delay and non-time-delay lenses (Gomer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Such differ- ences could arise, for example, from evolutionary effects, as the SLACS sample is at lower redshift than the TDCOSMO lenses (see, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Sonnenfeld et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2015, for a discussion of the evolu- tion of mass density profiles of massive elliptical galaxies).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Spatially resolved velocity dispersion measurements of lens galaxies for systems with measured time delays are critical to drastically improving the H0 precision, given the limited sam- ple size of time-delay lenses (Shajib et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Yıldırım et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The spatially resolved nature of the measured veloc- ity dispersion is especially powerful in simultaneously break- ing the MSD and the mass-anisotropy degeneracy (Cappellari 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Barnabè et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2009, 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Collett et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Shajib et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Spatially resolved velocity dispersion measurements for ∼40 time-delay lens galaxies will yield an independent ≲2% H0 measurement without any mass profile assumption (Birrer & Treu 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Additional constraints from velocity dispersion measurements of non-time-delay lens galaxies or magnification information for standardizable lensed type Ia supernovae can further improve the uncertainty to ≲ 1% (Birrer & Treu 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Birrer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2022a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' In this paper, we measure the spatially resolved velocity dis- persion for the lens galaxy in the strongly lensed quasar system RXJ1131−1231using the Keck Cosmic Web Imager (KCWI) in- tegral field spectrograph on the W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Keck Observatory (Mor- rissey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2012, 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' and constrain H0 without any mass profile assumption from this single time-delay lens system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' This is the first application of spatially resolved velocity dispersion from a time-delay lens to measure H0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' This lens system was pre- viously used to measure H0 by combining the observed imaging data, single-aperture velocity dispersion, time delays, and anal- ysis of the line-of-sight environment (Suyu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2013, 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' However, these previous studies assumed simple parametriza- tions for the mass profile, such as a power law or a combination of the NFW profile and the stellar profile with constant mass- to-light, which is the industry standard in modeling of galaxy- scale lenses (Shajib et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2022b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Birrer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (2016) marginal- ized over the MSD effect for the system RXJ1131−1231 to con- strain H0 using a single-aperture velocity dispersion measure- ment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Here, we allow the maximal freedom in the MSD by in- troducing one free parameter on top of the simply parametrized mass profile constrained by lens modeling, which is completely degenerate with H0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' This paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' In Section 2, we describe the observational strategy and data reduction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' In Section 3, we describe the procedures to extract the spatially resolved kine- matics map from the KCWI data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' In Section 4, we briefly review the lensing and dynamical formalisms and how we combine the two to mitigate the MSD in our analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Then in Section 5, we describe our dynamical models and present results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We infer the cosmological parameters from our analysis in the Section 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We discuss our results in Section 7 and conclude the paper in Sec- tion 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We performed the cosmological inference blindly in this pa- per.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The measurement of velocity dispersion was not blinded.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' However, we blinded the cosmological and other model parame- ters directly related to cosmological parameters in the dynamical modeling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Before unblinding, this analysis went through an in- ternal collaboration-wide review and code review.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' After all the coauthors had agreed that the necessary systematic checks were satisfactorily performed, we froze the analysis and unblinded on 5 January 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' All the sections in this paper except for the final discussion in Section 7 and summary in Section 8 were written before unblinding.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' After unblinding, we only made minor edits Article number, page 2 of 21 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Shajib et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' : H0 from spatially resolved kinematics of RXJ1131−1231 N E 1" A B C D G S Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' HST/ACS image of RXJ1131−1231 in the F814W band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The four quasar images are labeled with A, B, C, and D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The central deflec- tor is marked with G, of which we are measuring the spatially resolved velocity dispersion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' An arrow points to the nearby satellite S, which we mask out in the velocity dispersion measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='. The North and East directions and 1¨scale are also illustrated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' for clarity and grammatical corrections in the previous sections and added the unblinded numbers where relevant in the abstract, main text, and plots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Observations and data reduction In this section, we provide a brief description of the lens sys- tem RXJ1131−1231 (Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1), the spectroscopic observation with KCWI (Section 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='2), and the data reduction procedure (Sec- tion 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Description of lens system The quadruply imaged quasar lens system RXJ1131−1231 was discovered by Sluse et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The deflector in this system is an elliptical galaxy with redshift zd = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='295, and the source redshift is zs = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='657 (Sluse et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Due to its low red- shifts, the system is relatively bright and large in angular size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The Einstein ring in this system contains intricate features, pro- viding a wealth of information to constrain the lens mass model (see Figure 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Due to its early discovery and information-rich features, this system is one of the most studied lensed quasar systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The time delays for this system were measured by Tewes et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Suyu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (2013, 2014) performed cosmo- graphic analyses of this system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' These authors combined simply parametrized lens models based on the high-resolution imaging from the HST’s Advanced Camera for Surveys (ACS) instru- ment (HST-GO 9744;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' PI: Kochanek), the measured time delays, single-aperture velocity dispersion, and external convergence es- timate to infer H0 = 80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='0+4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5 −4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='7 km s−1 Mpc−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' However, such sim- ply parametrized lens models implicitly break the MSD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Birrer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (2016) performed an independent mass modeling of this system while marginalizing the MSD with a prior on the source size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' These authors found the prior choice on the anisotropy in the dynamical modeling to be the dominant systematic in infer- ring H0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' KCWI Spectroscopy We obtained integral field unit (IFU) spectroscopy of RXJ1131−1231 on 16 May and 7 June 2021 with the KCWI in- strument on the Keck Observatory (Morrissey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2012, 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We chose KCWI with the small IFU slicer and the low-resolution blue grating (BL) with a field-of-view (FoV) of 8′′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='4 × 20′′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The spectral resolution is R ≈ 3600, corresponding to an instrumental dispersion σinst ∼ 35 km s−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The reciprocal dispersion is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5 Å per pixel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The observed wavelength range 3600–5600 Å covers the Ca H&K lines with wavelengths λλ3933, 3968 Å at the red- shift of the lens galaxy (zd = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='295).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We primarily use these lines to determine the stellar velocity dispersion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The redshifted 4304 Å G-band is beyond the observed range, so it is not accessible with the KCWI for the RXJ1131−1231 system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We aligned the FoV’s longer side with the North direction (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', PA = 0◦) and dithered the individual exposures by 9′′ along the North-South direction.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' As the extent of the RXJ1131−1231 system is smaller than the FoV, each exposure contained the en- tire lens system within the FoV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' In different exposures, the lens system occupied the upper or lower portion of the FoV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Thus, the sky in an exposure with the system occupying the upper por- tion can be subtracted using another exposure with the system occupying the lower portion, and vice versa.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We obtained six ex- posures with a total integration time of 10,560 s on 16 May and three with a total integration time of 5,400 s on 7 June.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' There- fore, the total exposure time is texp = 15, 960 s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The airmass ranged from 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='2 to 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='48 over the integrating period.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Data Reduction We use the official Python-based data reduction pipeline1 (DRP) to reduce our data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The DRP converts the 2D raw data captured on the detector into a 3D datacube.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' It performs geometry cor- rection, differential atmospheric refraction correction, and wave- length calibration and produces a final standard-star-calibrated 3D datacube for each exposure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The calibration with the stan- dard star corrects for instrumental response and scales the data to flux units (Morrissey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We use the final output file with the suffix “_icubes” for further analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We stack the dithered datacubes through drizzling (Fruchter & Hook 2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Since the exposures are obtained on different dates, the world coordinate system information is not accurate enough to determine the relative positions of the dithered expo- sures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We follow Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (2021b) to determine the relative po- sitions by simultaneously fitting the point spread function (PSF) to the four quasar image positions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' To perform the drizzling on the datacubes, we repurpose the drizzling routine of the DRP for OSIRIS, another IFU spectrograph on the Keck Observatory2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' For the drizzling process, we set pixfrac = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='7 as recom- mended to reduce correlated uncertainties between the drizzled pixels (Avila et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We calculate the drizzled weight image and ensure that the ratio of RMS/median < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='2 in the region of interest so that the trade-off is balanced between improving the 1 developed by Luca Rizzi, Don Neill, Max Brodheim;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' https:// kcwi-drp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='readthedocs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='io/ 2 https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='com/Keck-DataReductionPipelines/ OsirisDRP Article number, page 3 of 21 A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' ms image resolution and increasing the background noise (Gonzaga et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The rectangular pixel size 0′′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1457′′ × 0′′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='3395 of the KCWI is kept the same in the drizzled output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We transform the datacube to have square pixels of size 0′′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1457 × 0′′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1457 through resampling while conserving the total flux.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We converted the pix- els into square sizes for the convenience of Voronoi binning the spectra using the software vorbin as described in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We directly estimate the PSF from the observed data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We produce a 2D image from the datacube by summing along the wavelength axis (see Figure 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We create a model for this KCWI image using a high-resolution template from the HST imaging (Figure 1) that has a pixel size 0′′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='05 and PSF full width at half maximum (FWHM) 0′′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' In the model, the template is con- volved with a Gaussian PSF with a free FWHM parameter, and the positioning of the template on the KCWI image grid is fitted with two additional free parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' By optimizing the model, we estimate that the PSF FWHM is 0′′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='96.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Kinematics maps This section describes our procedure to obtain the final kine- matics map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We use the pPXF package3 to fit the spectra with a library of stellar templates and extract the velocity dispersion (Cappellari 2017, 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' In Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1, we describe the stel- lar templates used for the analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' In Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='2, we present the measurement of the spatially-resolved kinematics map of the lens galaxy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' In Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='3, we test the systematics of the velocity dispersion measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Library of Stellar Templates The popularly used template libraries Medium-resolution Isaac Newton Telescope library of empirical spectra (MILES;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Sánchez-Blázquez et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2006) and INDO-US templates (Valdes et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2004) are both too low resolution to fit our datasets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The KCWI’s instrumental resolution of R ≈ 3600 leads to σinst ∼ 35 km s−1 for a Gaussian line spread function (LSF)4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' MILES has a resolution of σtemplate ∼ 64 km s−1 (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', R ∼ 2000), and the INDO-US templates have an approximately constant- wavelength resolution of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='2 Å, which corresponds to σtemplate = 39 km s−1 over the Ca H&K wavelength range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Therefore, we choose the X-shooter Spectral Library (XSL), which contains 628 stars covering three segments, including UVB, Vis, and NIR bands (Gonneau et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' As our data cover the rest-frame blue/UV range, we only use the UVB segment to fit the data, where its resolution is R ∼ 9700 and σtemplate ∼ 13 km s−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Measuring the velocity dispersion We choose a cutout centred on the lens system with 6′′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='235 × 6′′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='235 (43 pixels × 43 pixels) to initiate the analysis (see Fig- ure 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We estimate the lens galaxy light’s signal-to-noise ra- tio (S/N) in each spatial pixel (hereafter, spaxel) within this ini- tial cutout.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We then select a region with sufficient S/N from the lens galaxy and relatively low quasar contamination for measur- ing the velocity dispersion (the yellow contour in Figure 2’s left panel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We perform Voronoi binning within this selected region 3 https://pypi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='org/project/ppxf/ 4 We quantitatively verified that the shape of the instrumental LSF is Gaussian (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Figure 28 of Morrissey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Thus, the treatment of the instrumental LSF in pPXF is self-consistent and avoids any system- atic bias due to inconsistent definitions of the LSF’s FWHM (Robertson 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' to preserve the maximal spatial resolution and reduce the bias in the lower-S/N region (Cappellari & Copin 2003).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We elaborate on these steps below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' To estimate the lens galaxy’s S/N in each spaxel, we first si- multaneously fit the quasar and the lens galaxy in each spaxel to calculate the signal from each of them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We perform this fitting within the wavelength range 3400–4300 Å.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' As the four quasar images surround the lens galaxy, each spaxel receives a differ- ent contribution from the quasar light.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We take spectra at the central spaxel of image A as the quasar template, ignoring the lens galaxy’s small contribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Later in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='3, we also choose the quasar template from images B and C to account for the associated systematic uncertainty, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', the potential impact of chromatic microlensing that may change the contrast between the line and the continuum (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Sluse et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2007).