diff --git "a/BNE4T4oBgHgl3EQf5A7u/content/tmp_files/2301.05320v1.pdf.txt" "b/BNE4T4oBgHgl3EQf5A7u/content/tmp_files/2301.05320v1.pdf.txt" new file mode 100644--- /dev/null +++ "b/BNE4T4oBgHgl3EQf5A7u/content/tmp_files/2301.05320v1.pdf.txt" @@ -0,0 +1,3190 @@ +MNRAS 000, 1–24 (2021) +Preprint 16 January 2023 +Compiled using MNRAS LATEX style file v3.0 +Modeling Strong Lenses from Wide-Field Ground-Based +Observations in KiDS and GAMA +Shawn Knabel1,2 , B. W. Holwerda1 , J. Nightingale3 , T. Treu2 , +M. Bilicki4 , S. Brough5 , S. Driver6 , L. Finnerty2 +L. Haberzettl1 , +S. Hegde2 , A. M. Hopkins7 , K. Kuijken8 , J. Liske9 , K. A. Pimblett10 , +R. C. Steele1 , and A. Wright11 +1 University of Louisville, Department of Physics and Astronomy, 102 Natural Science Building, 40292 KY Louisville, USA. +2 University of California-Los Angeles, Department of Physics and Astronomy, PAB, 430 Portola Plaza, Box 951547, Los Angeles, CA 90095-1547, USA +3 Durham University, Institute for Computational Cosmology, Stockton Rd, Durham DH1 3LE, United Kingdom +4 Center for Theoretical Physics, Polish Academy of Sciences, al. Lotników 32/46, 02-668 Warsaw, Poland +5 School of Physics, University of New South Wales, NSW 2052, Australia +6 International Centre for Radio Astronomy Research (ICRAR), University of Western Australia, Crawley, Australia, WA 6009 +7 Australian Astronomical Optics, Macquarie University, 105 Delhi Rd, North Ryde, NSW 2113, Australia +8 Leiden Observatory, Leiden University, P.O. Box 9513, 2300RA Leiden, the Netherlands +9 Universität Hamburg, Hamburg Sternwarte, Gojenbergsweg 112, 21029 Hamburg, Germany +10 E.A.Milne Centre for Astrophysics, University of Hull, Cottingham Road, Kingston-upon-Hull, HU6 7RX, UK +11 German Center for Cosmological Lensing (GCCL), Astronomisches Institut, Ruhr-Universität Bochum, Universitätsstraße 150, 44780, Bochum, Germany +This is a pre-copyedited, author-produced PDF of an article accepted for publication in Monthly Notices of the Royal Astronomical Society following peer +review. +ABSTRACT +Despite the success of galaxy-scale strong gravitational lens studies with Hubble-quality +imaging, the number of well-studied strong lenses remains small. As a result, robust compar- +isons of the lens models to theoretical predictions are difficult. This motivates our application +of automated Bayesian lens modeling methods to observations from public data releases +of overlapping large ground-based imaging and spectroscopic surveys: Kilo-Degree Survey +(KiDS) and Galaxy and Mass Assembly (GAMA), respectively. We use the open-source lens +modeling software PyAutoLens to perform our analysis. We demonstrate the feasibility of +strong lens modeling with large-survey data at lower resolution as a complementary avenue +to studies that utilize more time-consuming and expensive observations of individual lenses +at higher resolution. We discuss advantages and challenges, with special consideration given +to determining background source redshifts from single-aperture spectra and to disentangling +foreground lens and background source light. High uncertainties in the best-fit parameters for +the models due to the limits of optical resolution in ground-based observatories and the small +sample size can be improved with future study. We give broadly applicable recommendations +for future efforts, and with proper application this approach could yield measurements in the +quantities needed for robust statistical inference. +Key words: gravitational lensing: strong methods: observational galaxies: fundamental pa- +rameters galaxies: elliptical and lenticular, cD galaxies: evolution galaxies: formation +1 +INTRODUCTION +Strong gravitational lensing is an essential probe of galaxy struc- +ture, enabling mass measurements in the center-most regions of the +foreground lensing galaxy without assumptions about stellar pop- +ulations. Numerous studies have shown that lensing galaxies are, +in every other respect, indistinguishable from other galaxies in the +observed mass range; therefore, their study offers insight into the +larger global population of galaxies at similar mass and redshift +(Auger et al. 2009a). Complementary to kinematic and stellar pop- +ulation synthesis (SPS) measurements, strong lensing allows the +decoupling of internal mass components (dark and baryonic) and +accurate central stellar population