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+filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf,len=1684
+page_content='MNRAS 000, 1–?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (2023)  Preprint 3 January 2023  Compiled using MNRAS LATEX style file v3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='0  Time-averaging Polarimetric and Spectral Properties of GRBs  Liang Li1,2,3⋆ Soroush Shakeri4,1,5†  1ICRANet, Piazza della Repubblica 10, I-65122 Pescara, Italy  2ICRA and Dipartimento di Fisica, Università di Roma “La Sapienza”, Piazzale Aldo Moro 5, I-00185 Roma, Italy  3INAF – Osservatorio Astronomico d’Abruzzo, Via M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Maggini snc, I-64100, Teramo, Italy  4Department of Physics, Isfahan University of Technology, Isfahan 84156-83111  5ICRANet-Isfahan, Isfahan University of Technology, Isfahan 84156-83111, Iran  Accepted XXX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Received YYY;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' in original form ZZZ  ABSTRACT  One of the most fundamental and yet open issues in gamma-ray burst (GRB) physics, is the comprehension of the nature of  their jet composition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The investigation of joint polarimetric and spectral properties is essential to probe the jet composition and  radiation mechanism of GRBs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Several distinct categories of jet properties—the “Kinetic-energy-dominated" (KED), “Poynting-  flux-dominated" (PFD), and “Hybrid-dominated" (HD) jets—have been observed in the observed GRB spectra, and the emission  dominated by different jet properties is expected to have a different level of polarization (πKED ≲ πHD ≲ πPED).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' In the present  paper,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' we collected a GRB sample in which all the bursts detected by the Gamma-ray Burst Monitor (GBM) on board the  NASA Fermi Gamma-ray Space Telescope whose polarization measurements are also reported in the literature and the epochs  of prompt emission are heavily overlapped with their polarization observations,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' aiming to establish a connection between the  polarization and jet properties of GRBs,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' and to confirm the validity of this correlation (πKED ≲ πHD ≲ πPED) from observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  With a detailed spectral analysis, we found that all the bursts are classified as the “Hybrid" jet type, implying that one cannot  rule out that the photosphere emission may also be the possible mechanism powering the high levels of polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Moreover,  we also discovered that the polarization degrees π are tightly correlated with the cosmological rest-frame peak energy (Ep,z) of  the νFν prompt emission spectrum, the isotropic-bolometric-equivalent emission energy (Eγ,iso), and the blackbody temperature  (kT).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Finally, we present different polarization models in the presence of ordered and random magnetic field configurations  with the properties of corresponding hybrid jets in order to interpret polarization measurements of the prompt emission in our  sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  Key words: gamma-ray burst: general, radiation mechanisms: non-thermal, radiation mechanisms: thermal  1 INTRODUCTION  Gamma-ray bursts (GRBs) are one of the most explosive, and elec-  tromagnetically the brightest transient phenomena in the Universe,  occurrence at cosmological distances.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' After decades of investiga-  tion, the origin of the jet composition (a hot baryonic-dominated  fireball or a cold Poynting-flux-dominated outflow), and the radi-  ation mechanism and energy dissipation mechanism (synchrotron,  or Comptonization of quasi-thermal emission from the photosphere)  in gamma-ray burst (GRB) physics are still unclear (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=', Rees &  Meszaros 1994;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Mészáros & Rees 2000;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Rees & Mészáros 2005;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  Pe’er et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2006;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Dai et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2006;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Pe’er 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Pe’Er & Ryde 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  Zhang 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Bégué et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  There are two crucial clues that can in principle be helpful in di-  agnosing the jet composition of GRBs, as well as their radiation  mechanism and energy dissipation mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The conventional  approach is to examine the spectral properties of prompt emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  ⋆ E-mail: liang.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='li@icranet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='org (LL)  † E-mail:s.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='shakeri@iut.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='ac.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='ir (SS)  Theoretically, a thermal component originating from photosphere  emission, or a non-thermal component originating from synchrotron  radiation, possibly also from inverse Compton scattering, is often  expected to be present in GRB spectral analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Phenomenologi-  cally, GRB spectra in the keV-MeV energy range can be typically  well-delineated by an empirical function, known as the Band func-  tion (Band et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 1993), which is generally considered to be a non-  thermal spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The Band spectrum features a smoothly broken  power law, with the peak energy Ep ≃ 210 keV (the energy at which  most of the energy is released) in νFν space and the asymptotic  power-law photon indices below (α ≃ −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='8) and above (β ≃ −2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='5)  the break energy (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=', Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The low-energy spectra dur-  ing GRB prompt emission phase are closely related to the energy  distribution of electrons (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=', Preece et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 1998;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Lloyd & Petrosian  2000;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Geng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' This fact can be utilized in order to diag-  nose GRBs radiation mechanism as well as their jet properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' For  instance, synchrotron emission predicts two different α values: α=-  3/2 and α=-2/3 (so-called the line-of-death (LOD) of synchrotron  emission, Preece et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 1998) correspond to the fast-cooling and  slow-cooling synchrotron emission, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' It has been shown  © 2023 The Authors  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='00576v1  [astro-ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='HE]  2 Jan 2023  2  Li & Shakeri  that the synchrotron emission in the presence of a decaying mag-  netic field can reproduce the Band-like spectrum of the GRB prompt  phase (Lan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' While photosphere models, on the other  hand, predict much harder values of α;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=', above α=-2/3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' For ex-  ample, a recent study (Acuner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2020) suggests that the spec-  tra that prefer the photospheric model all have low-energy power-  law indices α ∼>-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='5, as long as the data has a high significance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  Years of observations have revealed, however, that GRBs have di-  verse spectral properties, making it difficult for a single spectral  model (such as the Band-alone model) to accurately characterize all  the spectral shapes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' For instance, time-resolved and time-integrated  spectral analysis inferred from the broadband Fermi observations  have revealed that GRB prompt emission exhibits remarkably di-  verse spectral properties (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=', Abdo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Ryde et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  Axelsson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Acuner et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Li 2019a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2019,  2021, 2022b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Deng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' A kinetic-energy-dominated (KED)  jet characterised by a quasi-thermal Planck-like spectrum has been  detected in some bursts (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' GRBs 090902B, 220426A, Ryde et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Deng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2022;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Song et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2022), while  a cold Poynting-flux-dominated (PFD) outflow characterised by a  Band (or cutoff power-law1)-only function (Band et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 1993) has  been also observed in some other bursts (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' GRB 080916C2, GRB  130606B, and many others, Abdo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Li 2022a), even a  hybrid-dominated (HD) relativistic outflow with a hot fireball com-  ponent and a cold Poynting-flux component, characterized by either  a composited spectral scenario, with a non-thermal component and  a thermal component, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=', GRBs 100724B, 110721A, 150314A,  190114C, and several others, Axelsson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Guiriec et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Wang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Li 2022a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2022b), or a transition  from a fireball to a Poynting-flux-dominated outflow within a single  burst (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' GRBs 140206B, 160625B, and several others, Li 2019a),  have also been observed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  An alternative approach is to investigate their polarization prop-  erties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Theoretically, photon polarizations play a key role to un-  derstand the jet composition, angular structure, geometric config-  uration, magnetic composition and magnetic field configuration of  GRB jets, and radiation mechanism of GRB jets (Toma et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2009a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  Lundman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2013;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Zhang 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Although  magnetic field configurations with relatively large coherence lengths  more than gyroradius of charged particles can generate the same  energy spectrum via synchrotron mechanism, the level of polariza-  tion may significantly different for various magnetic field structures.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  Therefore joint spectral and polarization analysis is essential to de-  termine the magnetic field structure in outflow materials of GRBs  (Granot 2003;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Lyutikov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2003;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Granot & Königl 2003a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Kole  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' For instance, the center engine is anticipated to gen-  erate strong magnetic fields (a highly magnetized jet) and launch  them concurrently with the relativistic jets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' It is unclear, neverthe-  less, whether the GRB emission is caused by shock dissipation or  magnetic reconnection, and whether the outflow is dominated by the  photosphere or synchrotron emission (Toma et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2009a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  In fact, the generation of the polarization signal can be intrinsic  to the emission process or due to the propagation effects Shakeri  1 Recent studies (Li 2022b,a) supported by several pieces of additional ev-  idence (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=', inconsistent spectral parameter distributions and distinct Amati  and Yonetoku correlations) have shown that Band-like spectra and CPL-like  spectra may originate from distinct radiation processes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  2 It has been demonstrated in recent studies (Guiriec et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Vereshcha-  gin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2022) that a thermal component needs to be added during the initial  prompt emission of GRB 080916C to obtain an acceptable fit to the spectral  data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  & Allahyari (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Several emission models (induced synchrotron  emission, Rybicki & Lightman 1979;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' photosphere emission, Lund-  man et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2014a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' and Compton drag model, Lazzati et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2004)  have been proposed to explain the intrinsic polarization properties  of relativistic jets during prompt emissions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (i) Synchrotron emis-  sion model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' There are some studies (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=', Rybicki & Lightman 1979;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  Toma et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2009b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Lan & Dai 2020) showing that higher values  of linear polarized signal (polarization degree π ranging from 20%  to 70%) is expected to be measured with an ordered magnetic field  from the synchrotron emission from a relativistic jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' While jets with  random magnetic fields produce lower levels of polarization, this is  due to the polarization being canceled out so that the net polariza-  tion degree being close to zero for an on-axis observer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' A polariza-  tion detection which is less than 15% is believed to be originated  from a random magnetic field configuration within the jet (Mao &  Wang 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' For example, if the emission is dominated by the inter-  nal shock (IS) model, π is expected to range from 10% (the maxed  magnetic field configuration) to 70% (the large-scale ordered mag-  netic field configuration).