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We determine a single optimal template spectrum for the lens galaxy template.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' For this purpose, we binned the spectra from spaxels within a circular region of radius 0′′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5 centered on the lens galaxy and fit it with pPXF using the 628 stellar templates from the XSL and the quasar template.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We also include a Leg- endre polynomial of degree 3 as a component in the fitting to ac- count for any residual gradient in the continuum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' pPXF chooses 39 of the stellar templates and builds the optimal template by taking a weighted linear combination of them.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' See Figure 3 for the weighted distribution of spectral types of the full template li- brary and that of the 39 stars selected by pPXF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Among those stars in the XSL with stellar classes specified by the Simbad database (Wenger et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2000), G-type stars are selected with the highest total weight, consistent with the fact that massive elliptical galaxy spectra are dominated by G and K-type stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' In the pPXF fitting procedure, the stellar templates are broad- ened, corresponding to a freely varying velocity dispersion, but the velocity dispersion does not broaden the quasar template.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Once the optimal galaxy template is constructed, we use this template and the quasar template to fit the spectrum of each spaxel individually.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We use this optimal template to fit the galaxy spectra in individual spaxels instead of the full template library to avoid large spurious fluctuations in the measured velocity dis- persion from spaxel to spaxel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We show the decomposition of the spectra from one example spaxel into different components after fitting with pPXF in Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We calculate the signal of the lens galaxy’s spectrum in each spaxel by subtracting the mod- eled quasar component from the observed spectra.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The noise is estimated by adding in quadrature the Poisson noise of the total signal and the background noise estimated from an empty patch of the sky.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The noise values are multiplied by √ 2 to account for the fact that the square pixels are created from the rectan- gular pixels about double the size through resampling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We esti- mate the S/N using the restframe wavelength range 3985–4085 Å, slightly above the Ca H&K absorption lines in wavelength (see the purple shaded region in Figure 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' To perform Voronoi binning before the velocity dispersion measurement, we select the spaxels within a radius of 1′′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='55 from the lens galaxy center that avoid the brightest spaxels contain- ing images A, B, and C and the lensed arcs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We also exclude a circular region around image D with radius 0′′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' To avoid any po- tential bias due to contamination from the satellite galaxy S, we exclude the spaxel at its position (∆RA = 0′′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='09, ∆Dec = 0′′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='54 from the galaxy center, Suyu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We also exclude pixels with S/N < 1 Å−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' In the end, the spaxels within the selected re- gion have S/N > 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='4 Å−1 (see Figure 2 for the selected region).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 5 For reference, 1′′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5 corresponds to 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='6 kpc at zd = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='295 for a fiducial flat ΛCDM cosmology with H0 = 70 km s−1 Mpc−1 and Ωm = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Article number, page 4 of 21 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Shajib et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' : H0 from spatially resolved kinematics of RXJ1131−1231 N E 1" KCWI data of RXJ1131 1231 3400 3600 3800 4000 4200 Restframe wavelength (�) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='03 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='05 Data Best fit model (galaxy + quasar) Best fit quasar model Data quasar Residual (= data model) 0 200 400 600 800 1000 1200 Flux (arbitrary unit) Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Left: 2D representation (median-collapsed) of the 3D KCWI datacube for RXJ1131−1231.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The yellow contour traces the region with 1′′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5 radial extent from the center selected for stellar kinematic measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' A circular region with 0′′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5 radius around image D and the spaxel containing the satellite S are excluded from this selected region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' All the individual spaxels within this region have continuum S/N > 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='4 Å−1 for the lens galaxy’s light within 3985–4085 Å (the purple shaded range in the right panel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Right: The spectra (grey) from an example pixel (grey box in the left panel) and the estimate of the signal from the lens galaxy’s spectra (orange) after removing the contribution from the quasar light (blue).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The full model of the spectra is presented with the red line, and the model’s residual is plotted in emerald color.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The vertical purple shaded region marks where we compute the continuum S/N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' O B A F G K M L S C ~ Stellar type 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5 Normalized density All Set 1 Set 2 Set 3 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Distribution of the stellar spectral types in the XSL according to the Simbad database.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Unspecified stars are grouped in the ‘∼’ class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The dark grey color represents the full library of 628 stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Set 1 (or- ange) refers to the 39 stars selected by pPXF out of the full library to construct an optimal template 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Set 2 (blue) refers to 32 stars selected from a random half of the full library and set 3 (emerald) refers to 33 stars selected from the other half.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Sets 2 and 3 have 15 and 17 stars, re- spectively, in common with Set 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The alternating light grey and white vertical regions divide the spectral classes for easier visualization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We perform Voronoi binning using vorbin6 given the estimated S/N values for each spaxel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' In Figure 4, we show the 41 Voronoi bins obtained by setting the target S/N ≈ 23 Å−1 for each bin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' This target S/N was chosen so that the resultant S/N ≳ 20 Å−1 for each bin, which is standard practice (Figure 4, only bin 16 has S/N ≈ 18 Å−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' For each Voronoi bin, we measure the velocity dispersion by fitting the binned spectra using pPXF using the optimal galaxy template described above, the quasar template, and the additive Legendre polynomial to model any slight gradient in the popula- tion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' A few examples of pPXF fit of the binned spectra are shown in Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 6 https://pypi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='org/project/vorbin/ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Estimation of systematic uncertainty To estimate the systematic uncertainties in the velocity disper- sion measurement, we consider a range of plausible choices in the extraction procedure: the degrees of the additive Legendre polynomial used to correct the template continuum shape be- tween 2 to 4;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' the quasar template obtained from images A, B, and C;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' the fitted wavelength range chosen from 3300–4200 Å, 3350– 4250 Å, and 3400–4300 Å;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' and three sets of template spectra used in the fitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The first set of template spectra contains the complete XSL of 628 stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The second set contains half of the entire sample that is randomly selected, and the third set con- tains the other half.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The numbers of stars selected by pPXF in the three sets are 39, 32, and 33, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Sets 2 and 3 have 15 and 17 stars, respectively, in common with Set 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Figure 3 shows the distribution of spectral types in all three sets and the entire library.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We do not take the quasar template from image D as it is much fainter than the other images, and thus the galaxy contribution in the brightest spaxel on image D is non-negligible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Taking a combination of all of these choices yields 81 different setups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We illustrate the shift in the extracted velocity dispersion maps for one change of setting at a time in Figures 6 and 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We estimate the variance-covariance matrix of the binned ve- locity dispersions from these 81 setups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' To do this, we generate 1,000 random realizations of the measured velocity dispersion map for each of the 81 setups using the corresponding statistical uncertainty.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We create the variance-covariance matrix from the 81,000 realizations combined from all the setups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' In this way, the diagonal terms of the variance-covariance matrix encode the total variance from systematic and statistical uncertainties, and the off-diagonal terms encode the systematic covariances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' For example, if all 81 setups hypothetically provided the same velocity dispersion map and uncertainty, then the off-diagonal terms would be zero, and the diagonal terms would reflect only the statistical uncertainties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We show the systematic variance- covariance relative to the statistical variance in Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The systematic variance is subdominant relative to the statistical vari- ance (with a median of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='47 of the ratio between systematic and statistical covariances along the diagonal) except for bins 29 and 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' These two bins are closest to quasar images A and C, and Article number, page 5 of 21 A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' ms 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 Map of Voronoi bins 0 5 10 15 20 25 30 35 40 Bin number 16 18 20 22 24 26 28 30 S/N (� 1) Voronoi bins Target S/N Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Left: Voronoi binning of the selected spaxels within 1′′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5 from the galaxy center that avoid lensed arcs, quasar images, and the satellite galaxy S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The different colors illustrate the regions for each Voronoi bin in a cartographic manner for easier visualization, with the bin number specified within each bin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We perform the binning with a target S/N ≈ 23 Å−1 for each bin, which results in 41 bins in total.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Right: Resultant S/N for each Voronoi bin (red points).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 3400 3600 3800 4000 4200 Restframe wavelength (˚A) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='02 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='04 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='06 Flux (arbitrary unit) bin 1: σlos = 282 ± 7 km s−1 3400 3600 3800 4000 4200 Restframe wavelength (˚A) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='000 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='025 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='050 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='075 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='100 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='125 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='150 Flux (arbitrary unit) bin 6: σlos = 284 ± 11 km s−1 3400 3600 3800 4000 4200 Restframe wavelength (˚A) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='3 Flux (arbitrary unit) bin 20: σlos = 274 ± 13 km s−1 3400 3600 3800 4000 4200 Restframe wavelength (˚A) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='0 Flux (arbitrary unit) bin 37: σlos = 263 ± 16 km s−1 Data Best fit model (galaxy + quasar) Best fit quasar model Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' pPXF fitting to the spectra from four examples of Voronoi bins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The bin number and the measured velocity dispersion for the corresponding bin are specified in each panel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The grey line presents the full spectra, the red line traces the best-fit model, and the blue line shows the quasar component in the best-fit model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' thus largely susceptible to the choice of quasar template (see Figures 6 and 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=') We show the velocity dispersion and mean velocity maps av- eraged over the 81 setups in Figure 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We estimate a systematic velocity of 182 km s−1 using the pafit7 software program (Kra- jnovi´c et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2006) and subtract it from the mean velocity map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The systematic velocity is the result of a slight deviation in the true redshift from the fiducial value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The mean velocity map does 7 https://pypi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='org/project/pafit/ Article number, page 6 of 21 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Shajib et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' : H0 from spatially resolved kinematics of RXJ1131−1231 not show any significant evidence of ordered rotation above the systematic and statistical noise levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Thus it is consistent with the lens galaxy being a slow rotator.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We use this systematic- averaged velocity dispersion map and the variance-covariance matrix estimated above when computing the likelihood function for dynamical modeling in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' To test the impact of our choice for the Voronoi binning scheme, we adopt an alternative target S/N ≈ 28 Å−1 for each bin, which results in 27 bins.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We similarly produce another set of 81 model setups in this binning scheme and produce the variance-covariance matrix for these binned velocity disper- sions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We test the systematic impact of this different binning scheme on the cosmological measurement later in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We show the difference in the extracted kinematics between the two binning schemes in Figure 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Overview of lens and dynamical modeling This section reviews the theoretical formalism of lens and dy- namical modeling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Lensing observables and modeling We briefly review the strong lensing formalism in the context of time-delay cosmography in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1, describe the mass- sheet transform (MST) in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='2, and explain the internal and external components of the MST in Section 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Strong lensing formalism In the thin lens approximation applicable in this case, lensing observables are described using the surface mass density Σ(R) projected from the 3D mass density distribution ρ(r) in the lens galaxy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Formally, the lensing observables depend on the dimen- sionless convergence defined as κ(θ) ≡ Σ(θ) Σcr , (1) which is the surface mass density normalized by the critical den- sity Σcr ≡ c2Ds 4πGDdDds .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (2) Here, c is the speed of light, G is the gravitational constant, Ds is the angular diameter distance between the observer and the source, Dd is the angular diameter distance between the observer and the lens galaxy, and Dds is the angular diameter distance between the lens galaxy and the source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The on-sky deflection angle α(θ) relates to the convergence as κ(θ) = 1 2∇ · α(θ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (3) The time delay between two quasar images labeled A and B is given by ∆tAB = D∆t c �(θA − ς)2 2 − (θB − ς)2 2 − ψ(θA) + ψ(θB) � , (4) where θA is the angular position of image A, ς is the source’s angular position, ψ(θ) is the lensing potential, and the time-delay distance D∆t is defined as D∆t ≡ (1 + zd)DdDs Dds .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (5) 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Description of the MST The MST is a mathematical transform of the convergence pro- file that leaves invariant all the imaging observables, such as the image positions and the flux ratios (Falco et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 1985;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Schneider & Sluse 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' This transform scales the convergence and the unknown source position as κ → κ′ = λMSTκ + (1 − λMST), ς → ς′ = λMSTς.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (6) where λMST is the transformation parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The predicted time delay ∆t scales under the transform as ∆t → ∆t′ = λMST∆t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (7) Then, the inferred time-delay distance D∆t and the Hubble con- stant H0 based on the observed time delays will change as D′ ∆t = D∆t λMST , H′ 0 = λMSTH0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (8) However, the MST changes the predicted velocity dispersion, thus measuring it breaks the MSD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Notably, the MST also rescales the lensing magnifications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Thus, standardizable candles can also be used to break the MSD (Bertin & Lombardi 2006;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Birrer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2022a) provided that microlensing and millilensing can be mitigated (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Yahalomi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' More et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Foxley-Marrable et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Internal and external MST We can express the “true” (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', physically present) lensing mass distribution as κtrue = κgal + κext, (9) where κgal is the mass distribution of the central lens galaxy (or galaxies) that is (are) considered in the lens modeling, and κext is called the external convergence, which approximates the projected mass distribution of line-of-sight structures as a mass sheet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Since limθ→∞ κgal = 0 has to be satisfied, we find that limθ→∞ κtrue = κext, hence the interpretation of κext as the lensing mass far from (or, “external” to) the central deflector(s).