mass-to-light ratios (Auger et al. +2009b; Hopkins 2018). +© 2021 The Authors +arXiv:2301.05320v1 [astro-ph.CO] 12 Jan 2023 + +2 +S. Knabel +A fundamental issue in astronomy is relating the predicted dark +matter halo mass function to the observed galaxy mass function. The +masses of dark matter halos are not well-constrained by the amount +of visible matter in their constituent galaxies. Few single galaxies +corresponding to the lowest and highest halo masses are found, due +to feedback processes stopping star-formation (Behroozi et al. 2010, +2020). The galaxy stellar-to-halo mass relation (SHMR) represents +a fundamental barometer for accretion and feedback processes in +galaxy formation. Subhalo abundance matching (SHAM) assigns a +galaxy with a specific stellar mass to a specific subhalo but does +not consider (i) the enveloping host halo mass or (ii) whether the +galaxy is a central or a satellite; thus it suffers from assembly bias +(Zentner et al. 2014; Chaves-Montero et al. 2016). +Assembly bias is a secondary halo property that is related to +the clustering strength of haloes (Matthee et al. 2017; Zehavi et al. +2018), where the clustering of dark matter halos depends on their +mass and formation epoch. Investigations with cosmological simu- +lations have revealed that dark matter halo concentration, formation +time, and environment all play a role in the relation between the +central galaxy’s stellar mass and the mass of the dark matter halo +it occupies. Assembly bias appears to be mostly independent of +the cosmological parameters assumed (Contreras et al. 2021). At +high masses typical of lensing elliptical galaxies, inefficiency in the +stellar occupancy of dark matter haloes is ascribed to the effects +of AGNs (Somerville et al. 2015). Weak lensing studies (Velander +et al. 2014; Mandelbaum et al. 2013; Lin et al. 2016) and velocity +field studies (McCarthy et al. 2021; Posti & Fall 2021) appear to +show the effects of assembly bias on the scales of galaxy popu- +lations (Cui et al. 2021); assembly bias is especially noticeable at +∼ 1Mpc scales (Hearin et al. 2016): i.e. groups of galaxies. While +well-explored with hydrodynamical simulations (e.g. Hearin et al. +2015, 2016; Matthee et al. 2017; Artale et al. 2018; Zehavi et al. +2018, 2019; Contreras et al. 2019), observational studies have thus +far been limited by the need to average over large numbers of similar- +mass central elliptical galaxies to obtain a weak lensing or velocity +signal. +With strong lensing, one has the opportunity to directly mea- +sure stellar and halo masses in elliptical galaxies. Relations between +the environment and internal structure of elliptical galaxies have +been explored using SLACS lenses (Sloan Lens ACS) (Bolton et al. +2006) by Treu et al. (2010). They find that the SLACS lenses are +slightly biased toward overdense environments (12 of 70 are asso- +ciated with known groups or clusters), which is consistent with the +expectation for the most massive of elliptical galaxies. They find +this result to be unbiased when compared to similar massive galax- +ies from SDSS, again showing lens galaxies to be representative of +the overall elliptical galaxy population. They find the contribution +of the external environment to have little effect on the local poten- +tial (except in extreme overdensities) and the internal structure of +lens galaxies. SLACS and other lens studies have been conducted +using detailed observations of individual lenses with HST-quality +data. The application of lens modeling methods to larger wide-field +surveys offers an alternative avenue with advantages for conducting +experiments relating galaxy properties to environment and group +properties. This motivates the need for exploring lens modeling +methods in the context of large surveys. +In this paper we explore what can be done with ground-based +imaging and spectroscopy to model lens candidates after they have +been identified in imaging surveys. We discuss strategies for en- +suring quality control at each stage while extracting meaningful +measurements from ground-based data. Using Galaxy and Mass +Assembly (GAMA) survey single-aperture spectroscopy, we ex- +plore the utility of automated redshift determination as a tool for +identifying the background-source redshifts of strong lenses by ap- +plying this technique to lens candidates that were