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (ii) Dissipative photosphere model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The  dissipative photosphere model predicts a relatively low degree of po-  larization in the γ-ray band.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' However, a structured jet photosphere  model might also generate polarized photons by Compton scatter-  ing, but the degree of polarization would be energy-dependent from  the synchrotron model in ordered magnetic fields.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' For instance, it  is demonstrated that if the jet has considerable structure, the model  may create polarizations of up to 40% within δΘ ∼ Γ−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' However, in  the absence of dissipation and below the photosphere the polariza-  tion is rather limited to values below 15%-20% (Gill et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' To  restrict these models, a high-sensitivity gamma-ray polarimeter with  a broad band-pass to detect energy-dependent polarization signals is  required (Zhang 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Ito et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Lundman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2014a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Lund-  man et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2018a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (iii) Internal-collision-induced magnetic recon-  nection and turbulence (ICMART) model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' In the ICMART model  (Zhang & Yan 2011a), π is expected to range from 60 percent at the  beginning of the pulse and down to about 10 percent at the end of  the pulse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' A decaying polarization degree is predicted.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  It is highly speculated that the prompt emission is likely expected  to be strongly polarized owing to its non-thermal origin (a non-  thermal Band-like spectrum).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Observationally, higher levels of lin-  ear polarization measured from prompt γ-ray emission have been  reported by several authors (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=', Coburn & Boggs 2003;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Willis  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2005;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' McGlynn et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Yonetoku et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2012a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' For in-  stance, a higher polarization degree π = 80%±20% in GRB 021006  was claimed by Coburn & Boggs (2003) using the RHESSI data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  Later, several other cases were also reported, e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=', GRB 930131 (π >  35%), GRB 960924 (π > 50%), GRB 041219A, GRB 100826A  (π = 27% ± 11%), GRB 110301A (π = 70% ± 22%), and GRB  110721A (π = 84%+16%  −28%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Subsequent observations were also ob-  served in the optical band during the afterglow emission and were of  relatively low polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Compared with prompt γ-ray emission,  the levels of linear polarization measured from afterglow emission  are relatively lower.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=', GRB 060418 (π < 8%), GRB 090102 (π =  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='1% ± 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='3%), GRB 091208B (π = 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='4% ± 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='5%), and 120328A  (π = 28% ± 4%).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' However, higher degrees of polarization observa-  tions are still expected to be measured from early reverse shocks, up  to ∼ 60%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  Generally speaking, we can study GRB polarization and spec-  tral properties either in a time-integrated (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=', Li 2022a) or time-  resolved (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=', Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2021) manner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The former represents average  polarimetric and spectral properties and is treated as a single-time  event for the entire emission period.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The latter treats the entire emis-  sion period as divided into multiple-time events, and polarimetric  MNRAS 000, 1–?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (2023)  Time-averaging Polarimetric and Spectral Properties of GRBs  3  and spectral analyses are therefore performed on each event individ-  ually.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The time-integrated method depends more heavily on the sta-  tistical results of a large sample in order to produce a more trustwor-  thy result because different bursts have distinct observational prop-  erties (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=', angular structure).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' However, this issue does not arise  when a time-resolved technique is used in the same burst since it  ensures that other conditions (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=', magnetic field configuration) are  essentially the same and, therefore, makes it easier to obtain reliable  results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  Following these lines of argument, the emissions dominated by  different jet properties (KED, PFD, and HD) may have different lev-  els of prompt-GRB polarization measurements3 (Li 2019a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' As a  result, a different level of polarization degrees (πKED ≲ πHD ≲ πPED)  is naturally expected due to different jet properties if other condi-  tions are basically the same, where πKED, πHD, and πPED are the po-  larization degree in the KED, HD, and PHD jets, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' This  may provide a method to study the correlations between polarization  properties and their spectral properties, as well as their jet properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  A possible connection between the spectral and polarization proper-  ties has not yet been firmly established, though recent works provide  some statistical results (Chattopadhyay et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2019;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Kole et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  Therefore, we dedicate this work to examining whether any possi-  ble connections exist between polarization and jet properties, and  aim to confirm the validity of this correlation (πKED ≲ πHD ≲ πPED)  from observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Practically, several important factors need to be  taken into account in our analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (i) In order to potentially evaluate  all of the frequently-used GRB spectral models and thus diagnose  the jet properties, our analysis focuses on the bursts detected by the  Gamma-ray Burst Monitor (GBM, 8 KeV-40 MeV, Meegan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  2009) onboard the NASA Fermi Gamma-ray Space Telescope.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (ii)  To directly compare the spectral and polarization properties and thus  make our results more trustworthy, we select the bursts during which  polarization observations and spectral data are available during the  same epoch.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (iii) Realistically, systematic error is frequently at play  in polarization measurements and different polarization instruments  have different systematic errors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Therefore, a high-significance sig-  nal from polarization measurement is required.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' In this paper, we  collect a sample of the Fermi-GBM detected bursts along with the  polarized measurements reported in the literature using the time-  integrated spectral and polarization analysis approach based on their  statistical results, aiming to establish a connection between the po-  larization and jet properties of GRBs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  The paper is organized as follows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The sample and Methodol-  ogy are presented in Section 2 and Section 3, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Our re-  sults and their physical implication are summarized in Section 4 and  Section 5, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The conclusion is presented in Section 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  Throughout the paper, the standard Λ-CDM cosmology with the pa-  rameters H0 = 67.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='4 kms−1 Mpc−1, ΩM = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='315, and ΩΛ = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='685 are  adopted (Planck Collaboration et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  3 Polarization measurement is a measurement where π ranges from 0% to  100% (0% ≤ π ≤ 100%) and includes the non-detection (0%), so measur-  ing something consistent with zero is a measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Polarization detection,  however, indicates a different meaning, where 0% < π ≤ 100% and excludes  0%, since we have excluded part of the parameter space equivalent to detec-  tion measurements due to the fact that a non-detection of flux implies that we  did not measure something.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  2 THE SAMPLE  A comprehensive database of GRB polarimetric observations has  been created in a recent work (Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2022a) by extensively search-  ing for those GRBs in the literature whose polarization measure-  ments have been reported.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' A total of 73 bursts with polarization  detections were included in the database, covering a broad wave-  length range from radio to optical, X-ray, and γ-ray emission (see  Table 1 in Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2022a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The prompt emission data of these bursts  were observed by different satellites (Fermi, Swift, BeppoSAX, and  BATSE).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' On the other hand, the diagnosis of jet composition usually  requires a refined spectral analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Among these satellites, Fermi  covers the broadest energy range in the observation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Consequently,  in order to fully evaluate all current spectral models we pay spe-  cial attention to these Fermi-detected bursts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The Gamma-ray Burst  Monitor (GBM, 8 KeV-40 MeV, Meegan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2009) and the Large  Area Telescope (LAT, 20 MeV- 300 GeV, Atwood et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2009), on-  board the NASA Fermi Gamma-ray Space Telescope, together pro-  vide unprecedented spectral coverage for seven orders of magnitude  in energy (from ∼8 keV to ∼300 GeV).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Our statistical analysis in  the current work includes the prompt γ-ray emission spectral anal-  ysis and the connection between the spectrum and polarization are  thus based on the Fermi-detected bursts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' On the other hand, we fo-  cus on the GRBs whose polarization measurements were recorded  during the prompt emission in the γ-ray band in order to compare  the polarization and spectral properties during the same time period.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  Following are the specific observational properties of the five fas-  cinating bursts (see Table 1) that made up the smaller sample as a  result of these selection criteria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  GRB 100826A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' On August 26, 2010 at 22:58:22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='898 (T0)  UT, GRB 100826A, was detected by the Fermi/GBM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' A t90 of  (84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='993±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='724) s in the 10-1000 keV was measured using the  GBM data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The GBM lightcurve exhibits a complicated shape with  multiple-peak pulses, and the fluence (flux integrated over the burst  duration) in the energy range of 10-1000 keV during the t90 dura-  tion reported by the GBM team is (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='6388±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='001)×10−4 erg cm−2  (Figure 2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' This burst has no redshift measurement, a value of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='3  is estimated using the Yonetoku correlation (Yonetoku et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  Therefore, the isotropic-equivalent energy released from gamma-  ray emission in the cosmological frame for this burst can be cal-  culated as, Eγ,iso=(3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='39+0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='36  −0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='33)×1054 erg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The KED-to-PFD transition  pattern belonging to the “HD” jet type is diagnosed for this burst  by using a low-energy spectrum based on a detailed time-resolved  spectral analysis during prompt emission (see Section 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Yonetoku  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (2011a) reported that a relatively higher polarization degree  (πobs=27±11) with a 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='9σ linear polarization signal significance was  detected during the prompt emission (0-100 seconds after the trig-  ger) of GRB 100826A using a GAmma-ray Polarimeter (GAP) on  board a small Japanese solar-power-sail demonstrator, Interplanetary  Kite-craft Accelerated by Radiation of the Sun (IKAROS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  GRB 110301A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' On March 01, 2011 at 05:08:43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='070 (T0) UT,  GRB 110301A, was detected by the Fermi-GBM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' A t90 of (5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='693±  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='362) s in the 10-1000 keV was measured using the GBM data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The  lightcurve exhibits a complicated shape with multiple-peak pulses,  and the fluence in the energy range of 10-1000 keV from T0+0 s  to T0+5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='693 s reported by the GBM team is (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='5891±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='003)×10−5  erg cm−2 (Figure 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' This burst has no redshift measurement, a  value of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='36 is estimated by using the Yonetoku relation (Yone-  toku et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' With this estimated value of redshift, the isotropic-  equivalent energy released from gamma-ray emission in the cosmo-  logical frame for this burst can be calculated as, Eγ,iso=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='4×1052 erg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  A KED-to-PFD jet is diagnosed for this burst by using a low-energy  MNRAS 000, 1–?