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' All the lensing observables including imaging observables result from κtrue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' However, since only the central galaxies are usually considered in lens modeling with imaging observables, the lens model provides κ′ model with limθ→∞ κ′ model = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' This κ′ model is an MST of κtrue for λMST = 1/(1 − κext) as κ′ model = κgal + κext 1 − κext + 1 − 1 1 + κext = κgal 1 − κext .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (10) Lens mass models are usually described with simply parametrized models, such as the power law or a combi- nation of the NFW profile and the observed stellar distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' In that case, the assumption of a simple parametric form implicitly breaks the MSD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Therefore, the simply parametrized model κmodel can be expressed as another approximate MST of the κ′ model as κ′ model ≈ λintκmodel + (1 − λint)κs(θ), (11) where λint is called the internal MST parameter, and κs is a “vari- able” mass sheet with limθ→∞ κs(θ) = 0 to ensure that both Article number, page 7 of 21 A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' ms Range: 3350 4250 � Range: 3300 4200 � Polynomial degree 2 Polynomial degree 4 Stellar template set 2 Stellar template set 3 Quasar B Quasar C 20 0 20 20 0 20 20 0 20 20 0 20 20 0 20 20 0 20 20 0 20 20 0 20 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Absolute difference in km s−1 between the extracted velocity dispersion from two setups that differ by one setting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The baseline setup has the range: 3400–4300 Å, polynomial degree: 3, stellar template set 1, and quasar template from image A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The different setting for each case is specified at the top of each panel.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Range: 3350 4250 � Range: 3300 4200 � Polynomial degree 2 Polynomial degree 4 Stellar template set 2 Stellar template set 3 Quasar B Quasar C 2 0 2 2 0 2 2 0 2 2 0 2 2 0 2 2 0 2 2 0 2 2 0 2 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Same as Figure 6, but the difference is normalized by the statistical uncertainty of the baseline setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' limθ→∞ κ′ model = 0 and limθ→∞ κmodel = 0 are satisfied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' How- ever, for Equation (11) to be an approximate MST, the variable mass-sheet needs to satisfy κs(θ) ≃ 1 within the central region that lensing observables are sensitive to (θ ≲ 2θE, Schneider & Sluse 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' This can be achieved with the formulation (Blum et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2020) κs(θ) = θ2 s θ2 + θ2s , (12) where θs ≫ θE is a scale radius where the variable mass-sheet smoothly transitions from 1 − λint to 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' This approximate MST converges to the pure MST in the limit θs → ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Thus, the actual mass distribution of the central deflector(s) relates to the mod- eled mass distribution as κgal ≈ (1 − κext) [λintκmodel + (1 − λint)κs(θ)] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (13) The external convergence κext can be estimated by using rel- ative number counts of line-of-sight galaxies near the central de- Article number, page 8 of 21 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Shajib et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' : H0 from spatially resolved kinematics of RXJ1131−1231 10 20 30 40 Bin number 5 10 15 20 25 30 35 40 Bin number Fractional systematic covariance: xy h diag( 2 stat) i xy 2 stat,x 10 0 0 10 0 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Illustration of the systematic covariance relative to the statistical covariance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Σ is the variance-covariance matrix of the Voronoi-binned velocity dispersions (with target S/N ≈ 23 Å−1 for each bin), σstat,x is the statistical uncertainty in bin number x from our fiducial setup, and diag(σstat) is a diagonal matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Note that we assume no covariance in the statistical uncertainty from each setup for kinematic measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Thus the off-diagonal terms in the variance-covariance matrix purely represent the systematic covariance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Most diagonal terms are < 1 (with a median of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='47), showing that the systematic variances are subdom- inant to the statistical variances except for bins 29 and 31.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' These bins are close to images A and C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Thus, they are largely susceptible to the choice of the quasar template, as seen in Figures 6 and 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Velocity dispersion Velocity dispersion uncertainty Mean velocity Mean velocity uncertainty 225 250 275 300 los (km s 1) 20 40 los (km s 1) 50 0 50 vmean (km s 1) 20 30 vmean (km s 1) Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Maps of extracted velocity dispersion (top row) and mean ve- locity (bottom row) in Voronoi bins along with the corresponding un- certainties (right column).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The Voronoi binning was tuned to achieve S/N ≈ 23 Å−1 for each bin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The illustrated maps (left column) corre- spond to the average values after combining 81 model setups, and the uncertainty maps correspond to the square root of the diagonal of the variance-covariance matrices.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' A systematic velocity of 182 km s−1 was subtracted from the mean velocity map.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' los (km s 1) los/ los 20 0 20 2 0 2 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Absolute (left) and uncertainty-normalized (right) difference in the extracted velocity dispersion between two Voronoi binning schemes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The two binning schemes are obtained by setting the target S/N to 23 Å−1 and 28 Å−1 for each bin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We take the case with target S/N ≈ 23 Å−1 for each bin as the baseline in our analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' flector(s) (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Suyu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Greene et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Rusu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Buckley-Geer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2020), or by using weak lensing of distant galaxies by the line-of-sight mass distribution (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Ti- hhonova et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The measured velocity dispersion then constrains the internal MST parameter λint (Birrer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Yıldırım et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Dynamical modeling In this section, we describe the Jeans anisotropic multi- Gaussian-expansion (JAM) framework to model our dynamical observable, which is the spatially resolved stellar velocity dis- persion measured in Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The orbital motions of the stars, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', the distribution function f(x, v) of position x and velocity v, in the galactic potential Φ is described by the steady-state col- lisionless Boltzmann equation (Binney & Tremaine 1987, Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 4-13b) 3 � i=1 � vi ∂f ∂xi − ∂Φ ∂xi ∂f ∂vi � = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (14) We assume an axisymmetric case (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', ∂Φ/∂φ = ∂f/∂φ = 0 with φ being the polar angle in the spherical coordinate sys- tem), a spherically aligned velocity ellipsoid, and the anisotropy for each Gaussian component in the multi-Gaussian expan- sion (MGE;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Emsellem et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 1994;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Cappellari 2002) to be spa- tially constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Slow rotators such as the deflector galaxy in RXJ1131−1231 are in general expected to be weakly triaxial or oblate but never flat and instead quite close to spherical in their central parts (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Cappellari 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' For this reason, we expect the spherical alignment of the velocity ellipsoid of jamsph (Cap- pellari 2020) to provide a better approximation to the galaxy dy- namics than the cylindrical alignment jamcyl solution (Cappellari 2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Then, the above equation gives two Jeans equations in spherical coordinates (Jeans 1922;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Bacon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 1983;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' de Zeeuw et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 1996;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Cappellari 2020) ∂ � ζ⟨v2 r⟩ � ∂r + (1 + β)ζ⟨v2 r⟩ − ζ⟨v2 φ⟩ r = −ζ ∂Φ ∂r , (1 − β) ∂ � ζ⟨v2 r⟩ � ∂θ + (1 − β)ζ⟨v2 r⟩ − ζ⟨v2 φ⟩ tan θ = −ζ ∂Φ ∂θ , (15) Article number, page 9 of 21 A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' ms where the following notations are used ζ⟨vpvq⟩ ≡ � vpvq fd3v, β ≡ 1 − ⟨v2 θ⟩ ⟨v2r⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (16) Here, β is the anisotropy parameter, and the velocity dispersion ellipsoid is assumed to be spherically aligned, giving ⟨vrvθ⟩ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The line-of-sight second moment ⟨v2 los⟩ is the integral given by S ⟨v2 los⟩(x, y) = � ∞ −∞ dz ζ⟨v2 z⟩.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (17) where S (x, y) is the surface density of the dynamical tracer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Given that there is no evidence of significant ordered rotation and the only significantly nonzero velocities are likely due to systematic errors (see Figure 9), we assume ⟨vlos⟩ = 0 and define ⟨v2 los⟩ = σ2 los.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The observed line-of-sight velocity dispersion is given a luminosity-weighted integral as � σ2 los � obs = � ⟨v2 los⟩ � obs = � ap dxdy I⟨v2 los⟩ ⊗ PSF � ap dxdy I ⊗ PSF , (18) where the symbol “⊗ PSF” denotes a convolution with the PSF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' In the equation above, we have chosen the surface brightness profile I(x, y) as a substitute for the surface density S (x, y) of the dynamical tracer since the constant factor between surface brightness and surface number density cancels out in this ex- pression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We use the dynamical modeling software jampy8 to compute the observed velocity dispersion by solving the Jeans equation from Equation (15) for a given 3D potential Φ(r) and anisotropy profile β(r).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Specifically, we use the jam_axi_proj() routine with the keyword align=‘sph’.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' See Cappellari (2008, 2020) for a detailed formalism in computing Equation (18) by jampy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Cosmological inference from combining dynamical and lensing observables We parametrize the 3D potential Φ(r) using the lens model pa- rameters ξmass and the internal MST parameter λint to conve- niently use the lens model posterior from Suyu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (2013) as a mass model prior in the dynamical modeling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Thus from Equa- tion (13), the surface mass density for our dynamical model is given by Σ(θ) = Σcr(1 − κext) [λint κmodel(θ) + (1 − λint)κs(θ)] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (19) We include D∆t and Dd as free parameters in our model, which give the critical density Σcr as Σcr = c2 4πG D∆t (1 + zd)D2 d = c2 4πG Dmodel ∆t (1 + zd)(1 − κext)λintD2 d , (20) where Dmodel ∆t is the time-delay distance predicted by the lens mass model κmodel(θ) for the time delays observed by Tewes et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We approximate the surface mass density Σ(θ) with an MGE (Emsellem et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 1994;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Cappellari 2002;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Shajib 2019) using the 8 https://pypi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='org/project/jampy/ software program mgefit9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' jampy deprojects the MGE compo- nents into an oblate or prolate spheroid with an inclination angle i (Cappellari 2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The deprojected 3D mass density provides the 3D potential Φ for the kinematic computation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We also take the MGE of the surface brightness I(x, y) for deprojection to 3D with the inclination angle i for the kinematic computation by jampy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The combination of lens imaging observables and the stellar kinematics is sensitive to λint(1 − κext)Ds/Dds (Birrer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2021a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We apply a prior on κext using the estimated κext distribution from Suyu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (2014) to help break the de- generacy in distributing the total MSD into external and internal components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Bayesian framework According to Bayes’ theorem, the posterior of the model param- eters Ξ = {ξmass, ξlight, Dmodel ∆t , i, κext, λint, Dd, β} as p(Ξ | D) ∝ p(D | Ξ) p(Ξ), (21) where p(D | Ξ) is the likelihood given data D and p(Ξ) is the prior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' In this study, the data D is the measured velocity disper- sions in Voronoi bins (Figure 9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The observational information from the published time delays, lens models using HST imag- ing, and the line-of-sight effects (Tewes et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Suyu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2013, 2014) is incorporated by adopting those previous posteri- ors as the prior on our model parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The likelihood of the observed velocity dispersion vector σlos ≡ [σ1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' , σNbin], with Nbin being the number of Voronoi bins, is given by L(σlos | Ξ) ∝ exp � −1 2σT losΣ−1σlos � , (22) where Σ is the variance-covariance matrix.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Specific priors used in this Bayesian framework are given in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We ob- tain the posterior probability distribution function (PDF) of the model parameters using the Markov-chain Monte Carlo (MCMC) method using the affine-invariant ensemble sampler emcee (Goodman & Weare 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Foreman-Mackey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We ensure the MCMC chains’ convergence by running the chains for ≳20 times the autocorrelation length after the chains have stabilized (Foreman-Mackey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Dynamical models We first describe our baseline dynamical model in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1 and then perform various checks on systematics in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Baseline dynamical model This subsection describes the baseline settings in our dynamical model, namely the specific parametrization of the mass model (Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1), the dynamical tracer profile (Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='2), the probability of oblate or prolate axisymmetry (Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='3), the inclination angle (Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='4), and the choice of anisotropy profile (Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Parametrization of the mass model We adopt the power-law mass model as our baseline model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' In this model, the mass profile is defined with Einstein radius θE, 9 https://pypi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='org/project/mgefit/ Article number, page 10 of 21 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Shajib et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' : H0 from spatially resolved kinematics of RXJ1131−1231 logarithmic slope γ, projected axis ratio qm, and position angle ϕmass.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The convergence profile κmodel in Equation (19) for the power-law model is given by κpl model(θ1, θ2) = 3 − γ 2 ������������ θE � qmθ2 1 + θ2 2/qm ������������ γ−1 (23) Here, the coordinates (θ1, θ2) are rotated by ϕmass from the (RA, Dec) coordinate system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We adopt the lens model posterior from Suyu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (2013) as a prior in our dynamical model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' For sim- plicity, we set the position angle ϕmass the same as the observed position angle of light ϕlight.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We use the estimated κext distribu- tion for the power-law model as the prior (see Figure 3 of Suyu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We set θs = 12′′ (≃ 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5θE) in the approximate mass-sheet κs (Equation 12) so that the imaging constraints alone cannot dif- ferentiate the power-law mass profile and its approximate MST from Equation (11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We obtain this lower limit by running the jupyter notebook that produces Figure 3 of (Birrer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='10 However, we adjusted the fiducial lens model parameters in the notebook to match with those for RXJ1131−1231.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We take a uni- form prior for the internal MST parameter λint ∼ U(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='13).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The upper limit of 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='13 is set by the requirement that the trans- formed mass profile under the approximate MST must be mono- tonic so that the MGE can approximate the transformed pro- file sufficiently well (Shajib et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Previous studies also found similar or more restrictive upper limits for λint to satisfy the physical requirement of non-negative density (Birrer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Yıldırım et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The appropriate number of MGE components for the mass or light profile is automatically chosen by jampy with a maxi- mum of 20 components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We check that the MGE approximates the input mass or light profile very well (with a maximum 1% deviation at < 10′′ and maximum 10% deviation between 10′′– 50′′).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' These deviations from the density profile have an oscilla- tory pattern due to the MGE approximation’s nature, except near the end of the fitted ranges.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Thus the deviation in the integrated mass profile often averages out in the line-of-sight integration up to a very large radius.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We perform the MGE fitting up to 100′′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Thus, the large mismatch between the MGE approximation and the original profile occurs largely outside the integration limit ∼ 70′′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The chosen number of maximum Gaussian components is not a dominant source of numerical error.