identified in the +ground-based imaging of the Kilo-Degree Survey (KiDS) using ma- +chine learning techniques (Petrillo et al. 2019b; Li et al. 2020). With +GAMA spectroscopic redshifts and other measurements in conjuc- +tion with KiDS cutout images, we construct lens models utilizing +an automated lens modeling program called PyAutoLens. +Our paper is organized as follows: Section 2 describes the +KiDS and GAMA data used, as well as the parent samples used in +our selection. Section 3 describes how background-source redshifts +are identified in single-aperture spectra from GAMA Autoz cata- +logs to create a subsample for modeling. Section 4 describes the +PyAutoLens software and the lens modeling methods we used to +perform our analysis. Section 5 outlines the assessment of quality +of the models and redshift determinations. Section 6 presents re- +sults for the four highest-quality models. Section 7 discusses some +challenges that our prescription of second-redshift determination +introduced, as well as recommendations for improving that method. +Section 8 discusses galaxy environment and potential applications +of a refined method to future studies. Section 9 lists our conclusions. +Throughout this paper we adopt a Planck Collaboration (2015) cos- +mology (𝐻0 = 67.7 km/s/Mpc, Ω𝑚 = 0.307). +2 +DATA +2.1 +GAMA Spectroscopy and AUTOZ Redshifts +Galaxy and Mass Assembly (GAMA, Driver et al. 2009, 2011; +Liske et al. 2015) is a multi-wavelength survey built around a +deep and highly complete redshift survey of five fields with the +Anglo-Australian Telescope. GAMA has three major advantages +over SDSS in the identification of blended spectra: (i) the spec- +troscopic limiting depth is 2 magnitudes deeper (𝑚𝑟 < 19.8 mag +compared with SDSS main survey depth 𝑚𝑟 < 17.7 (Eisenstein +et al. 2001)1), (ii) the completeness is close to 98% (Liske et al. +2015), and (iii) the Autoz redshift algorithm can identify spectral +template matches with signal from two different redshifts (Baldry +et al. 2014). These properties and the overlap of GAMA and KiDS +fields make these two surveys exceptionally well-suited to provide +the data required for our study of lens modeling. +The Autoz (Baldry et al. 2014) cross-correlation redshift soft- +ware has been uniformly applied to the GAMA (Liske et al. 2015) +spectroscopic data, resulting in a public database that can be found +in GAMA-DR3 AATSpecAutozAll v27 (hereafter Autoz cata- +log) and SpecAll v27 tables (http://www.gama-survey.org/ +dr3/). The Autoz algorithm outputs four flux-weighted cross- +correlation peaks (denoted 𝜎) of redshift matches to template spec- +tra of emission-line and passive galaxies (denoted ELG and PG re- +spectively) from SDSS-DR5. 𝜎1 corresponds to the highest cross- +correlation or "best-fit" redshift match, 𝜎2 the second-best, etc. +These matches have proven to be highly successful and are the base +redshift measurement for GAMA objects. GAMA-DR3 also com- +piled SDSS-BOSS spectra for overlapping targets that are included +in table SpecAll, but these spectra did not utilize Autoz for redshift +determination. +Holwerda et al. (2015) analyzed Autoz catalog cross- +correlation outputs and identified 104 strong lensing candidates +1 The spectroscopic luminous red galaxy (LRG) sample used to select +SLACS lenses is limited to 𝑚𝑟 < 19.5 thanks to the 4000Å break. +MNRAS 000, 1–24 (2021) + +3 +from their blended spectra, all of which showed a passive galaxy +(PG) with an emission line galaxy (ELG) at higher redshift between +cross-correlation 𝜎1 and 𝜎2. This identification selected candidates +from a two-dimensional parameter space defined by the second +cross-correlation peak 𝜎2 and the parameter 𝑅, which describes the +significance of 𝜎2 compared to the following "poorer" matches: +𝑅 = +𝜎2 +√︂ +𝜎2 +3 +2 + +𝜎2 +4 +2 +(1) +Candidates with second cross-correlation peak 𝜎2 ≥ 4.5 and 𝑅 ≥ +1.85 were considered likely candidates for strong lensing. Knabel +et al. (2020) further analyzed and made a cleaner selection of 47 +candidates. +The completeness of GAMA allows detailed environment +measures including population density and separation (Brough +2011; Alpaslan et al. 2014, 2015), and the GAMA team internal +GroupFinding catalogs include the total mass and placement of +the galaxies in an identified group via a friends of friends algorithm +(Robotham et al. 2011). In fact, GAMA was