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (2023)  4  Li & Shakeri  spectrum based on a detailed time-resolved spectral analysis during  prompt emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' A linear polarization signal (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='7σ) with a very high  polarization degree (π=70±22) for this burst was claimed by Yone-  toku et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (2012b) using the IKAROS/GAP data 0-7 seconds after  the trigger (Figure 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  GRB 110721A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' On July 21, 2011 at 04:47:43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='761 (T0)  UT, GRB 110721A, was detected by the Fermi-GBM.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' A t90 of  (21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='822±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='572) s in the 10-1000 keV was measured using the GBM  data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The lightcurve exhibits a single-peak pulse, and the fluence in  the energy range of 10-1000 keV from T0+0 s to T0+21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='822 s as re-  ported by the GBM team is (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='5891±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='003)×10−5 erg cm−2 (Figure  4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' This burst has a value of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='382 of redshift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' With this redshift, we  calculate the isotropic-equivalent energy released from gamma-ray  emission in the cosmological frame for this burst, Eγ,iso=3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='0×1052  erg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' A peak-KED jet is diagnosed for this burst by using a low-  energy spectrum based on a detailed time-resolved spectral analysis  during prompt emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' A linear polarization signal (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='3σ) with a  very high polarization degree (π=85+16  −22) for this burst was claimed  by Yonetoku et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (2012b) using the IKAROS/GAP data 0-11 sec-  onds after the trigger (Figure 4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  GRB 140206A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' On 6 February 2014 at 06:36:12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='843 UT (T0),  a long burst, GRB 140206B, was detected by Fermi-GBM and sev-  eral other satellites (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=', INTEGRAL/IBIS).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Its GBM lightcurve in  the 10-900 keV exhibits three clearly separated emission episodes  (G1, G2, and G3) as shown in the left panel of Figure 5, with T90 of  146.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='690±4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='419 s was measured by GBM data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' GRB 140206B is a  very bright burst, and the fluence (flux integrated over the burst dura-  tion) in the energy range of 10-1000 keV from T0+0 s to T0+146.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='690  s reported by the GBM team is (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='23±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='003)×10−4 erg cm−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' This  burst has a value of 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='73 for redshift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' With this redshift, we calculate  the isotropic-equivalent energy released from gamma-ray emission  in the cosmological frame for this burst, Eγ,iso=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='3×1054 erg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The  spectral analysis has been performed in great detail in Li (2019a),  and three different spectral components (KED-to-PFD) have been  identified, a short-thermalized precursor early on, followed up with  the main burst with a non-thermal emission later on, and in the last  with a fainter burst with still a non-thermal emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Interestingly,  immediately following up with the short-thermalized precursor, a  clear polarization signal with 90% confidence was observed 4-26  seconds after the trigger as reported in Götz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (2014) using the  INTEGRAL/IBIS data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' This signal is a linear polarization with an  up-limit polarization degree of π > 28 observed in the γ-ray energy  band (Figure 5).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  GRB 160802A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' GRB 160802A was detected by GBM on Au-  gust 2, 2016 at UT 06:13:29.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='63.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' A T90 of (16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='384±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='362) s in the  10-1000 keV was measured using the GBM data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The prompt emis-  sion light curve shows two clearly separated active periods, with a  quiescent time interval between the two periods of about 10 sec-  onds.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The earlier period consists of overlapping pulses while the lat-  ter period shows a clear single-peak pulse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The fluence in the energy  range of 10-1000 keV from T0+0 s to T0+21.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='822 s as reported by  the GBM team is (6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='8399±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='0057)×10−5 erg cm−2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' This burst has  no redshift measurement, a value of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='36 is estimated by using the  Yonetoku relation (Yonetoku et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Using this estimated value  of redshift, we further calculate the isotropic-equivalent energy re-  leased from gamma-ray emission in the cosmological frame for this  burst, Eγ,iso=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='2×1053 erg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' A peak-KED jet for each period is di-  agnosed for this burst by using a low-energy spectrum based on a  detailed time-resolved spectral analysis during prompt emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' A  linear polarization signal (∼3σ) with a very high polarization degree  (π=85±29) for this burst was claimed by Yonetoku et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (2012b) us-  ing the AstroSat/GZTI data 0-20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='34 seconds after the trigger (Figure  6).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  3 METHODOLOGY  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='1 Spectral Analysis Techniques  In order to diagnose the jet properties for a given burst, a de-  tailed time-integrated or time-resolved spectral analysis is re-  quired.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The spectral analysis is performed by a pure Python pack-  age, namely, the Multi-Mission Maximum Likelihood  Framework (3ML,Vianello et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Moreover, a Bayesian  approach and Markov Chain Monte Carlo (MCMC) iterations to  explore the best parameter space was used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Our spectral analy-  sis includes the following main steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' First is to select detec-  tors, sources, and background intervals;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Second, we used the  Bayesian block method (BBlocks, Scargle et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2013) to bin the  Time-Tagged Events (TTE) lightcurve of the brightest detector (with  the minimum viewing angle), and the significance (S, Vianello 2018)  for each BBlocks time bin was also calculated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Third, we use a  typical GRB spectral model (Band function, Band et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 1993) to fit  all the spectra selected by the BBlocks method and the best model  parameters are obtained by adopting a fully Bayesian approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' For  a detailed Bayesian spectral analysis and the reduction procedure  applied to a GRB spectrum, we refer to Li (2019a,b, 2020);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  (2021);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Li & Zhang (2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='2 Using the Yonetoku correlation to infer their redshift values  In order to study the intrinsic properties in the cosmological rest  frame, a redshift measurement for each burst is needed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Unfortu-  nately, we currently have 3 bursts (GRB 100826A, GRB 110301A,  and GRB 160802A) without known redshift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Several works to in-  fer redshifts using empirical relations of GRB have been reported in  the literature(Amati et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2002;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Yonetoku et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' For example,  (Yonetoku et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2004) discovered a new and much tighter relation-  ship between the spectral peak energy (Ep) and the peak luminos-  ity (Lp) using the combined data detected by the BeppoSAX and  BATSE satellites, and claimed that one can use the Ep-Lp relation to  estimating redshift without knowing distances in the BSTASE cata-  log.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' We, therefore, attempt applying the Yonetoku relation(Yonetoku  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2004) to estimate redshift values for these bursts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  Our procedure to estimate the pseudo-redshift using the Yonetoku  relation includes the following steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  First, we perform a spectral fit to the peak spectrum (the brightest  time bin was selected by using the Bayesian blocks method(Scargle  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2013) at the highest statistical significance S) of each burst.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  The peak flux Fγ and peak energy Ep on the observer’s frame from  the spectral fits are thus obtained, where Fγ is the observed peak flux  integrated between (1-104) keV in units or erg cm−2 s−1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  Second, in order to use the Ep,z-Lp,iso relation, a bolometric lu-  minosity in a common cosmological rest-frame energy band (1-104  keV) is needed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' It can be obtained by using the spectral parameters to  conduct a k-correction extrapolating the observed energy band to 1-  104 keV.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' For a given burst, the k-correction factor (kc) can be derived  using the following procedure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The observed flux Fobs (erg cm−2 s−1),  in a fixed detector energy bandwidth [e1, e2] (for instance, for the  Fermi-GBM observation, e1=8 keV, e2=40 MeV), can be written as:  Fobs  [e1,e2] =  � e2  e1  EN(E)dE,  (1)  MNRAS 000, 1–?