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Setting this maxi- mum number to a very high value, such as 100, shifts the com- puted velocity dispersion by only < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5% within the observed region, which is insignificant compared to the 1% numerical sta- bility targeted by jampy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Dynamical tracer profile We update the light profile fitting for the lens galaxy from Suyu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (2013) using a larger HST image cutout than that therein, which did not contain the full extent of the lens galaxy’s light profile (see Figure 11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The lensed arcs and quasar images are first subtracted from the cutout using the prediction of the best- fit lens model from Suyu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We use the software pack- age lenstronomy11 to fit the residual light distribution attributed to the lens galaxy (Birrer & Amara 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Birrer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 10 https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='com/TDCOSMO/hierarchy_analysis_2020_ public/blob/6c293af582c398a5c9de60a51cb0c44432a3c598/ MST_impact/MST_pl_cored.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='ipynb 11 https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='com/lenstronomy/lenstronomy Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Values of the light model parameters for the double Sérsic model in our fitting of a large cutout and those from Suyu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The position angle ϕlight is defined as East of North.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Parameter This analysis Suyu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (2013) Sérsic profile 1 I0 (e−1 s−1 pixel−1) 32.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='8 ±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1 36.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='4 ±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='4 θeff (′′) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='437 ±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='005 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='49 ±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='01 ns 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='10 ±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='93 ±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='03 ql 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='865 ±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='001 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='878 ±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='004 Sérsic profile 2 I0 (e−1 s−1 pixel−1) 441 ±7 356 ±12 θeff (′′) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='300 ±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='003 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='362 ±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='009 ns 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='60 ±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='02 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='59 ±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='03 ql 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='847 ±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='002 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='849 ±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='004 ϕlight (◦) 120.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5 ±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='3 121.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='6 ±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5 Following Suyu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (2013), we use the double Sérsic model to fit the light profile, which is a superposition of two concentric Sérsic profiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The Sérsic profile is defined as I(θ1, θ2) = I0 exp ������������� −bn ������������ � qlθ2 1 + θ2 2/ql θeff ������������ 1/ns + bn ������������� , (24) where I0 the amplitude, ql is the axis ratio, θeff is the effective radius, ns is the Sérsic index, and bn = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='999n − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='327 is a nor- malizing factor so that θeff becomes the half-light radius (Sérsic 1968).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The coordinates (θ1, θ2) are rotated by ϕlight from the (Ra, Dec) coordinate system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We first mask circular regions at the quasar image positions due to slightly saturated pixels producing significant residuals in the subtracted cutout (see Figure 11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We then iteratively mask the other pixels with significant residuals above statistical expec- tations to effectively perform an outlier rejection while preserv- ing the shape of a Gaussian tail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' For each iteration of this pro- cess, we take a discrepancy threshold, which we decrease from 5σ to 2σ with step size 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5σ across these iterations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We then randomly mask a subset of the pixels with residuals more than the discrepancy level at the given iteration such that the number of remaining pixels with such high residuals is statistically ex- pected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The final masked area after the iterations is illustrated in Figure 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We tabulate the best-fit light model parameters in Ta- ble 1 and compare them with those from Suyu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The circularized half-light radius for our best-fit model is θeff = 1′′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='91, which is slightly larger than the value θeff = 1′′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='85 from Suyu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (2013) based on the same imaging data but from a smaller cutout (illustrated in 11).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We then take the MGE of the fitted double Sérsic profile as the light distribution I(x, y) in our dy- namical modeling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We propagate the uncertainties and covari- ances from the light profile fitting into the dynamical modeling.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' To do that, we sample from the multivariate normal distribution corresponding to all the light model parameters for each call of the likelihood function within the MCMC process and then take the MGE of the light profile given the sampled parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Oblate or prolate shape of the axisymmetry The oblateness, prolateness, or triaxiality of a slow rotator galaxy can, in principle, be constrained from the kinematic mis- alignment angle ∆ϕkin ≡ ���ϕkin − ϕlight ���.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' However, we do not Article number, page 11 of 21 A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' ms N E 1" Data 1" Reconstructed E N 1" Normalized Residuals E N 4 3 2 1 0 1 log10 flux 4 3 2 1 0 1 log10 flux 3 2 1 0 1 2 3 (data model) / noise Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Fit of the lens galaxy’s surface brightness profile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Left: the HST/ACS imaging in the F814W filter of the lens system RXJ1131−1231 with the quasar images and the lensed arcs subtracted using the prediction from the best-fit lens model from Suyu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (2013), thus leaving only the lens galaxy’s light to be fitted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The orange circle shows the large circular region considered for fitting in our analysis, and the yellow square shows the smaller cutout used for lens modeling by Suyu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The cyan annulus contains the region where pixels were fitted to reconstruct the source by Suyu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Thus the lensed arcs from the quasar host galaxy were subtracted only within this annulus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The red contours mark quasar image positions with significant residuals due to saturated pixels, which we mask.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Middle: The fitted light profile with a double Sérsic model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The black pixels correspond to masked pixels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The additional masked pixels within the orange circle not described above are randomly selected through an iterative process that performs outlier rejection while preserving the Gaussian tail (see Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='2 for details).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Right: Normalized residual of the best-fit model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' detect any significant rotational pattern in the vmean map (Fig- ure 9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Thus, the uncertainty for the constrained kinematic major axes is too large to be meaningful, and we cannot directly con- strain this galaxy’s oblateness from the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Instead, we obtain the probability of oblateness from a population prior based on 189 slow rotator elliptical galaxies that are in the Sloan Digi- tal Sky Survey’s (SDSS’s) Mapping Nearby Galaxies at APO (MaNGA) sample (Abolfathi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Graham et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We take the distribution of ∆ϕkin for this sample of slow rota- tors (Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2018), where ∆ϕkin = 0◦ corresponds to a purely oblate shape, and ∆ϕkin = 90◦ corresponds to a purely prolate shape.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (2018) find two distinct peaks in the distribution at ∆ϕkin = 0◦ and ∆ϕkin = 90◦ (see Figure 12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We, therefore, fit the data points with a double Gaussian profile with the means set at ∆ϕkin = 0◦ and ∆ϕkin = 90◦ (see the fit in Figure 12).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Although the slow rotators with 0◦ < ∆ϕkin < 90◦ have triaxial shapes, we choose only oblate or prolate axisymmetric shapes in our dynamical modeling for computational simplicity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' There- fore, we take ∆ϕkin < 45◦ as the oblate case and ∆ϕkin > 45◦ as the prolate case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We obtain the prior probability p(oblate)pop of the galaxy being oblate as p(oblate)pop = � 45◦ 0◦ d(∆ϕkin) p(∆ϕkin)pop ≃ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='65, (25) and thus p(prolate)pop = 1 − p(oblate)pop ≃ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The jampy software package, by default, adopts the oblate case for deprojection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We implement the prolate case in jampy by setting qprolate = 1/q > 1 and switching the x and y axes in the input coordinate system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Due to the switching of x and y axes, σ parameters of the MGEs for mass and light models need to be scaled as σprolate = qσ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Inclination The observed axis ratio of light ql,obs = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='850 ± 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='002 relates to ql,int through the inclination angle i as q2 l,obs = q2 l,int sin2 i + cos2 i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (26) We impose a prior on the intrinsic axis ratio ql,int from a sam- ple of massive elliptical galaxies in the SDSS with stellar mass 0 20 40 60 80 Kinematic misalignment, kin ( ) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5 Probability density (�90) oblate prolate Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=" (2018)'s population double Gaussian fit Fig." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Population prior on kinematic misalignment angle ∆ϕkin ≡ ���ϕkin − ϕlight ��� for a sample of slow rotator elliptical galaxies from the SDSS’s MaNGA dataset (Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Here, ∆ϕkin = 0◦ corresponds to a purely oblate shape, and ∆ϕkin = 90◦ corresponds to a purely prolate shape.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The vertical dashed grey lines mark ∆ϕkin = 0◦, 45◦, and 90◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The red points with error bars show the measurements from Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We fit this distribution with a double Gaussian model (blue line) with the means fixed to ∆ϕkin = 0◦ and ∆ϕkin = 90◦.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We take ∆ϕkin < 45◦ as the oblate case and ∆ϕkin > 45◦ as the prolate case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Integrating the double Gaussian model from 0◦ to 45◦ gives the prior probability of oblateness p(oblate)pop ≃ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='8 < log10(M⋆/M⊙) < 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5 at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='04 < z < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='08 (Chang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The distribution of ql,int by Chang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (2013) is differ- ent for oblate and prolate assumptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Therefore, we adopt the specific prior corresponding to the oblate or the prolate case (see Figure 13).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Anisotropy profile We investigate two choices to parametrize the anisotropy pro- file.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The first choice is a single spatially constant β = 1 − σ2 θ/σ2 r value for all the light MGE components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Numerically, we sam- Article number, page 12 of 21 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Shajib et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' : H0 from spatially resolved kinematics of RXJ1131−1231 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='0 Intrinsic axis ratio of light, ql,int 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5 Probablity density oblate case prolate case Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Prior on the intrinsic axis ratio ql,int of light for oblate (solid line) and prolate (dashed line) cases from Chang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The pri- ors correspond to massive elliptical galaxies from the SDSS survey at 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='04 < z < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='08 with 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='8 < log10(M⋆/M⊙) < 11.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' ple σθ/σr with a uniform prior (σθ/σr) ∼ U(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='78, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='14).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' This range of σθ/σr allows −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='31 < β < 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We adopt this range using the β values of eight slow rotator galaxies measured by Cappellari et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (2007, see Figure 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' These measurements of β by Cappellari et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (2007) are from Schwarzschild modeling of data with one of the highest S/N values in the literature, al- lowing to constrain the Gauss–Hermite moments up to order six.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Applying the student’s t-distribution on the sample mean of this small sample, we find the 95% confidence interval of the pop- ulation mean for β to be [-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='10, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='17] and the standard devia- tion to be 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' These values infer that 95% of the population is contained within β ∈ [−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='31, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='38], which we take as the bound- aries of our prior range.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The second choice of the anisotropy profile has two free parameters: the inner light MGE compo- nents with σ < rbreak = θeff = 1′′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='91 are assigned one value for (σθ/σr)inner and the outer light MGE components with σ ≥ rbreak are assigned another independent value of (σθ/σr)outer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Thus, this parametrization with two free parameters allows radial vari- ability in the anisotropy profile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Both the inner and outer ratios have uncorrelated uniform priors (σθ/σr) ∼ U(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='78, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='14).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' For these two choices of parametrization, we compute the Bayesian information criterion (BIC) given by BIC ≡ k log(Nbin) − 2 log ˆL, (27) where k is the number of free model parameters, Nbin is the num- ber of data points, and ˆL is the maximum likelihood.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We approx- imate ˆL from the highest likelihood value sampled in the MCMC chain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The single-parameter β model provides the lowest BIC value excluding the two-parameter β model with ∆BIC ≈ 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='7 (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', positively excluded;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Raftery 1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We check that the dif- ference between the highest and the second highest likelihood values among the MCMC samples is ≪ ∆BIC, thus this ∆BIC value is robust against our approximation of ˆL from the high- est likelihood value in the sampled chain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The non-detection of varying anisotropy in our data is consistent with that ob- served in nearby elliptical galaxies, as even high-S/N SAURON data for a large sample of galaxies are accurately described by JAM models with constant anisotropy, as used here, within the noise of the kinematics (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Cappellari et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We com- pare the posterior distributions of the model parameters for the two anisotropy models in Figure 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' An example of a best-fit kinematic model and the corresponding residual with the single- parameter β model and oblate axisymmetry is illustrated in Fig- ure 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The reduced χ2 ν value is 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='83 with ν = 41 degrees of freedom.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The distribution of residuals is similar to a normal dis- tribution expected from a perfect model for data with Gaussian noise, illustrating that our model is appropriate for the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We show the range of velocity dispersion radial profiles sampled by our model in Figure 16 and compare it with the radially averaged measurements of the velocity dispersion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' This illustration shows that our model reproduces the uncertainty range of the measure- ment.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Checking potential systematics due to modeling choices In this section, we perform several checks on potential system- atics for different choices in the dynamical model setup.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Comparison between power-law and composite mass models In addition to the power-law mass model, Suyu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (2014) also adopted a composite mass model individually describing the lens galaxy’s dark matter and baryonic components.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The dark matter distribution was modeled with an elliptical NFW profile in the potential.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The parameters in this profile are the normalization of the NFW component κs, the NFW scale radius rscale, and the mass axis ratio qm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The baryonic component was modeled with a mass-follow-light profile with a free mass-to-light ratio (M/L) parameter.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Thus, this mass model parametrization has one more free parameter than the power-law model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' See Suyu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (2014) for parametric definitions of these profiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We implement this composite mass profile as κcomp model in Equation (19) and adopt the model posterior from Suyu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (2014) as a prior in our model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We appropriately convert the ellipticity defined in the potential by Suyu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (2014) to an ellipticity defined in the convergence in our model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We take the MGE of this composite surface density model as done for the power-law surface density model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' How- ever, since the dark matter and baryonic components have differ- ent ellipticities, we take the MGE of each component separately to preserve the ellipticity information in deprojection.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Specifi- cally, We take the MGE of the approximate MST with λint of the dark matter profile and the MGE of an accordingly rescaled baryonic profile, which effectively results in the total mass pro- file being transformed as the approximate MST with λint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' This mass model with one more free parameter than the power-law model has a higher BIC score with ∆BIC = 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Thus, the BIC excludes the composite model with positive evidence (Raftery 1995).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The median values of Dd from the power-law and composite mass models differ by 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='9% (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='07σ, Figure 17), and the median D∆t values differ by 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='26% (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='06σ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Therefore, we conclude that our power-law mass model with an additional degree of freedom to scale with the MST robustly describes the observed data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Comparison between prolate and oblate axisymmetry We compare the inferred Dd between the purely oblate and purely prolate cases in the deprojected 3D spheroidal shape of the mass and light models (Figure 18).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The median Dd values from these two cases differ by 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='6% (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='3σ), and the median D∆t values differ by 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='94% (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='04σ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Our final distance poste- rior is the combination of oblate and prolate cases, with weights p(oblate)pop = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='65 and 1 − p(oblate)pop = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='35, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Article number, page 13 of 21 A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' ms 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='64 E ( ) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='2 blinded Dd 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5 blinded D t 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='0 blinded int 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='85 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='00 ( / r)outer 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='85 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='00 / r 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='2 ext 60 80 i ( ) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='75 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='77 qm 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='9 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='0 2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='76 qm 60 80 i ( ) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='07 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='23 ext 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='87 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='05 / r 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='87 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='05 ( / r)outer 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1 blinded int 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5 blinded D t 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='3 blinded Dd different parameters for inner and outer MGE components same for all MGE components Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Constraints from axisymmetric JAM modeling on the power-law mass model parameters (θE, γ, and qm), internal MST parameter λint, external convergence κext, anisotropy profile parameter(s), and the cosmological distances D∆t and Dd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' assuming two anisotropy parametrizations: (i) one single constant β ≡ 1 − (σθ/σr)2 for all light MGE components (orange contours), and (ii) one free (σθ/σr)inner ≡ (σθ/σr) for light MGE components with σ < rbreak = θeff = 1′′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='91 and another free (σθ/σr)outer for light MGE components with σ > rbreak(blue contours).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The blinded parameters are blinded as pblinded ≡ p/⟨p⟩ − 1 so that the distributions only reveal fractional uncertainties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The darker and lighter shaded regions in the 2D plots trace 68% and 95% credible regions, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The mass model parameters Einstein radius θE, power-law slope γ, axis ratio q, and position angle PA are additionally constrained through a prior from the imaging data from Suyu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The two anisotropy parametrizations provide equally good fits to the kinematics data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' However, the BIC selects the constant-β anisotropy model over the other one with one additional free parameter (∆BIC value is 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Thus, this difference between the oblate and prolate cases is marginalized in our final cosmological distance posterior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We also compare the predictions from axisymmetric and spherical mass models in Figure 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The median Dd from the spherical model matches very well with the axisymmetric pro- late model, but the median D∆t differs by 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='0% (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='08σ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The galaxy is only mildly elliptical in projection (ql ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='85), and the resulting axisymmetric models are not very flat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' For this rea- son, the relatively small difference between the axisymmetric and spherical models is not surprising.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Article number, page 14 of 21 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Shajib et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' : H0 from spatially resolved kinematics of RXJ1131−1231 Data Model Residual 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5 (data model)/noise 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='4 density Residual distribution 300 250 los (km s 1) 300 250 los (km s 1) 2 0 2 (data model)/noise Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Observed velocity dispersion map in Voronoi bins (first panel), the best-fit dynamical model with a power-law mass model, constant β anisotropy profile, and oblate shape (second panel), the normalized residual for the best-fit dynamical model (third panel), and the distribution of the normalized residual (orange, fourth panel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The reduced χ2 quantity is χ2 ν = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='83 with degrees of freedom ν = 41.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The grey dashed line in the fourth panel shows a normal distribution expected for residuals from a perfect model to the data with Gaussian noise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The residual distribution for 41 points is similar to this Gaussian distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='00 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='25 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='50 ( ) 240 260 280 300 Velocity dispersion (km s 1) oblate prolate Radially binned measurements Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Radial profile of the line-of-sight velocity dispersion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The red points are radially binned values from the 2D maps, with the horizontal error bars illustrating the widths of the annuli.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The lines show the radial profiles for random samples from the dynamical model posterior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The radial profile of the model is averaged over the major, minor, and inter- mediate axes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The solid purple lines correspond to 65 random samples for the oblate case, and the dashed green lines correspond to 35 ran- dom samples for the prolate case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Note that the model was fit to the 2D kinematics data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' However, we illustrate the 1D radial profile only for visualization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Comparison between Voronoi binning schemes Here, we compare the Voronoi binning schemes with two choices for the target S/N in each bin: ≈ 23 Å−1 and ≈ 28 Å−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The two cases match very well with only a 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='21% differ- ence (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='02σ) in the median values of Dd (Figure 19) and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='28 % difference (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='01σ) in the median D∆t values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' As a result, we conclude that our choice of the Voronoi binning scheme is not a significant source of systematic error in our analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Based on the systematics tests performed above, we adopt a robust final distance posterior from the model with the power- law parametrization for the mass profile that the approximate in- ternal MST is applied to.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We marginalize the oblate and prolate axisymmetrical cases by combining the posteriors from these two choices with weights of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='65 and 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='35, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' In the next section, we present the unblinded values from the distance posterior and infer the value of H0 from it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='87 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='05 / r 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='2 blinded Dd 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5 blinded D t 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='0 blinded int 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1 blinded int 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5 blinded D t 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='2 blinded Dd Power-law mass model Composite mass model Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Comparison of the constrained Dd from power-law (blue con- tours) and composite (orange contours) mass models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The blinded pa- rameters are blinded as pblinded ≡ p/⟨p⟩−1 so that the distributions only reveal fractional uncertainties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The darker and lighter shaded regions in the 2D plots trace 68% and 95% credible regions, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Cosmological inference In this section, we infer cosmological parameters from the joint distribution of Dd and D∆t, accounting for their covariance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The unblinded point estimates of these distances are Dd = 865+85 −81 Mpc (a 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='6% measurement) at zd = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='295, and D∆t = 2180+472 −271 Mpc (a 17% measurement) for zs = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='657.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We infer H0 and Ωm from our distance posterior for a flat ΛCDM cosmology (see Figure 20, left panel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We leave the ex- ploration of more exotic cosmologies based on our distance pos- terior for future studies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We approximate the likelihood function L(H0, Ωm | Dd, D∆t) of the cosmological parameters using a 2D Gaussian kernel density estimate (KDE) from the 2D distance posterior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We adopt two choices of prior for Ωm: one is a uni- form prior Ωm ∼ U(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='05, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5), and the other is a Gaussian prior Ωm ∼ N(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='334, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='018) from the Pantheon+ analysis of type Ia Article number, page 15 of 21 A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' ms 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='87 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='05 / r 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='3 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='0 blinded Dd 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5 blinded D t 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='0 blinded int 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1 blinded int 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5 blinded D t 0 blinded Dd spherical axisymmetric prolate axisymmetric oblate Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Comparison of the constrained Dd between oblate (blue) and prolate (blue) cases of the deprojected spheroidal shape in the dynam- ical model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The blinded parameters are blinded as pblinded ≡ p/⟨p⟩ − 1 so that the distributions only reveal fractional uncertainties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The darker and lighter shaded regions in the 2D plots trace 68% and 95% credible regions, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' supernovae relative distances (Brout et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We infer the posterior joint PDF of H0 and Ωm by performing MCMC sam- pling using emcee, given the likelihood function and prior choice.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We infer H0 = 77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1+7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='3 −7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1 km s−1 Mpc−1(a 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='4% measurement) with the uniform Ωm-prior, and H0 = 76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='0+7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='3 −6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='6 km s−1 Mpc−1 (a 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1% measurement) with the Pantheon+ Ωm-prior (solid con- tours in the right panel of Figure 20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We show the D∆t–Dd re- gion allowed by our priors in the left panel of Figure 20, which also shows the region allowed by our distance posterior that provides information for the cosmological inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Other cos- mological models beyond flat ΛCDM (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Bonvin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Wong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2020) or combining other cosmological probes in a cosmology-independent manner (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Taubenberger et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2019) can utilize the additional cosmological information contained by our full 2D posterior outside the regions probed by our cosmo- logical priors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' For comparison, we also perform cosmological inference us- ing only the 1D posterior of Dd (dashed contours in right panel of Figure 20).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' This gives H0 = 75.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5+8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='3 −7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='2 km s−1 Mpc−1 (a 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='3% measurement) for the uniform Ωm-prior, and H0 = 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='4+8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1 −6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='2 km s−1 Mpc−1 (a 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='6% measurement) for the Pantheon+ Ωm-prior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The Dd-only constraints are lower by ∼1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='4% (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='15σ) than that from the full 2D distance posterior (for the uniform Ωm-prior).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' This slight difference arises from the projection difference of the 2D posterior along the Dd direction and along the narrow track allowed by our choice of cosmological priors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Discussion We now compare our results with previous works (Section 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1), discuss the improvement of the constraint in this paper over 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='87 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='05 / r 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='2 blinded Dd 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5 blinded D t 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='0 blinded int 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1 blinded int 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5 blinded D t 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='2 blinded Dd target S/N 23 � 1 target S/N 28 � 1 Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Comparison of the constrained Dd between two choices of the target S/N for each bin in the Voronoi binning scheme.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The blinded pa- rameters are blinded as pblinded ≡ p/⟨p⟩−1 so that the distributions only reveal fractional uncertainties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The darker and lighter shaded regions in the 2D plots trace 68% and 95% credible regions, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' single-aperture stellar kinematics (Section 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='2), and describe the limitations of this work (Section 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Comparison with previous time-delay H0 measurements Our measured value H0 = 77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1+7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='3 −7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1 km s−1 Mpc−1 is consistent with previous measurements from lensing time delays with dif- ferent treatments of the MSD (see Figure 21).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' These previous studies can be divided into two approaches: the first breaks the MSD by assuming simple parametric mass profiles such as the power law or composite (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', NFW halo and stars with constant mass-to-light ratio), and the second breaks the MSD based solely on stellar kinematics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Our study belongs to the second approach by allowing the freedom in the model to be maximally degener- ate with H0 and constraining it solely from the spatially resolved stellar kinematics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' However, it is illustrative to compare our re- sult with the first approach to discuss the validity of their mass model assumptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Following the first approach, Suyu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (2013, 2014) mea- sured H0 = 80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='0+4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5 −4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='7 km s−1 Mpc−1 from this same system RXJ1131−1231 with simple parametric mass profiles using HST imaging.