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (2023)  Time-averaging Polarimetric and Spectral Properties of GRBs  5  where E is in units of keV, and N(E) is a GRB photon number spec-  trum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The total luminosity emitted in the bandwidth [e1,e2], defined  in the cosmological rest-frame, is given by:  L[e1(1+z),e2(1+z)] = 4ˆπD2  L(z)Fobs  [e1,e2],  (2)  which DL(z) is the luminosity distance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' To express the luminosity  L in the cosmological rest-frame energy band, [E1=1 keV, E2 =104  keV], common to all sources, the Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (2) can be rewritten as:  L[E1,E2] = 4ˆπD2  LFobs  � E1  1+z , E2  1+z  � = 4πD2  Lk[e1,e2,E1,E2,z]Fobs  [e1,e2],  (3)  where the k-correction factor, kc, is therefore defined as:  kc = k[e1,e2,E1,E2,z] =  Fobs  � E1  1+z ;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' E2  1+z  �  Fobs  [e1,e2]  =  � E2/(1+z)  E1/(1+z) EN(E)dE  � e2  e1 EN(E)dE  ,  (4)  Last, with the k-correction factors known, the peak luminosity can be  derived from the observed γ-ray flux Fγ according to L = 4ˆπd2  LFγkc,  where dL is the luminosity distance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  Finally, as long as the prompt emission spectral properties can be  obtained, the Yonetoku relation can be used to infer redshift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' With  the above Steps, one can use Equation (2) in Yonetoku et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (2004)  to estimate their redshift values,  Lp  1052ergs−1 = (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='34+2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='29  −1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='76)×105  �Ep(1+z)  1keV  �2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='0±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='2  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  (5)  Table 2 lists the spectral properties obtained from the peak spec-  tral analysis and the estimated redshift values inferred from the Yo-  netoku relation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  4 RESULTS  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='1 Spectral Properties and their inferred jet properties  Five bursts were claimed to have a high-significance polarization  detection (Table 1) and GBM data (Table 4) taken at their prompt  emission, thereby providing an “ideal” sample to study the possi-  ble connection between jet properties and polarization straightfor-  wardly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  In practice, either time-integrated or time-resolved spectral analy-  sis is frequently used to diagnose their jet properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Several meth-  ods have been widely used to diagnose the jet properties based on  their spectral analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The simplest method is to use the low-energy  spectrum (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=', Preece et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 1998) to resolve the jet properties for  a given pulse/burst (Method-I).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' In this method, a single empirical  model (such as the Band model) based on a time-resolved tech-  nique is typically used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The KED jets, therefore, can be defined  as all α indices, within uncertainties, in a given burst, obtained  from time-resolved spectral analysis, are systematically above the  synchrotron limit throughout the entire burst/pulse duration, being  consistent with a matter-dominated fireball jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The PFD jets, on  the other hand, are consistent with the scenario that all α indices,  within uncertainties, in a given burst are below the synchrotron limit  throughout the burst/pulse duration, this suggests a Poynting-flux-  dominated jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The HD jets represent the moderate scenario, and  can be presented that some α indices, obtained from time-resolved  spectral analysis, are above the synchrotron limit (α >2/3) while  some others are below the synchrotron limit (α <2/3) throughout  the burst/pulse duration.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The HD jets can be further divided into two  subcategories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (1) the peak-KED pattern since the thermal emission  component (the spectra that violate the LOD line) is only detected  around the peak of the pulse (thermal component dominates the peak  of a pulse/burst);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' and (2) the KED-to-PFD (thermal to non-thermal  component) transition pattern (Li 2019a), since the thermal emission  component is detected at the beginning of the burst, and followed by  non-thermal emission component.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' However, it may be difficult to  classify jets as either KED or PFD jets based on the spectral index  alone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' In contrast to an optically-thin synchrotron emission, a photo-  spheric quasi-thermal component would, in fact, have a harder low-  energy spectral index, but this does not guarantee that the jet is KED  (Gill et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Therefore, a more reliable approach is to find the  best model (Method-II) by comparing various frequently-used spec-  tral models using certain statistical information criteria, such as the  Akaike Information Criteria (AIC;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Akaike 1974), Bayesian Infor-  mation Criteria (BIC;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Schwarz 1978), and the Deviance Information  Criterion (DIC;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Spiegelhalter et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2002;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Moreno et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Af-  ter the identification of the best spectral model, one can assess the jet  properties using the spectral properties inferred from the best model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  Moreover, we may also directly fit the spectral data with a physical  model (such as the synchrotron emission model, Burgess et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2020;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  Method-III), so as to diagnose the jet properties and any potential  connection with their polarization properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Our analysis in this  task incorporates both Method-I and Method-II (primary method).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  Method III will be used elsewhere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  We first perform time-integrated spectral analysis (treating the  entire epoch of polarization observation as one time bin) by using  various GRB spectral models, including power-law (PL), blackbody  (BB), cutoff power law (CPL), Band function, PL+BB, CPL+BB,  and Band+BB, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' We adopted both AIC and BIC to eval-  uate different spectral models and select the preferred one, and the  preferred model is the one that provides the lowest AIC and BIC  scores.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' As such, we define  PFD jets: a single non-thermal (Band-like) spectral compo-  nent was found in the time-integrated spectral analysis, like GRB  080916C (Abdo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  KED jets: a dominate thermal (BB-like) spectral compo-  nent was found in the time-integrated spectral analysis, like GRB  090902B (Ryde et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2010) and GRB 220426A (Deng et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2022).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  HD jets: a hybrid spectrum of thermal (BB-like) and non-  thermal (Band-like) components was observed in the time-integrated  spectral analysis in a single burst, like GRB 110721A (Axelsson  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2012), and GRB 140206A (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=', Li 2019a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  Our refined time-integrated spectral analysis suggests that the  Band+BB model can best characterize the spectral shape of all the  five bursts (see Table 3).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The global properties of our sample used in  the spectral analysis are reported in Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' These include the GRB  name (column 1), observed duration T90 of burst4 (column 2), 10-  1000 KeV fluence (column 3), together with the used detectors (col-  umn 4), the selected source (column 5) and background (column 6)  intervals, and the best model (column 7).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The best-fit spectral param-  eters of the sample with the Band+BB model are reported in Table 5,  including GRB name (column 1), source duration (column 2), and  corresponding significance (column 3), and Band component nor-  malization K (column 4), low-energy power-law index α (column  5), peak energy Ep (column 6) of the νFν spectrum, and high-energy  power-law index β (column 7);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' and BB component normalization K  (column 8), and temperature kT (column 9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  We next perform time-resolved spectral analysis (treating the  entire epoch of polarization observation as divided into multiple-  4 The time interval during which 90% of the total observed counts have been  detected.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  MNRAS 000, 1–?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (2023)  6  Li & Shakeri  time events) for each individual BBlocks time bin using the Band  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Temporal evolution of α is presented in Figures 2-6 for GRB  110826A, GRB 110301A, GRB110721A, GRB 140206A, and GRB  160802A, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' With the BBlock time bins selected and the  corresponding significance (S) values calculated, the data points are  shown in different S ranges5: S < 10, 10 ≤ S ≤ 20, and S > 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  For a subset of GRBs, a mixture of thermal (blackbody contribution  from the photosphere emission) and non-thermal (synchrotron emis-  sion from relativistic electrons) components was observed in a sin-  gle burst (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=', Li 2019a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Previous studies (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=', Burgess et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2014)  showed that the characteristic energy (Ep) of non-thermal emission is  correlated to the characteristic energy (kT) of thermal emission with  a power-law relation in form of Ep ∝ T q, where q ranges from ∼1-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  Burgess et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (2014) studied a set of bright Fermi single-pulse GRBs  and claimed that one can use this correlation to identify whether the  jet is dominated by kinetic (q ∼ 1) or magnetic energy (q ∼ 2) de-  pending on the value of the exponent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' GRB 110721A was identified  as the baryonic jet type in Burgess et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (2014) with q = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='24±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='11,  which is also consistent with our finding in the current analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  Our time-integrated spectral analysis indicates that all five bursts  belong to the HD jet type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' This finding is quite interesting since only  a subset of GRBs (a fairly low percentage) have an observed ther-  mal component in their spectral analysis, as suggested by several  statistical studies (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=', Li 2022a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Recently, (Li 2022a) has made a  great effort to collect a complete GRB sample in which all bursts  were detected by Fermi/GBM with known redshift, and created a  spectral parameter catalog based on their model-wise properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' He  discovered that ∼ 5% (7/153) of the analyzed bursts were found to  require a subdominant thermal component in their time-integrated  spectral analysis, including GRB 110721A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Our results imply that  high-degree polarization measurements may also be associated with  a thermal component originating from photosphere emission.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Our  time-resolved spectral analysis, on the other hand, further suggests  that two bursts exhibit the peak-KED pattern (GRB 110721A and  GRB 160802A) while the other three bursts (GRB 110301A, GRB  140206A, and GRB 160625B) display the KED-to-PFD transition  pattern across the entire burst durations since all α indices are  above the synchrotron limit early on (α >2/3), and then drop be-  low the synchrotron limit later on (α <2/3), indicating a thermal-  to-nonthermal transition signature.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Interestingly,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' after carrying out  a detailed time-resolved spectral analysis for a sample of the multi-  pulsed bursts,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Li (2019a) reported that the jet properties for a good  fraction of the multi-pulsed bursts exhibit a transition from thermal  to non-thermal component among pulses within a single burst,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' and  claimed that such “transition" jet properties are clearly observed in  four bursts (GRB 140206B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' GRB 140329B,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' GRB 150330A,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' and  GRB 160625B),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' and the polarization properties in those transition  bursts would also differ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='2 The Observed Parameter Correlations: Polarization  Degrees versus Other Relevant Quantities  The most interesting result that draws our attention is that all five  bursts in our target sample have a relatively high-degree polarization  measurement and are associated with the “HD” jet properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' In  the following discussion, we, therefore, pay special attention to this  interesting observation and its theoretical interpretation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  5 Note that the results obtained for those lower-S spectra may not be robust,  since the spectral fits would not be well determined due to lack of enough  photons.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  Much evidence points towards the fact that correlation analysis  plays a crucial role in the understanding of GRB physics as it pro-  vides a crucial clue to revealing its nature (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=', Amati et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2002;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  Yonetoku et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2004;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Liang & Zhang 2005;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Dainotti et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  Xu & Huang 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Zhang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Liang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Dain-  otti & Amati 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Li 2022a,  and references therein).