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (2019) combined the HST imaging and adaptive-optics-assisted imaging from the Keck Telescope to measure H0 = 78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='3+3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='4 −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='3 km s−1 Mpc−1 ˙Although these studies used single-aperture stellar kinematics, the MSD was already broken by the assumption of parametric mass profiles, and the single-aperture velocity dispersion helped tighten the constraint and made the inferred H0 values from the power-law and com- posite models more consistent(Suyu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Our measured value – albeit with a larger uncertainty due to the maximal free- dom allowed in the mass model – has a median value very close to these previous measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Such a good agreement in the medians suggests that these previous studies’ simple parametric Article number, page 16 of 21 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Shajib et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' : H0 from spatially resolved kinematics of RXJ1131−1231 2000 3000 D t (Mpc) 600 800 1000 Dd (Mpc) 800 1000 Dd (Mpc) Our measurement 60 80 100 H0 (km s 1 Mpc 1) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='4 m 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='4 m m ∼U(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='05,0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5) m ∼N(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='334,0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='018) from Dd only from Dd only Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Left: Final 2D posterior of the time-delay distance D∆t and the angular diameter distance Dd (emerald contour).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The darker and lighter shaded regions in the 2D plots trace 68% and 95% credible regions, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We infer H0 and Ω from this distance posterior accounting for the covariance in a flat ΛCDM cosmology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We take a wide uniform prior on H0 ∼ U(0, 150) km s−1 Mpc−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The blue-shaded region corresponds to a uniform prior Ωm ∼ U(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='05, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5) and the orange-shaded region corresponds to a Gaussian prior Ωm ∼ N(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='334, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='018) from the Pantheon+ analysis of type Ia supernovae relative distances (Brout et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Right: Posterior PDF of H0 and Ωm in flat ΛCDM cosmology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We constrain H0 to 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='4% and 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1% precision for the uniform and Pantheon+ Ωm-priors, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We show the cosmological parameter posterior from only the 1D Dd posterior with dashed contours with colors matching the associated Ω prior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' In this case, the H0 precision is 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='3% and 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='6% for the uniform and Gaussian priors, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The Dd-only constraint on the H0 is lower by ∼1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='4% (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='15σ) than the constraint from the full 2D posterior, for the uniform Ωm-prior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' mass models are close to the ground truth, and no bias is de- tected within the precision afforded by the data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Future spatially resolved velocity dispersion measurements for more time-delay lens systems or better quality data for this system (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', from the James Webb Space Telescope) will allow us to make a more definitive statement on the validity of the parametric mass model assumptions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Following the second approach, Birrer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (2016) ana- lyzed this same system RXJ1131−1231 using HST imaging and single-aperture velocity dispersion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' These authors marginalized the effect of MSD by incorporating a source on the prior but found that the H0 posterior strongly depends on the shape of the anisotropy prior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' These authors use two different choices for this prior to find H0 = 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5+8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='0 −7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='8 km s−1 Mpc−1 and H0 = 86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='6+6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='8 −6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='9 km s−1 Mpc−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' This large difference illustrates that single aper- ture velocity dispersion imposes only a weak constraint on the anisotropy profile and, thus, on the MSD.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' This result highlights the need for spatially resolved velocity dispersion, such as the one presented in this study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Our measured H0 has a precision of 9% while allowing the data to constrain the MSD effect that is maximally degenerate with H0, illustrating the power of spa- tially resolved kinematics in constraining the anisotropy profile and the MSD, despite the seeing-limited nature of our data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' In the future, exquisite data from the James Webb Space Telescope (JWST) will provide an even more dramatic improvement (4% H0 precision forecasted, Yıldırım et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We also compare our result with the measured values of H0 from the current TDCOSMO sample of seven time-delay lenses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' With the power-law mass model assumptions, the combination of seven time-delay lenses gives a 2% measurement with H0 = 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='2+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='6 −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='6 km s−1 Mpc−1 (Wong et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Millon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2020b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' However, relaxing this mass profile assumption and constrain- ing the MSD solely from the single-aperture stellar kinematics of the TDCOSMO sample leads to a 9% uncertainty on the re- sultant H0 = 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5+5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='6 −6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1 km s−1 Mpc−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' In this study, we achieve the same 9% precision from a single system, highlighting the superb constraining power of spatially resolved kinematics over single-aperture ones.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' It is also worth comparing with the result obtained by Birrer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (2020) when combining the seven TDCOSMO lenses with information obtained from the external SLACS sample of non- time-delay lenses, H0 = 67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='4+4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1 −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='2 km s−1 Mpc−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Given the un- certainties, our new measurement is not statistically inconsistent with that result, although the difference is clearly important from a cosmological standpoint.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' With the data in hand, we cannot con- clude whether (a) the difference is real and the SLACS sam- ple cannot, therefore, be combined with the TDCOSMO sam- ple, or whether (b) it is due to a statistical fluctuation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' This study demonstrates that, as we gather more and better data for spatially resolved kinematics and external samples of non-lenses, we will soon be able to conclude whether the difference is real or not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' In the context of the “Hubble tension”, our new measurement strengthens the tension by reaffirming the previously obtained time-delay H0 measurements that agreed with other local mea- surement values, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', from SH0ES (Riess et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Although the 9% uncertainty in H0 from our measurement alone is not suf- ficient to resolve the tension, it demonstrates that time-delay cos- mography can provide a powerful independent perspective with the help of future data from telescopes such as Keck, JWST, and the extremely large telescopes (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', see forecasts from Shajib Article number, page 17 of 21 A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' ms et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Yıldırım et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2021;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Birrer & Treu 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We cannot help noticing that the median of our measurement is somewhat higher than the mean of the local values (∼73 km s−1 Mpc−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' However, the difference is not significant, given the uncertain- ties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Therefore our likely explanation is that the difference origi- nates from the inevitable statistical fluctuation pertaining to this system, as the initial H0 measurements using simple parametric assumption all provided such higher values (Suyu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2013, 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Birrer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2016;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We conclude by stressing that some dispersion around the mean is, of course, ex- pected, and indeed Millon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (2020b) shows that the seven TDCOSMO lenses scatter around the mean by an amount con- sistent with the estimated errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Improvement from the spatial resolution of the stellar kinematics We investigate the improvement in constraints provided by the spatially resolved nature of the stellar kinematics presented in this paper over the unresolved or single-aperture case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Suyu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (2013) presents a single-aperture measurement of the line- of-sight velocity dispersion σlos = 323 ± 20 km s−1 obtained within a 0′′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='81 × 0′′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='7 aperture with a 0′′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='7 seeing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' This mea- surement was from the Low-Resolution Imaging Spectrometer (LRIS;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Oke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 1995) on the Keck Observatory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The probed wavelength range was ∼3900–4700 Å, which probes mostly the redward range of the Ca H&K lines with a little overlap with the range probed by our data (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', 3300–4200 Å).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' If we take a luminosity-weighted-sum of the spatially resolved velocity dis- persion map within the same 0′′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='81×0′′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='7 aperture, we get 288±5 km s−1, which is 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='7σ (11%) lower than the previous single- aperture measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Although the 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='7σ difference is not sta- tistically significant, some parts of it can be due to potential sys- tematics in the kinematic extraction procedure or due to differ- ent wavelength ranges probed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' It is generally considered that the minimum error, considering systematics, on velocity dispersion measurements is 5%, even for very high-S/N data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' However, to illustrate the improvement in precision from the spatially resolved nature of the velocity dispersion presented in this study, we take a fiducial single-aperture measurement value of 288 ± 18 km s−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' This mean value is from the luminosity- weighted sum within the single aperture mentioned above, and the 18 km s−1 uncertainty comes from applying the 6% uncer- tainty of the 323 ± 20 km s−1 measurement on the fiducial mean.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We take the galaxy’s major axis to align with the rectangular aperture’s longer side.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Rotating the aperture by 90◦ only changes the predicted velocity dispersion integrated within the aperture by ≲ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1%, which is unsurprising given the mild ellipticity (ql ∼ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='85) of the galaxy and the 0′′.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='96 seeing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We compare the key dynamical model parameters between the spatially resolved and single-aperture cases in Figure 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' As expected, the internal MST parameter λint and the anisotropy profile parameter σθ/σr are almost completely unconstrained in the case of the single- aperture stellar kinematics due to the mass-anisotropy degener- acy (Treu & Koopmans 2002;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Courteau et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' However, the angular diameter distance Dd can be constrained to 15.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='7% precision, largely by the anisotropy prior (cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' the 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='6% constraint on Dd from the spatially resolved data).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' This single-aperture pre- cision level on Dd agrees very well with the 17.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='9% precision on Dd (= 810+160 −130 Mpc) obtained by Jee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (2019) from the same system RXJ1131−1231 based on the previously available single-aperture stellar kinematics mentioned above.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The Hubble constant H0 can be inferred to 12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5% precision with the uniform Ωm prior from the full 2D posterior of the fiducial single-aperture case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Although the improvement in H0 precision (by ∼3%) from the spatially resolved kinematics does not appear to be dramatic, this is due to the fact that the projection of D∆t–Dd posterior along the narrow track allowed by our chosen prior happens to give a small difference between the two cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The improvement could have appeared more drastic if the full 2D posterior had a different orientation from the prior region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' In reality, the full cos- mological information (illustrated by the area enclosed within the 95% contour) contained by the single-aperture data is much less than that from the spatially resolved data presented in this study (see the D∆t–Dd contours in Figure 22).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Limitations of this study One limitation of our study is the data quality.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Although our data are the first of their kind from a cutting-edge ground-based facil- ity such as the Keck Observatory, there are opportunities to ob- tain better-quality data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The KCWI instrument is seeing-limited.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Thus the S/N on the lensing galaxy is degraded by contamina- tion from the nearby quasars, and the spatial resolution of the ve- locity dispersion map is limited by the seeing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Adaptive-optics- assisted IFU spectroscopy from the ground or observations from space, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', with the JWST, can deliver exquisite spatially re- solved data for improved H0 precision in the future (Yıldırım et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2020, 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Future data with higher spatial resolution will be particu- larly powerful in constraining the anisotropy profile better.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Our measurement has only weak constraints on the anisotropy pro- file, which is largely bounded by the adopted uniform prior (see Figure 14).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' This prior is obtained from a sample of eight local massive ellipticals with one of the highest quality spatially re- solved kinematics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' However, this is a small sample size.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' A tighter anisotropy prior from larger samples of massive ellipticals, even better if they are from a redshift range that matches with the one for our system, will be helpful to mitigate further the degener- acy induced by the anisotropy profile, i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', the mass-anisotropy degeneracy (Treu & Koopmans 2002;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Courteau et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Conclusion We measured the spatially resolved stellar velocity dispersion of the lens galaxy in RXJ1131−1231 using the KCWI IFU spectro- graph on the Keck Observatory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We combined the new spatially resolved stellar kinematics with previously obtained lens mod- els derived from HST imaging data, observed time delays, and estimated line-of-sight lensing effects (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', the external conver- gence) to infer H0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Combining the spatially resolved velocity dispersion with lens imaging and time delays simultaneously al- leviates the MSD in the measured D∆t and additionally measures the angular diameter distance Dd.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' In order to prevent conscious or unconscious experimenter bias, we blindly performed the dynamical modeling and the cos- mographic inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We unblinded the H0 value after all the co- authors had agreed on the modeling choices after various checks on systematics, and the analysis was frozen.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The main conclu- sions from our study are as follows: – The 2D distance posterior of Dd and D∆t gives H0 = 77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1+7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='3 −7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1 km s−1 Mpc−1 for a uniform prior on Ωm ∼ U(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='05, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5), and H0 = 76.