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Here, an  attempt has been made to explore the correlations between the po-  larization properties and several typical GRB observed quantities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  For instance, the polarization degrees π correlated with (i) the cos-  mological rest-frame peak energy (Ep,z) of the νFν prompt emission  spectrum, (ii) the isotropic-bolometric-equivalent emission energy  Eγ,iso, (iii) the magnetization parameter σ0, (iv) the blackbody tem-  perature kT, (v) the redshift z, and (vi) the corresponding energy  fluence Sγ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Using the same observed epoch during the prompt emis-  sion phase, our target sample allows for a reasonable comparison.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  Our analysis includes the following steps.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (1) For a given burst in our  target sample, we first select the same time interval for the prompt  emission data as for the polarization measurement.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (2) We then at-  tempt to perform a spectral fit to the selected prompt emission data  using PL, BB, CPL, Band, PL+BB, CPL+BB, and Band+BB func-  tions, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The Band+BB model has an AIC/BIC-statistic  improvement of at least 10 with respect to the Band-alone and other  models for these bursts, which suggests Band+BB as the preferred  model that would fit the data and a thermal component existing in  the spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Since the thermal flux ratio (FBB/Ftot) for these bursts  is less than 50% (see Table 5), the thermal components thus are sub-  dominant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Interestingly, Chattopadhyay et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (2019) analyzed the  prompt emission and polarization data of 11 bright bursts detected  during the first year of operation of CZTI, and reported that of these  bursts, four bursts (GRB 160106A, GRB 160509A, GRB 160802A,  and GRB 160910A) in their spectral analysis showed a deviation  from the Band model and an additional thermal blackbody is needed  in order to model their spectrum more precisely.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (3) With the spec-  tral analysis done in Step (2), we are able to obtain the spectral peak  energy (Ep,z) and the blackbody temperature (kT).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Eγ,iso can also be  calculated in the cosmological frame with a redshift known (GRB  110721A and GRB 140206B), and with a k-correction applied by  integrating the observed energy spectrum over 1 KeV/(1+z) to 10  MeV/(1+z).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' We note here that for the remaining three bursts (GRB  100826A, GRB 110301A, and GRB 160802A) with an unknown  redshift, we use the Yonetoku relation (Yonetoku et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2004) to es-  timate their redshift values (see Section 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Using these hybrid-  spectrum observed properties and following the method described  in Gao & Zhang (2015) and Li (2020), we also calculate the mag-  netization parameter σ0 for these bursts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Finally, with these Steps  completed, we therefore present π-Ep,z (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='7a), π-Eγ,iso (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='7b),  π-kTz (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='7c), π-σ0 (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='7d), π-z (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='7e), and π-Sγ (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='7f) plots  in Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Interestingly, these scatter plots all seem to exhibit a  monotonic power-law decay in their log-log space (except for the  π-σ0 correlation), with a similar decay slope ranging from -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='40 to  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Our results indicate that a higher Ep,z, Eγ,iso, and kTz tend to  have a lower-degree polarization π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' However, we should note that  the sample size is too small to be reliable enough to support the de-  rived conclusion, so the results may not be statistically significant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  5 PHYSICAL IMPLICATION  There are several parameters to impact on the degree of polariza-  tion in GRBs including the geometry of the jet, its angular struc-  ture, the bulk Lorentz factor of outflow material, the magnetic field  configuration and observer’s point of view.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Here, we consider an  MNRAS 000, 1–?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (2023)  Time-averaging Polarimetric and Spectral Properties of GRBs  7  ultra-relativistic axi-symmetric jet which lunched by a central en-  gine weather a black hole or an rapidly rotating magnetar (e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='g.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=', Usov  1992;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Thompson 1994;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Dai & Lu 1998;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Wheeler et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2000;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Zhang  & Mészáros 2001;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2007;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Metzger et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Lei et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Metzger et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2011;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Bucciantini et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2012;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Lü & Zhang  2014;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Li et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' During the prompt emission, we have ultra-  relativistic jet with bulk lorentz factor Γ ≫ 1 leading to strong beam-  ing effect of GRB outflow materials where the Doppler factor can be  approximated as  δD ≈  2Γ  1+(Γ ˜θ)2 ,  (6)  Due to the relativistic beaming effect of GRB jets, the measured ra-  diation energy of the bursts is smaller than its isotropic energy as  Eγ = fbEγ,iso by a factor fb = ∆Ω/4π = (1 − cosθ j) ≈ θ2  j/2 where  θ j is the half opening angle of the ejecta.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' In principle, different  GRBs can be viewed from different observing angles θobs with re-  spect to the jet’s central axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Only those observers whose line-of-  sight (LOS) intersects the surface of the jet can detect the GRBs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' In  the ultra-relativistic regime, the observed emission mainly receives  from a region that is limited to a cone with angular size ˜θ ≲ 1/Γ  around LOS.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' At the early time prompt emission when the LOS in-  tersects the jet surface, if θobs/θ j ≲ 1−(Γθ j)−1 and Γθ j ≳ O(10), the  jet’s edge remains invisible to the observer Gill et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  In this case, the emission region can be approximated as an ex-  panding thin spherical shell of width ∆ ≪ R/Γ2 (in the lab frame)  in which particles cool relatively fast compared to the dynamical  time scale of the system.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' As the GRB jet has slowed down signifi-  cantly when the opening angle θ j ≃ Γ−1 then the jet break happens  and the edge effects become important.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The flux density measured  by a distant observer from each fluid element in an infinite thin-shell  approximation for the prompt emission is given by (Granot 2005)  Fν(t) =  (1+z)  16π2d2  L(z)  �  δ3  DL′  ν′(r)d ˜Ω,  (7)  where dL(z) is the luminosity distance of the source, and d ˜Ω =  d ˜φd(cos ˜θ) is the solid angle with ˜θ and ˜φ as the polar angle and  the azimuthal angle measured from the LOS, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The co-  moving spectral luminosity L′  ν′(r) for the synchrotron emission is  L′  ν′(r) = L′  ν′(R)  �  1−(ˆn′ · ˆB′)2� 1+α  2 ,  (8)  where α = −dlog(Fν)/dlog(ν) is the spectral index, ˆn is the ob-  server’s LOS in the comoving frame of the GRB jet and ˆB is the  local direction of the magnetic field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The spectral luminosity L′  ν′(R)  in the comoving frame of the fluid in terms of frequency ν′ and the  peak frequency ν′  p at which the most of the power is emitted is given  by  L′  ν′(R) = L′  ν′p  � ν′  ν′p  �−α  ,  (9)  here we consider a constant luminosity with a radius which the peak  value L′  ν′p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' We assume to have synchrotron emission from accelerat-  ing electrons in the magnetig ���eld with isotropic velocity distribu-  tion and the energy distribution as a power law ne ∝ γ−p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  In our scenario, we assume that each pulse originates from a sin-  gle thin shell and Γ can in principle change for different pulses.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The  state of polarization of a radiation field can be expressed in terms of  the Stokes parameters I (intensity), Q and U (linear polarizations), V  (circular polarization).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' In spite of linear polization, only a few mech-  anisms can generate the high value of circular polarization in the  usual scattering processes in GRBs, and the measured circular polar-  ization has only been reported once in a GRB afterglow Wiersema  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Therefore we will not consider circular polarization  in this paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Stokes parameters Q and U are differences in flux for  two orthogonal directions on the sky which are coordinate dependent  quantities (Rybicki & Lightman 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Westfold 1959), we define the  local degree of linear polarization Π =  �  Q2 +U2/I where  U  I = Πsin2θp ,  Q  I = Πcos2θp ,  θp = 1  2 arctan  �U  Q  �  , (10)  and θp is the polarization position angle (PA).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The direction of the  polarization vector in the synchrotron emission is orthogonal to the  LOS of the observer ˆn and the local direction of the magnetic field  ˆB in the jet,  ˆΠ = (ˆn× ˆB)  |ˆn× ˆB)|  ,  (11)  The polarization measurements can help in order to probe the  magnetic field structure inside the shock wave.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Moreover, the de-  gree of the polarization depends on the GRB jet’s angular structure  and the observer’s viewing angle from jet symmetry axis (Lazzati  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2004).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The magnetic field structure in KED and PFD flows  has a different origin and can be classified into three categories (Gill  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Gill et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2021): (i) a locally ordered magnetic field  (Bord) with angular coherent length θ j > θB ≳ 1/Γ, (ii) a toroidal  magnetic field (Btrod) which has an ordered axisymmetric configura-  tion in the transverse direction with respect to the jet (iii) a tangent  magnetic field which could be in principle parallel (B∥) or perpen-  dicular (B⊥) to the local fluid velocity.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' In the PFD the magnetic field  is dynamically dominated and usually has a large coherence length  such as Btrod which can be produced by a rotating central engine or  in a high magnetized flow, other locally and globally ordered field  configuration are also possible in this case.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' On the other hand in  KED we may have a tangled magnetic field structure with B⊥ or/and  B∥ components, however generating such an anisotropic field con-  figurations in shock waves seems to be challenging (Gill & Granot  2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' A globally ordered magnetic field may naturally be advected  from near the central source, while the random magnetic fields gen-  erated in the shock dissipation region (Kumar & Zhang 2015;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Geng  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Gill et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2018;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Fan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2008).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The magnetic field  structures that are generated at relativistic collision-less shocks, due  to the two-stream instabilities, are expected to be tangled within the  shock plane (Medvedev & Loeb 1999).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  The degree of linear polarization generated in the synchrotron  emission from an isotropic electron distribution with power-law en-  ergy spectrum, and for a given direction of magnetic field is given  by (Rybicki & Lightman 2008;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Westfold 1959)  Πlin  max =  α+1  α+5/3 =  peff +1  peff +7/3,  (12)  where peff = 2α + 1 is the effective power-law index of the electron  distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  peff =  �  �  �  2,  νc < ν < νm,  slow cooling  p,  νm < ν < νc,  fast cooling  p+1,  ν > max(νc,νm),  either fast or slow cooling  (13)  and, therefore  Πlin  max =  �  �  �  �  �  9/13,  νc < ν < νm,  fast cooling  (p+1)  (p+7/3),  νm < ν < νc,  slow cooling  (p+2)  (p+10/3),  ν > max(νc,νm),either fast or slow cooling  (14)  MNRAS 000, 1–?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (2023)  8  Li & Shakeri  This polarization may originate from a very small region (point-  like emitter) in which the magnetic field has a specific orientation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  Only in the case of ordered magnetic field with the coherence length  comparable or larger than the visible surface of the emitting region,  the highest value of the polarization Πlin  max in Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (19) can be gen-  erated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The photon index in the Synchrotron radiation is limited to  −1/3 ⩽ α ≲ 3/2 which regarding Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (19) leads to the maximum  degree of polarization 50% ≲ Π ≲ 75%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' In the left panel of Fig-  ure (8), we see predicted polarization values using this theoretical  model with observed data using our target sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Here α indices  are obtained using the spectral analysis defined in §4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' We find that  the observed data are well distributed along the line predicted by this  model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  In general, the measured polarization is obtained by integrating  the local stokes parameters over the flux of the GRB jet as  Π(tf ) =  ¯  Q(tf )  I(t f ) =  �  dFν cos2θp  �  dFν  ,  (15)  assuming to have an axisymmetric flow and taking into account sym-  metry consideration, we see that ¯U = 0 and consequently the instan-  taneous total degree of the linear polarization is ¯Π = | ¯Q|/I.