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='0+7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='3 −6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='6 km s−1 Mpc−1for a Gaussian prior on Ωm from the Pantheon+ analysis (Brout et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' – Our 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='4% measurement from a single system with spatially resolved kinematics provides a similar precision as, and is in Article number, page 18 of 21 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Shajib et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' : H0 from spatially resolved kinematics of RXJ1131−1231 60 70 80 90 H0 (km s 1 Mpc 1) Probability density RXJ1131 1231 with the MSD broken assuming simple parametric mass models (Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2019) Seven lenses with the MSD broken assuming simple parametric mass models (Millon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2020, TDCOSMO-I) Seven lenses with the MSD broken using single- aperture kinematics (Birrer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2020, TDCOSMO-IV) RXJ1131 1231 with the MSD broken using spatially resolved kinematics (this work) Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Comparison of our 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='4% H0 measurement (red, 77.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1+7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='3 −7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1 km s−1 Mpc−1) from the single system RXJ1131−1231 with previous mea- surements from Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (2019, blue), Millon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (2020b, grey), and Birrer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (2020, emerald).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The distributions show the H0 posteriors as described in the figure legend, and the points with error bars mark the mean and 68% credible intervals of the corresponding posterior with matching color.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' For the same flexible mass models, our analysis on a single system provides a similar precision on H0 with that from seven lenses with only single-aperture stellar kinematics (emerald, 73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='3+5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='8 −5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='8km s−1 Mpc−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Moreover, the median value of our measurement falls very close to those from previous analyses on the same system but with simple parametric assumption on the mass model breaking the MSD (blue, 78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='3+3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='4 −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='3km s−1 Mpc−1, cf.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' also 80.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='0+4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5 −4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='7 km s−1 Mpc−1by Suyu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' excellent agreement with, the current TDCOSMO sample of seven time-delay lenses based only on single-aperture stellar kinematics (H0 = 74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5+5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='6 −6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1 km s−1 Mpc−1, Birrer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Note that the system RXJ1131−1231 analyzed here is part of that sample of seven.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' – The median value of H0 from our analysis is very close to the previously inferred values assuming simple parametric mass models (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', H0 = 78.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='3+3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='4 −3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='3 km s−1 Mpc−1, Chen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Thus we do not detect any potential bias in those mass profile assumptions within the precision afforded by our data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' – Our measurement is in excellent agreement with that ob- tained by Millon et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (2020a), based on the standard as- sumption of simply parametrized forms for the mass density profile of the lens to break the MSD (74.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='2+1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='6 −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='6 km s−1 Mpc−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' In conclusion, our study provides an important validation of previous work by our collaboration on the determination of H0 from time-delay cosmography (summarized in Figure 21).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' This analysis also showcases the power of spatially resolved kinemat- ics in breaking the degeneracies that limit the H0 precision when mass profile assumptions on the galaxy density profile are re- laxed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' As the first application of such methodology performed on real data, this study stands as an important proof of concept to pioneer future studies on many more time-delay lens systems.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' In the broader context of the "Hubble tension", the mea- surement presented here is on the high end of the distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' However, the precision is not yet sufficient to rule out the val- ues below 70km s−1 Mpc−1, generally favored by early universe probes (Abdalla et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Larger samples of time-delay lenses with spatially resolved kinematics are needed to reach a conclu- sive answer without making assumptions about the mass den- sity profile of the deflectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' With JWST data already scheduled and ground-based data similar to those presented here for 7 sys- tems, ∼ 3% precision should be attainable in a relatively short time scale (Birrer & Treu 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Beyond that, a sample of ∼40 lensed quasars or supernovae with spatially resolved kinemat- ics can provide the ∼1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='2% precision on H0 that is necessary to resolve or confirm the “Hubble tension” at 5σ confidence level, with maximally flexible models, thanks to spatially resolved stel- lar kinematics (Birrer & Treu 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Acknowledgements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We thank Elizabeth Buckley-Geer, Thomas E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Collett, Philip J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Marshall, and Chiara Spiniello for useful discussions and comments that improved this study and the manuscript.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Support for this work was provided by NASA through the NASA Hubble Fellowship grant HST-HF2-51492 awarded to AJS by the Space Telescope Science Institute, which is operated by the Associ- ation of Universities for Research in Astronomy, Inc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', for NASA, under contract NAS5-26555.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' TT and GCFC acknowledge support by NSF through grants NSF- AST-1906976 and NSF-AST-1836016, and from the Moore Foundation through grant 8548.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' PM and CDF acknowledge support for this work from the National Science Foundation under Grant No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' AST-1907396 SHS thanks the Max Planck Society for support through the Max Planck Research Group and the Max Planck Fellowship.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' SHS is supported in part by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy - EXC-2094 - 390783311.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' This project has received funding from SNSF and from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (COSMICLENS : grant agreement No 787886).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' VNB gratefully acknowledges assistance from National Science Foun- dation (NSF) Research at Undergraduate Institutions (RUI) grant AST-1909297.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Note that findings and conclusions do not necessarily represent views of the NSF.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' This work used computational and storage services associated with the Hoffman2 Shared Cluster provided by UCLA Institute for Digital Research and Education’s Research Technology Group.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The data presented herein were obtained at the W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California and the National Aeronautics and Space Adminis- tration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The Observatory was made possible by the generous financial support of the W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Keck Foundation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Maunakea has always had within the indigenous Hawaiian community.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' We are most fortunate to have the opportunity to conduct observations from this mountain.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' This research made use of jampy (Cappellari 2008, 2020), pPXF (Cappellari 2017, 2022), pafit (Krajnovi´c et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2006), vorbin (Cappellari & Copin 2003), mgefit (Cappellari 2002) , lenstronomy (Birrer & Amara 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Birrer et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Article number, page 19 of 21 A&A proofs: manuscript no.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' ms 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='87 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='05 / r 600 1000 Dd (Mpc) 2000 4000 D t (Mpc) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='0 int 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='7 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='0 int 3000 D t (Mpc) 900 Dd (Mpc) spatially resolved single aperture Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Comparison of the distance constraints between spatially resolved velocity dispersion and single-aperture velocity dispersion.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Here, the integrated velocity dispersion is taken as the fiducial value of 287 ± 18 km s−1 to match the mean of our spatially resolved mea- surement, but the uncertainty of a single-aperture velocity dispersion measurement (Suyu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The darker and lighter shaded regions in the 2D plots trace 68% and 95% credible regions, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' The single-aperture velocity dispersion cannot constrain the anisotropy pro- file parameter σθ/σr and the internal MST parameter λint, with both limited by the prior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' As a result, the D∆t–Dd posterior is constrained much more weakly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2021), numpy (Oliphant 2015), scipy (Jones et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2001), astropy (Astropy Col- laboration 2013, 2018), jupyter (Kluyver et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2016), matplotlib (Hunter 2007), seaborn (Waskom et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2014), emcee (Foreman-Mackey et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2013), and getdist (https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='com/cmbant/getdist).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' References Abdalla, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Abellán, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Aboubrahim, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2022, Journal of High Energy Astrophysics, 34, 49 Abolfathi, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Aguado, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Aguilar, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2018, The Astrophysical Journal Supplement Series, 235, 42 Aiola, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Calabrese, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Maurin, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2020, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Cosmology Astropart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', 2020, 047–047 Astropy Collaboration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2013, A&A, 558, A33 Astropy Collaboration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2018, AJ, 156, 123 Avila, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Koekemoer, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Mack, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', & Fruchter, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2015, Optimizing pixfrac in Astrodrizzle: An example from the Hubble Frontier Fields, Tech.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' rep.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Bacon, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Simien, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', & Monnet, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 1983, Astronomy and Astrophysics, Vol.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 128, p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 405-410 (1983), 128, 405 Barnabè, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Czoske, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Koopmans, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2009, Monthly Notices of the Royal Astronomical Society, 399, 21 Barnabè, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Dutton, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Marshall, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2012, Monthly Notices of the Royal Astronomical Society, 423, 1073 Bertin, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' & Lombardi, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2006, ApJ, 648, L17 Binney, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' & Tremaine, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 1987, Galactic dynamics Birrer, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' & Amara, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2018, Physics of the Dark Universe, 22, 189 Birrer, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Amara, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', & Refregier, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2016, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Cosmology Astropart.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', 8, 020 Birrer, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Dhawan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', & Shajib, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2022a, ApJ, 924, 2 Birrer, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Millon, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Sluse, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2022b, Time-Delay Cosmography: Mea- suring the Hubble Constant and other cosmological parameters with strong gravitational lensing Birrer, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Shajib, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Galan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2020, A&A, 643, A165 Birrer, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Shajib, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Gilman, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2021, JOSS, 6, 3283 Birrer, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' & Treu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2021, A&A, 649, A61 Birrer, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Treu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Rusu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2019, MNRAS, 484, 4726 Blakeslee, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Jensen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Ma, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='-P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Milne, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', & Greene, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2021, ApJ, 911, 65 Blum, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Castorina, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', & Simonovi´c, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2020, arXiv e-prints, arXiv:2001.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='07182 Bonvin, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Courbin, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Suyu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2017, MNRAS, 465, 4914 Brout, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Scolnic, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Popovic, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2022, The Astrophysical Journal, 938, 110 Buckley-Geer, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Lin, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Rusu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2020, MNRAS, 498, 3241 Cappellari, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2002, MNRAS, 333, 400 Cappellari, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2008, MNRAS, 390, 71 Cappellari, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2016, ARA&A, 54, 597 Cappellari, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2017, MNRAS, 466, 798 Cappellari, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2020, Monthly Notices of the Royal Astronomical Society, 494, 4819 Cappellari, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2022, Full spectrum fitting with photometry in ppxf: non- parametric star formation history, metallicity and the quenching boundary from 3200 LEGA-C galaxies at redshift z 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='8 Cappellari, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' & Copin, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2003, Monthly Notices of the Royal Astronomical Society, 342, 345 Cappellari, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Emsellem, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Bacon, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2007, MNRAS, 379, 418 Cappellari, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Scott, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Alatalo, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2013, MNRAS, 432, 1709 Chang, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='-Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', van der Wel, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Rix, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2013, The Astrophysical Journal, 773, 149 Chen, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Fassnacht, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Suyu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2019, MNRAS, 490, 1743 Chen, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='-F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Fassnacht, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Suyu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2021a, A&A, 652, A7 Chen, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Treu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Fassnacht, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2021b, Monthly Notices of the Royal Astronomical Society, 508, 755 Collett, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Oldham, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Smith, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2018, Science, 360, 1342 Courbin, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Eigenbrod, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Vuissoz, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Meylan, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', & Magain, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2005, 225, 297 Courteau, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Cappellari, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', de Jong, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2014, Reviews of Modern Physics, 86, 47 de Zeeuw, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Evans, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', & Schwarzschild, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 1996, Monthly Notices of the Royal Astronomical Society, 280, 903 Di Valentino, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Mena, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Pan, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2021, Classical and Quantum Gravity, 38, 153001 Efstathiou, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2021, MNRAS, 505, 3866 Emsellem, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Monnet, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Bacon, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', & Nieto, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='-L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 1994, A&A, 285, 739 Falco, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Gorenstein, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', & Shapiro, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 1985, ApJ, 289, L1 Foreman-Mackey, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Hogg, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Lang, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', & Goodman, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2013, PASP, 125, 306 Foxley-Marrable, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Collett, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Vernardos, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Goldstein, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', & Bacon, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2018, Monthly Notices of the Royal Astronomical Society, 478, 5081 Freedman, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2021, ApJ, 919, 16 Freedman, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Madore, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Hatt, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2019, ApJ, 882, 34 Freedman, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Madore, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Hoyt, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2020, ApJ, 891, 57 Fruchter, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' & Hook, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2002, Publications of the Astronomical Society of the Pacific, 114, 144 Gilman, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Birrer, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', & Treu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2020, A&A, 642, A194 Gomer, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Sluse, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Van de Vyvere, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Birrer, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', & Courbin, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2022, A&A, 667, A86 Gonneau, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Lyubenova, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Lançon, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2020, A&A, 634, A133 Gonzaga, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Hack, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Fruchter, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', & Mack, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2012, The DrizzlePac Handbook Goodman, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' & Weare, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2010, Communications in Applied Mathematics and Computational Science, 5, 65–80 Graham, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Cappellari, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Li, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2018, Monthly Notices of the Royal Astronomical Society, 477, 4711 Greene, Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Suyu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Treu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2013, ApJ, 768, 39 Hunter, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2007, Computing in Science and Engineering, 9, 90 Jeans, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 1922, Monthly Notices of the Royal Astronomical Society, 82, 122 Jee, I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Suyu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Komatsu, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2019, Science, 365, 1134 Jones, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Oliphant, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Peterson, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', & Others.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2001, SciPy: Open source scien- tific tools for Python Kluyver, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Ragan-Kelley, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Pérez, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2016, in Positioning and Power in Academic Publishing: Players, Agents and Agendas, ed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Loizides & B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Schmidt (IOS Press BV, Amsterdam, Netherlands), 87 – 90 Knox, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' & Millea, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2020, Phys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' D, 101, 043533 Kochanek, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2020, MNRAS, 493, 1725–1735 Kourkchi, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Tully, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Eftekharzadeh, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2020, ApJ, 902, 145 Krajnovi´c, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Cappellari, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', de Zeeuw, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', & Copin, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2006, Monthly No- tices of the Royal Astronomical Society, 366, 787 Li, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Mao, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Cappellari, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2018, The Astrophysical Journal, 863, L19 Millon, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Courbin, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Bonvin, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2020a, Astronomy and Astrophysics, 640, A105 Millon, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Galan, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Courbin, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2020b, A&A, 639, A101 More, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Suyu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Oguri, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', More, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', & Lee, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='-H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2017, The Astrophys- ical Journal, 835, L25 Article number, page 20 of 21 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Shajib et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' : H0 from spatially resolved kinematics of RXJ1131−1231 Morrissey, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Matuszewski, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Martin, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2012, 8446, 844613 Morrissey, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Matuszewski, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Martin, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2018, The Astrophysical Journal, 864, 93 Navarro, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Frenk, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', & White, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 1996, ApJ, 462, 563 Navarro, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Frenk, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', & White, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 1997, ApJ, 490, 493 Oke, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Cohen, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Carr, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 1995, Publications of the Astronomical Society of the Pacific, 107, 375 Oliphant, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2015, Guide to NumPy, 2nd edn.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' (USA: CreateSpace Independent Publishing Platform) Pesce, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Braatz, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Reid, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2020, ApJ, 891, L1 Planck Collaboration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2020, A&A, 641, A6 Raftery, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 1995, Sociological Methodology, 25, 111 Refsdal, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 1964, MNRAS, 128, 307 Riess, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Yuan, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Macri, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2022, The Astrophysical Journal, 934, L7 Robertson, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2013, Publications of the Astronomical Society of Australia, 30, e048 Rusu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Fassnacht, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Sluse, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2017, MNRAS, 467, 4220 Rusu, C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Wong, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Bonvin, V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2020, MNRAS, 498, 1440 Schneider, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Ehlers, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', & Falco, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 1992, Gravitational Lenses Schneider, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' & Sluse, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2013, A&A, 559, A37 Schneider, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' & Sluse, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2014, A&A, 564, A103 Shajib, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2019, MNRAS, 488, 1387–1400 Shajib, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Birrer, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Treu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2020, MNRAS, 494, 6072 Shajib, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Birrer, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Treu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2019, MNRAS, 483, 5649 Shajib, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Glazebrook, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Barone, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2022a, LensingETC: a tool to op- timize multi-filter imaging campaigns of galaxy-scale strong lensing systems Shajib, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Treu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', & Agnello, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2018, MNRAS, 473, 210 Shajib, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Vernardos, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Collett, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2022b, Strong Lensing by Galax- ies Sluse, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Claeskens, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='-F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Hutsemékers, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', & Surdej, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2007, Astronomy and Astrophysics, 468, 885 Sluse, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Surdej, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Claeskens, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='-F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2003, A&A, 406, L43 Sonnenfeld, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Treu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Marshall, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2015, ApJ, 800, 94 Suyu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Auger, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Hilbert, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2013, ApJ, 766, 70 Suyu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Marshall, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Auger, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2010, ApJ, 711, 201 Suyu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Treu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Hilbert, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2014, ApJ, 788, L35 Sánchez-Blázquez, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Peletier, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Jiménez-Vicente, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2006, Monthly Notices of the Royal Astronomical Society, 371, 703 Sérsic, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 1968, Atlas de Galaxias Australes Taubenberger, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Suyu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Komatsu, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2019, A&A, 628, L7 Tewes, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Courbin, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Meylan, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2013, A&A, 556, A22 Tihhonova, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Courbin, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Harvey, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2018, MNRAS, 477, 5657 Treu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Agnello, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Baumer, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2018, MNRAS, 481, 1041 Treu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' & Koopmans, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' V.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2002, MNRAS, 337, L6 Treu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' & Marshall, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2016, A&A Rev.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', 24, 11 Treu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Suyu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', & Marshall, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2022, Strong lensing time-delay cosmog- raphy in the 2020s Valdes, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Gupta, R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Rose, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Singh, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', & Bell, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2004, The Astro- physical Journal Supplement Series, 152, 251 Van de Vyvere, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Gomer, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Sluse, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2022a, Astronomy and Astro- physics, 659, A127 Van de Vyvere, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Sluse, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Gomer, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' R.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', & Mukherjee, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2022b, Astronomy and Astrophysics, 663, A179 Verde, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Treu, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', & Riess, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2019, Nature Astronomy, 3, 891–895 Waskom, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Botvinnik, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Hobson, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2014, seaborn: v0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='0 (November 2014) Wenger, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Ochsenbein, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Egret, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2000, Astronomy and Astrophysics Supplement Series, 143, 9 Wong, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Suyu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Chen, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2020, MNRAS, 498, 1420 Yahalomi, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Schechter, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', & Wambsganss, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2017, A Quadruply Lensed SN Ia: Gaining a Time-Delay.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='Losing a Standard Candle Yıldırım, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Suyu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Chen, G.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' C.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='-F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', & Komatsu, E.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2021, arXiv:2109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='14615 [astro-ph] [arXiv:2109.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='14615] Yıldırım, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', Suyu, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=', & Halkola, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 2020, Monthly Notices of the Royal Astronomical Society, 493, 4783 1 Department of Astronomy & Astrophysics, University of Chicago, Chicago, IL 60637, USA;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' e-mail: ajshajib@uchicago.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='edu 2 Kavli Institute for Cosmological Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' University of Chicago,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Chicago,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' IL 60637,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' USA 3 Department of Physics and Astronomy,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' University of California,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Davis,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' CA 95616,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' USA 4 Department of Physics and Astronomy,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' University of California,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Los Angeles,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' CA 90095,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' USA 5 Sub-Department of Astrophysics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Department of Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Univer- sity of Oxford,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Denys Wilkinson Building,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Keble Road,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Oxford,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' OX1 3RH,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' UK 6 Technical University of Munich,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' TUM School of Natural Sciences,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Department of Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' James-Franck-Str.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 1, Garching, 85748, Ger- many 7 Max Planck Institute for Astrophysics, Karl-Schwarzschild-Str.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 1, Garching, 85748, Germany 8 Institute of Astronomy and Astrophysics, Academia Sinica, 11F of ASMAB, No.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='1, Section 4, Roosevelt Road, Taipei, 10617, Taiwan 9 Physics Department, California Polytechnic State University, San Luis Obispo, CA 93407, USA 10 Fermi National Accelerator Laboratory, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content='O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Box 500,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Batavia,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' IL 60510,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' USA 11 STAR Institute,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Quartier Agora,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Allée du Six Août,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 19c,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 4000 Liége,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Belgium 12 Kavli Institute for Particle Astrophysics and Cosmology and Depart- ment of Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Stanford University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Stanford,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' CA 94305,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' USA 13 SLAC National Accelerator Laboratory,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Menlo Park,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' CA,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 94025 14 Department of Physics and Astronomy,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Stony Brook University,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Stony Brook,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' NY 11794,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' USA 15 Institute of Physics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Laboratory of Astrophysics,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Ecole Polytech- nique Fédérale de Lausanne (EPFL),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Observatoire de Sauverny,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' 1290 Versoix,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' Switzerland Article number,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'} +page_content=' page 21 of 21' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/CdE0T4oBgHgl3EQfyQI7/content/2301.02656v1.pdf'}