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' We per-  form an integration over the equal time surface (EATS) for a single  pulse  �  ¯  Q(t)dt/  �  I(t)dt in order to obtain pulse integrated polariza-  tion of the prompt emission which leads to  Πord  Πmax =  � ymax  0  dy(1+y)−2−α �  dφΛ(y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='φ)cos2θp  � ymax  0  dy(1+y)−2−α �  dφΛ(y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='φ)  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  (16)  The above formula is valid for the prompt emission from an ultra-  relativistic thin-shell for an on-axis observer (θobs = 0) where ymax =  (Γθmax)2 and θmax defined as the maximum angle from LOS Granot  (2003a).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The factor Λ(y,φ) is an average over the magnetic field  orientations in the plane of the ejecta as  Λ(y,φ) ≡ ⟨(1−(ˆn′ · ˆB′)2)  1+α  2 ⟩ ,  (17)  The polarization angle θp and Λ(y,φ) take different forms regarding  the configuration of the magnetic field in the plane the GRB jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' In  the case of an ordered magnetic field Bord we have :  Λord(y,φ) ≈  �  (1−y  1+y)2 cos2 φ+sin2 φ  � 1+α  2  ,  (18)  θp = φ+arctan  �  (1−y  1+y)cotφ  �  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  (19)  The time-integrated linear polarization in the presence of an ordered  magnetic field in the plane normal to the jet velocity is plotted as  a function of the spectral index in the right panel of Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (8).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' As it  is seen the polarization degree increases towards higher values of α  and lower values of ymax which can cover the observed polarization  of GRB 110721A, GRB 160802A, and GRB 110301A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Therefore  for a configuration with the globally ordered magnetic field, high  values of linear polarization even larger than 50% are obtainable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  The degree of polarization for a magnetic field with locally tan-  gled or random configuration is obtained by averaging over all direc-  tions of the local magnetic field within the plane of the shock (Granot  & Königl 2003a;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Sari 1999;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Gruzinov 1999;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Nava et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The  presence of a random magnetic field leads to negligible values of net  linear polarization measured by an on-axis observer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' In the case of a  random field behind the shock wave only if the observer is off-axis  and the circular symmetry is broken, non-zero net polarization is  measurable.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The total linear polarization arising from the whole jet  which is subjected to a random field with a direction perpendicular  to the jet velocity is given by Granot (2003a)  Π⊥  Πmax =  � y2  y1 dy(1+y)−2−α sin[2Ψ1(y)]G(y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='α)  Θ(1−ζ)  � y1  0  dy H(y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='α)  (1+y)α+2 +  � y2  y1 dy dy H(y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='α)  (1+y)α+2  � π−Ψ(y)  π  �,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  (20)  where Θ(1 − ζ) is the Heaviside step-function with ζ ≡ θobs/θ j as a  parameter to define observer’s point of view,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' and  G(y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='α) = 1  2π  � π  0  dφ  �(1−y)2  (1+y)2 cos2 φ−sin2 φ  ��  1− 4ycos2 φ  (1+y)2  � α−1  2  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (21)  H(y,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='α) =  � π  0  dφ  �  1− 4ycos2 φ  (1+y)2  � 1+α  2  ,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  (22)  cosΨ(y) = (1−ζ2)y j −y  2ζ√yy j  .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  (23)  In above expressions y1,2 = (1∓ζ)2yj and y j = (Γθ j)2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The variation  of the linear polarization in the presence of a random field configura-  tion measured by an off-axis observer is displayed in Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (9).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' In the  left panel, the spectral indices are selected to be consistent with aver-  age values reported in Table (5) for our target sample and for y j = 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  In the right panel, yj is changed while α = 1, it is found that the ap-  peared peak has a width in order of 1/√y j.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' From Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (9), we see that  the polarization degree is limited to small values for ζ < 1 while it  is sharply increased for ζ ≈ 1 and finally reaches to an asymptotic  limit at ζ > O(1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' It is seen that the Synchrotron radiation with B⊥  can potentially generate wide range of polarization values from low  levels to moderate values which cover observed values associated to  our sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' In principle, various viewing angles θobs and different  angular structures of the jet affect the measured fluence of GRBs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  Note that the fluence significantly decreases for a top-hat jet view-  ing from outside the jet’s sharp edge, so high levels of polarization  in off-axis jets may only be obtainable in very close bursts.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' In fact,  the detectibility of GRB polarization needs high-fluence sources and  usually, the fluence rapidly drops below the detector threshold for a  large off-axis observer.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  The time-resolved spectral analysis in §4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='1 showed thermal to  non-thermal (KED-to-PFD) transitions in our sample where a sub-  dominant component of the thermal emission during bursts is ob-  served.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Observing hard values of the spectral indices during the  bursts can be served as hints that LOS is not highly off-axis, since  high latitude emission leads to a softer spectrum Lundman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  (2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  As it was reported in §4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='2, a correlation between the polariza-  tion and the isotropic energy π-Eγ,iso (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='7b) has been observed  within our sample, it is worth mentioning that higher polariza-  tion values are recorded for closer bursts GRB 110301A (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='36),  GRB 110721A (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='382), GRB 160802A (z=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='90) and lower val-  ues for farther sources GRB 140206B (z=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='73) and GRB 100826A  (z=2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='3) (Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='7e).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The observed fluences of GRB 140206B and GRB  100826A is higher than other sources (see Table.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 4 and Fig.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='7f) and  due to their higher redshifts ζ can not obtain large values, however,  low values of ζ would be enough to reproduce their measured polar-  izations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  The local degree of linear polarization for a tangled or random  field configuration for a thin ultrarelativistic shell modeling of the  prompt emission by assuming α = 1 is obtained by averaging over  all local magnetic field directions as  Πlin  rnd = Πlin  max  (b−1)sin2 θB  2+(b−1)sin2 θB  (24)  MNRAS 000, 1–?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (2023)  Time-averaging Polarimetric and Spectral Properties of GRBs  9  where b ≡ 2⟨B2  ∥⟩/⟨B2  ⊥⟩ denotes the anisotropy of the magnetic field  distribution as the ratio of the parallel B∥ to the perpendicular B⊥  components with respects to the shock direction, and θB is the an-  gle between the LOS from the observer and the direction of the  shock Sari (1999);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Gruzinov (1999).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' In the case of a globally ordered  magnetic field configuration aligned with the jet direction (B → B∥,  b → ∞), Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (24) returns back to Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (19) and gives the maximum  value of the linear polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  The polarized emission may also originate from independent  magnetic patches with various field orientation Li (2022a) where  magnetic patches are locally coherent but distributed randomly in  observed emission region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' In this case the measured polarization  from different patches is estimated as Π = Πmax/  √  N, where N is the  number of magnetic patches or equivalently multiple pulses where  the coherence length of the magnetic field is as large as the emis-  sion region in a single pulse and observed polarization is an average  over multiple pulses (Gruzinov & Waxman 1999;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Granot & Königl  2003b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  The magnetic field which is generated within IS for KED jets has  usually a coherence length much smaller than the angular size of the  emission region which causes negligible net polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' It has been  shown that even by taking into account the angular structure of the  flow the polarization is limited to Π ≲ 20% for photospheric emis-  sion of a relativistically expanding fireball Ito et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (2014);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Lund-  man et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (2014a);' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Parsotan et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The observed high val-  ues of the polarization for GRB 110721A and GRB 160802A while  they show the peak-KED pattern cannot be explained simply by the  sub-photospheric dissipation model based on Comptonisation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Be-  cause the multiple scatterings at large optical depths region leads to  wash out the directionality of polarization vectors (Lundman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  2018b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' To explain the strong polarized signals, models invoking dis-  sipation of ordered magnetic field are favored (Lyutikov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2003;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  Zhang & Yan 2011b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' McKinney & Uzdensky 2012).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' A structured jet  photosphere model may also generate polarized photons via Comp-  ton scattering but with a different energy-dependence compare to  the synchrotron model in the ordered magnetic field (Chang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  2014b,a, 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  The Jitter radiation emitted by ultra-relativistic electrons acceler-  ating in a small-scale random magnetic field (Medvedev 2000), can  also generate a hard energy spectrum with the photon index as high  as α = +0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Due to the random distribution of the magnetic field,  jitter radiation is highly symmetric in the electron radiative plane,  leading to the vanishing polarization degree for an on-axis observer  (Mao & Wang 2013, 2017;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Mao et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The maximum level  of polarization is obtainable when the emitting plane is viewed from  the edge on, it can even reach up to 90% (Prosekin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  However, for smaller off-axis viewing angles which can yield mea-  surable fluences, jitter radiation causes almost negligible polariza-  tion degree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Meanwhile, regardless of the viewing angle the Jitter  radiation cannot produce the observed high degree of polarisation  close to the spectral peak energy of the jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  To summarize, polarization features can be explained either by the  synchrotron radiation in the ordered/random magnetic field (Granot  2003b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Granot & Königl 2003b;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Nakar et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2003), the jet structure  (Lazzati & Begelman 2009), or the observer’s viewing angle with re-  spect to the jet (Lazzati et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2004), even in the case of thermal radi-  ation from the jet photosphere (Lundman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2014b).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' For a hybrid  spectrum which include thermal and non-thermal components, we  expect to see relatively high values of the polarization in the prompt  emission which can be produced by synchrotron emission mecha-  nism in the ordered magnetic field of the jet, and for random field  configurations only for off-axis observers (Gill et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' How-  ever, the spectral properties of our target sample demonstrated that  off-axis observations specially for the large viewing angle is not the  case, and the observed values of the polarization most probably is  a hint of the ordered magnetic field originating from the central en-  gine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Since from PFD jets towards HD and KED jets, polarization  washout effects are increased gradually due to thermal photons, we  would expect that the inequality πKED ≲ πHD ≲ πPED is satisfied if  other conditions are fixed for a given jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Due to the different de-  grees of polarization predicted by different emission models in var-  ious energy bands, it is essential to have a high-sensitivity gamma-  ray polarimeter with a wide band-pass to detect energy-dependent  polarization signals and constrain different models (Zhang 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  However, it should be noted that due to several free parameters in  polarization models, upcoming more precise observations and theo-  retical investigations are needed to discriminate between competing  models in order to explain observed joint polarization and spectral  properties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  6 CONCLUSION  Early polarization observations during the prompt emission phase  play a crucial role in understanding the radiation mechanism and  jet composition of GRBs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Observations over the past few decades  suggest that the jet composition of GRBs may have diverse prop-  erties.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' If the jet composition is matter-dominated (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=', a fireball),  the GRB prompt emission spectra would include a bright thermal  component originating from the fireball photosphere.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Alternatively,  if the jet composition is Poynting-flux-dominated, the GRB prompt  emission spectra would include a dominant non-thermal compo-  nent originating from the synchrotron radiation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Moreover, if the jet  composition is hybrid-dominated, the GRB prompt emission spec-  tra would include a thermal component originating from the fire-  ball photosphere and a non-thermal component originating from the  synchrotron radiation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' It is highly speculated that the prompt emis-  sion is likely expected to be strongly polarized owing to its non-  thermal origin.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Consequently, a different level of polarization de-  grees (πKED ≲ πHD ≲ πPED) during the prompt emission phase is nat-  urally expected due to the different types of jet composition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' In this  paper, we have collected a GRB sample in which all the bursts de-  tected by Fermi/GBM and whose polarization detection in the emis-  sion region was also reported in the literature, containing five inter-  esting bursts (GRB 100826A, GRB 110301A, GRB 110721A, GRB  140206A, and GRB 160802A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Using the time-averaging polariza-  tion observations and selecting the same epoch for the GBM data  taken during the prompt emission phase, we then attempted to ex-  plore the correlations between jet properties and polarization prop-  erties of GRBs and aimed to confirm the validity of this correlation  (πKED ≲ πHD ≲ πPED) from observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  We first performed a detailed time-averaged spectral analysis for  each burst in our target sample by using several frequency-used GRB  spectral models and selected the best one by using information crite-  ria (AIC and BIC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The jet properties of GRBs can be classified into  three categories based on their spectral analysis: the “KED”, “PFD”,  and “HD” types.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Using the spectral properties we then inferred their  jet properties and discovered that all five bursts belong to the “HD”-  jet type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The lack of the other two types of jets (KED and PED)  prevents us from validating this correlation (πKED ≲ πHD ≲ πPED).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  Hopefully, upcoming instruments will provide high-sensitivity po-  larization observations in the future, leading to well-sampled, well-  studied data sets, enabling such statistical analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  We next conducted a time-resolved spectral analysis for each in-  MNRAS 000, 1–?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (2023)  10  Li & Shakeri  dividual burst by dividing the emission period into multiple-time  slices using the BBlocks method using the Band-alone model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Our  refined time-resolved spectral analysis, on the other hand, further  suggested that the “HD”-type has two subcategories: the peak-KED  pattern and the KED-to-PFD transition pattern.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' In our attempt to as-  sess the jet properties of GRBs using Band-α evolution, we discov-  ered that two bursts exhibit the peak-KED pattern (GRB 110721A  and GRB 160802A) whereas the other three bursts show the KED-  to-PFD transition pattern (GRB 110301A, GRB 140206A, and GRB  160625B).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' All five bursts found in the “HD”-type imply that the pho-  tosphere emission may also be a possible mechanism to power the  high-degree polarization observation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  We also made an attempt to explore the correlations between the  polarization properties and several typical GRB observed quantities.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  Using the same observed epoch during the prompt emission phase,  our target sample allows for a reasonable comparison.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The corre-  lations we attempted to study included the polarization degrees π  correlated with (i) the cosmological rest-frame peak energy (Ep,z)  of the νFν prompt emission spectrum, (ii) the isotropic-bolometric-  equivalent emission energy Eγ,iso, (iii) the magnetization parameter  σ0, (iv) the blackbody temperature kT, (v) the redshift z, and (vi) the  corresponding energy fluence Sγ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' As a result, we discovered that a  higher Ep,z, Eγ,iso, and kTz tend to have a lower-degree polarization  π.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  Lastly, we discovered that all five bursts in our target sample have  a relatively high-degree polarization detection that seems to corre-  late with the “HD”-jet type.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' If it is an intrinsic characteristic of  GRBs, this could provide a clue to studying the radiation mechanism  and jet composition of GRBs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' We have also discussed some physical  interpretations of this interesting phenomenon.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Since the configura-  tion of the magnetic field inside the jet is one of the crucial param-  eters to determine the polarization degree, we discussed two main  configurations (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' ordered and random fields), and their connec-  tion to the jet composition is clarified.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' We considered polarization  patterns as a function of different dynamical parameters associated  to the outflow materials, the spectral indices and the observer’s LOS  with respect to the jet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Combining the spectral analysis and the polar-  ization measurements allowed us to find out the detection of polar-  ization values Π > 50% during prompt emission of GRB 160802A,  GRB 110721A and GRB 110301A is a piece of strong evidence for  the synchrotron emission mechanism in the presence of an ordered  magnetic field which can be advected from the GRB central engine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  Regarding the different properties of our target sample, we conclude  that geometrical effects and large off-axis observations are unlikely  responsible for the measured polarizations assuming random mag-  netic fields within the jets.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  Finally, there are some caveats that are worth mentioning when  applying our analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (i) Spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' We have resolved the jet proper-  ties based on the low-energy spectrum.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' However, it may be difficult  to classify jets as either KED or PFD jets based on the spectral index  alone.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Indeed, a photospheric quasi-thermal component would have  a harder low-energy spectral index as compared to an optically-thin  synchrotron, but that does not guarantee that the jet is KED (an ex-  ample, see Gill et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (ii) Polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The degree of polariza-  tion ultimately probes the (local) structure of the B-field in the emis-  sion region.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' An ordered field would necessarily yield high polariza-  tion whereas a tangled field would yield a very small polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' It  is unclear, however, whether these field configurations are exclusive  to a given jet configuration (or a particular level of magnetization).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  In addition, the angular structure of the jet also plays an important  role in governing the observed polarization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Thus, due to the large  range of model parameters, it is difficult to attribute a given level of  polarization to a given jet composition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' More discussion is provided  in a recent review article (Gill et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (iii) Different instrument  analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Currently, it is not clear why different instruments, namely,  POLAR, IKAROS-GAP, and ASTROSAT/CZTI, are finding differ-  ent levels of polarization for a small sample of GRBs (Chattopad-  hyay et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' There is no consensus.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' POLAR is finding a rather  low-level polarization, which is consistent with zero within 3σ of  their quoted central values, whereas both IKAROS and AstroSAT  are finding much higher levels.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Hard X-ray to soft gamma-ray po-  larization measurements are very tricky and the analysis has to be  carried out very carefully.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' As such, some of these measurements are  probably not representative of GRBs and need to be further verified  by future more precise instruments.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (iv) Time-resolved polarization  analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' In the current analysis, none of the cases have shown time-  resolved polarization measurements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Even though the GRBs in our  target sample have time-resolved spectral indices, not having corre-  sponding polarization measurements makes it difficult to ascertain  the properties of the B-field and outflows.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  Acknowledgements.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' We thank Ramandeep Gill, Jonathan Gra-  not, Rahim Moradi, Mi-Xiang Lan, Asaf Pe’er, Jin-Jun Geng,  Christoffer Lundman, Remo Ruffini, and ICRANet members for  many discussions on GRBs physics and phenomena.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' This research  made use of the High Energy Astrophysics Science Archive Re-  search Center (HEASARC) Online Service at the NASA/Goddard  Space Flight Center (GSFC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  Data availability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The data underlying this article will be shared  on reasonable request to the corresponding author.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
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+page_content=' 2012, A&A , 538, A134  Yonetoku, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
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+page_content=' 2004, ApJ , 609, 935  Yonetoku, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
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+page_content=' 2011a, ApJ , 743, L30  —.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2011b, ApJ , 743, L30  —.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2012a, ApJ , 758, L1  —.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2012b, ApJ , 758, L1  Zhang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2014, International Journal of Modern Physics D, 23, 1430002  —.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2018, The Physics of Gamma-Ray Bursts, doi:10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='1017/9781139226530  Zhang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
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+page_content=' 2001, ApJ , 552, L35  Zhang, B.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=', & Yan, H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2011a, ApJ , 726, 90  —.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2011b, ApJ , 726, 90  Zhang, F.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
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+page_content=', Yan, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='-Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=', & Wei, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='-M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2012, ApJ , 750, 88  Zhang, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='-N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=', Kole, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=', Bao, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='-W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' 2019, Nature Astronomy,  arXiv:1901.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='04207  MNRAS 000, 1–?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (2023)  12  Li & Shakeri  Table 1 A sample of GRB polarimetric observations  GRB  PD  PA  Energy band  Time  Significance  Instrument  Ref.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  z  (Fermi ID)  (π%)  (◦)  (t-t0)  (σ)  (For polarization)  100826A(957)  27±11  159±18, 75±20  γ-ray  0-100s  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='9σ  IKAROS-GAP  Yonetoku et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (2011b)  NA  110301A(214)  70±22  73±11  γ-ray  0-7s  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='7σ  IKAROS-GAP  Yonetoku et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (2012a)  NA  110721A(200)  84+16  −28  160±11  γ-ray  0-11s  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='3σ  IKAROS-GAP  Yonetoku et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (2012a)  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='382  140206A(275)  > 28  80±15  γ-ray  4-26s  90% confidence  INTEGRAL-IBIS  Götz et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (2014)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='73  160802A(259)  85±29  ∼-32  hard X-rays  0-20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='34s  ∼3σ  AstroSat-CZTI  Chand et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (2018)  NA  MNRAS 000, 1–?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (2023)  Time-averaging Polarimetric and Spectral Properties of GRBs  13  Table 2 Estimated values of redshift using the Yonetoku relation  GRB  tstart∼tstop  S  Eobs  p  Fobs  p  kc  Lp  z  (s)  (keV)  (erg cm−2 s−1)  (erg s−1)  (Estimated)  100826957  18.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='208∼22.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='288  107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
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+page_content='10)×10−5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='85  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='27±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='10)×1053  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='3  110301214  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='876∼4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='126  107.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='60  126±6  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='36±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='16)×10−5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='02  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='46±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='17)×1053  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='36  160802259  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
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+page_content='171  73.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='79  385±39  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='04±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='80)×10−5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
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+page_content='90  MNRAS 000, 1–?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (2023)  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='14  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='Li & Shakeri  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='Table 3 Comparison of AIC/BIC between the best model and other models  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
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+page_content='t1 ∼ t2  ' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
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+page_content='0∼20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='34  6840/6847  7480/7487  3984/3994  3898/3912  4383/4397  3839/3856  3840/3861  MNRAS 000, 1–?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (2023)  Time-averaging Polarimetric and Spectral Properties of GRBs  15  Table 4 Global properties of the Sample  GRB  T90  Fluence  Detectors  ∆Tsrc  [∆T(bkg,1),∆T(bkg,2)]  Spectral model  (Fermi ID)  (s)  (erg cm−2)  (s)  (s)  (Preferred)  100826A(957)  84.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='993±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='724  (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='64±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='01)×10−4  n7(n8)b1  (0 to 100)  (-20 to -10, 200 to 250)  Band+BB  110301A(214)  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='693±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='362  (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
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+page_content='822±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
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+page_content='01)×10−4  n0(n1)n3b0  (4 to 26)  (-40 to -20, 70 to 90)  Band+BB  160802A(259)  16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
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+page_content='84±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='01)×10−5  (n2)b0  (0 to 20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='34)  (-20 to -10, 60 to 80)  Band+BB  MNRAS 000, 1–?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (2023)  16  Li & Shakeri  Table 5 Spectral Fit Results of the Sample with the Band+BB Model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  GRB  t1∼t2  S  K  α  Ep  β  K  kT  Flux  Flux ratio  (s)  (Band)  (Band)  (Band)  (Band)  (BB)  (BB)  (FBB/Ftot)  (s)  (ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
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+page_content='keV−1)  (keV)  (ph.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
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+page_content='keV−1)  (keV)  (erg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
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+page_content='s−1)  100826957  0∼82  102.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
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+page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (2023)  Time-averaging Polarimetric and Spectral Properties of GRBs  17  1  0  2  4  6  8  10  redshift  10  1  100  101  102  103  GRB 100826A  Estimated value  0  2  4  6  8  10  redshift  10  1  100  101  102  103  GRB 110301A  Estimated value  0  2  4  6  8  10  redshift  10  1  100  101  102  103  GRB 160802A  Estimated value  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Estimated redshift using the Yonetoku relation for three bursts (GRB 100826A, GRB 110301A, and GRB 160802A).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The yellow and cyan lines  represent the left and right function of Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (5), and their intersection point (purple color) is the estimated value of redshift.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  MNRAS 000, 1–?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (2023)  18  Li & Shakeri  1  20  0  20  40  60  80  100  120  140  Time (s)  0  20  40  60  80  100  =27±11%  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
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+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='5  (S > 20)  (10 < S < 20)  (S < 10)  100826A  101  102  103  104  105  Photon Energy - keV  100  101  102  103  104  keV × [keV  1S  1cm  2]  Band fits  Blackbody  Band+Blackbody  NAI7  NAI8  BGO1  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Left panel: prompt emission GBM light curve (overlaid in gray) and polarization observations in γ-ray/hard X-ray energy bands (cyan shaded area),  as well as the temporal evolution of α based on the time-resolved spectral analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The horizontal dashed line represents the limiting value of α = −2/3 for  electrons in the slow-cooling regime.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Right panel: the spectral data and its best-fit model (Band+BB) during the time epoch (see Table 1 and Table 4) of the  matching polarization observations.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  MNRAS 000, 1–?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (2023)  Time-averaging Polarimetric and Spectral Properties of GRBs  19  1  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
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+page_content='0  Time (s)  0  20  40  60  80  100  =70±22%  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
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+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='5  (S > 20)  (10 < S < 20)  (S < 10)  110301A  101  102  103  104  105  Photon Energy - keV  100  101  102  103  104  keV × [keV  1S  1cm  2]  Band fits  Blackbody  Band+Blackbody  NAI7  NAI8  NAIb  BGO1  nai  bgo  Figure 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Same as Figure 2 but for GRB 110301A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  MNRAS 000, 1–?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (2023)  20  Li & Shakeri  1  15  10  5  0  5  10  15  20  25  30  Time (s)  0  20  40  60  80  100  = (84+16  28)%  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='5  (S > 20)  (10 < S < 20)  (S < 10)  110721A  101  102  103  104  105  Photon Energy - keV  101  102  103  104  keV × [keV  1S  1cm  2]  Band fits  Blackbody  Band+Blackbody  NAI6  NAI7  NAI9  BGO1  nai  bgo  Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Same as Figure 2 but for GRB 110721A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  MNRAS 000, 1–?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (2023)  Time-averaging Polarimetric and Spectral Properties of GRBs  21  1  20  0  20  40  60  80  100  120  140  Time (s)  0  20  40  60  80  100  (Upper limit)  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='5  (S > 20)  (10 < S < 20)  (S < 10)  140206A  101  102  103  104  105  Photon Energy - keV  101  102  103  104  keV × [keV  1S  1cm  2]  Band fits  Blackbody  Band+Blackbody  NAI0  NAI1  NAI3  BGO0  nai  bgo  Figure 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Same as Figure 2 but for GRB 140206A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  MNRAS 000, 1–?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (2023)  22  Li & Shakeri  1  20  10  0  10  20  30  40  Time (s)  0  20  40  60  80  100  = 85 ± 29  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='5  (S > 20)  (10 < S < 20)  (S < 10)  160802A  101  102  103  104  105  Photon Energy - keV  101  102  103  104  keV × [keV  1S  1cm  2]  Band fits  Blackbody  Band+Blackbody  NAI2  BGO0  nai  bgo  Figure 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Same as Figure 2 but for GRB 160802A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  MNRAS 000, 1–?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (2023)  Time-averaging Polarimetric and Spectral Properties of GRBs  23  1  101  102  103  104  Ep, z[keV]  100  101  102  103  a  100826A  110301A  110721A  140206B  160802A  100  101  102  103  Power-law index= -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='41±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='24  1051  1052  1053  1054  1055  E , iso (erg)  100  101  102  103  b  100826A  110301A  110721A  140206B  160802A  100  101  102  103  Power-law index= -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='20±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='04  100  101  102  103  104  KT,z[keV]  100  101  102  103  c  100826A  110301A  110721A  140206B  160802A  100  101  102  103  Power-law index= -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='32±0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='18  100  101  102  1+  0  100  101  102  103  d  100826A  110301A  110721A  140206B  160802A  100  101  102  103  0  1  2  3  4  5  6  7  8  9  redshift  100  101  102  103  e  100826A  110301A  110721A  140206A  160802A  10  6  10  5  10  4  10  3  10  2  Fluence (erg cm  2)  100  101  102  103  f  100826A  110301A  110721A  140206A  160802A  Figure 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Scatter plots of polarization degree π versus several other observed quantities: (a) the cosmological rest-frame peak energy (Ep,z) of the νFν prompt  emission spectrum, (b) the isotropic-bolometric-equivalent emission energy Eγ,iso, (c) the magnetization parameter σ0, (d) the blackbody temperature kT, (e)  the redshift z, and (d) the corresponding energy fluence Sγ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Data points with different colors indicate the different bursts in our target sample.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The solid lines  (grey) are the best fit using the power-law model with 2σ (95% confidence interval) error region (shadow area).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  MNRAS 000, 1–?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (2023)  24  Li & Shakeri  1  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='5  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='0  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='5  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='0  100  101  102  100826A  110301A  110721A  160802A  140206A  100  101  102  lin  max =  + 1  + 5/3  ymax=1  ymax=2  ymax=5  ymax=10  ymax=102  110721A  160802A  110301A  100826A  140206A  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='5  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='5  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
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+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='0  α  Π/Πmax  Figure 8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Left: The maximum degree of the linear polarization applying synchrotron emission model (Πlin  max Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (19)) with observed data using α indices based  on a time-integrated spectral analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' Right: Time integrated polarization degree in the presence of an ordered magnetic field Bord with in the plane of ejecta  (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (19)) measured by an on-axis observer (θobs = 0), the evolution of the polarization is plotted in terms of α for different values of ymax = (Γθmax)2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  MNRAS 000, 1–?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (2023)  Time-averaging Polarimetric and Spectral Properties of GRBs  25  1  α=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='72  α=0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='84  α=1  α=1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='2  Random B⟂  yj = 10  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='8  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='0  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='2  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='8  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='0  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='1  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='2  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='3  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
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+page_content='5  ζ=θobs/θj  Π/Πmax  yj=103  yj=102  yj=10  yj=1  α = 1  Random B⟂  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='6  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
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+page_content='4  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='6  1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
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+page_content='4  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='6  ζ=θobs/θj  Π/Πmax  Figure 9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' The time integrated polarization for a random magnetic field B⊥ which lies entirely in the plane of the shock (Eq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (20)) as a function of the off-axis  parameter ζ = θobs/θ j for different values of spectral index α (left) and yj = (Γθ j)2 (right) as labeled.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='  MNRAS 000, 1–?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content='?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}
+page_content=' (2023)' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/KNAyT4oBgHgl3EQfsfkS/content/2301.00576v1.pdf'}