conceived to probe the +effects of group environment on galaxy properties. In this context we +describe galaxies either as "group member" galaxies or as those not +in galaxy groups, which we designate as "isolated galaxies". Stellar +masses are taken from the GAMA-DR3 StellarMassesLambdar +v20 catalog (Taylor et al. 2016). +2.2 +Kilo-Degree Survey (KiDS) and Machine Learning +Strong Lens Samples +The Kilo-Degree Survey (KiDS, de Jong et al. 2013, 2015, 2017; +Kuijken et al. 2019) is a VLT Survey Telescope (VST) program +of medium-deep imaging in SDSS-ugri filters primarily to identify +weak lensing. The deep imaging, high resolution (0.65 arcsec seeing +in SDSS r-band), and wide sky-coverage (1350 deg2) also make this +survey ideal for efforts to identify strong lens candidates from imag- +ing. Image-based deep learning efforts have been the most promising +of recent developments in automated lens-finding algorithms. Their +efficiency and versatility make them ideal for astronomical classi- +fication problems involving large datasets, including the detection +of strong gravitational lenses (e.g. in Subaru Hyper-Supreme Cam +(Speagle et al. 2019), DECAM (Huang et al. 2020), and Dark Energy +Survey data (Jacobs et al. 2019)). Petrillo et al. (2017) developed +a machine learning method to identify strong lenses in KiDS using +a convolutional neural network (CNN) with artificially-constructed +lens images as the training set. Training and target catalogs were +intentionally constructed utilizing SDSS-LRG (Petrillo et al. 2017) +color-magnitude selection cuts to return the largest of known strong +lenses that result in the most readily identifiable lens features (Ein- +stein radii close to and greater than 1 arcsecond). The result is the +Lenses in KiDS sample (LinKS, Petrillo et al. 2019a,b)2 of some +1300 strong lensing candidates, 421 of which overlap with the equa- +torial regions of the Galaxy and Mass Assembly (GAMA) survey. +Knabel et al. (2020) compared data from LinKS objects with the Au- +toz spectroscopic identifications in GAMA (Holwerda et al. 2015) +as well as with KiDS-GalaxyZoo (Holwerda et al. 2019, Kelvin et +al. in prep.) citizen science identifications in the overlapping equa- +torial fields. A disparity between the candidate samples in terms +of stellar mass and redshift is attributed to selection effects. Of the +2 https://www.astro.rug.nl/lensesinkids/ +subsample of 421 LinKS candidates in GAMA (hereafter referred +to as "LinKS" or "LinKS in GAMA" sample) there was no overlap +with the subsample of 47 GAMA spectroscopic candidates. Knabel +et al. (2020) further subselected 47 LinKS candidates to represent +the highest quality of the sample (hereafter referred to as "LinKS +from Knabel-2020" sample). +Li et al. (2020) followed a slightly modified approach from +the lens-search prescription utilized by the LinKS team to search +for strong lens candidates in KiDS-DR4. They included several +more LRGs and applied their CNN to a sample of "bright galax- +ies" (BG) that did not undergo LRG color-magnitude cuts. Their +search returned some LinKS candidates and resulted in 286 new +candidates within the KiDS survey, 48 of which were identified +in the GAMA equatorial regions. 39 of those have matches in the +StellarMassesLambdar mass catalog, and there are no overlaps +between this sample and that of GAMA spectroscopy or Galaxy- +Zoo. This candidate sample, which we will refer to as "Li-BG", +shares essentially the same parameter space as LinKS candidates, +even with the exclusion of the LRG selection (Knabel et al. 2020). +This is not necessarily surprising considering Petrillo et al. (2019b) +report no significant advantage to the inclusion of color images in +the CNNs, as the networks appear to focus more on morphological +features and brightness than color separation. Still, the extension be- +yond the typical red elliptical galaxy as candidate objects suggests +the potential for more variability in candidate characteristics. +3 +AUTOZ SECOND REDSHIFT SELECTION AND +QUALITY CONTROL +We examine the Autoz cross-correlation values for each LinKS +and Li-BG lens candidate. Each candidate has been matched to the +closest GAMA object by right-ascension and declination within a +positional tolerance of 2 arcseconds. Not every object in the equa- +torial fields is featured in the Autoz catalog; these candidates are +removed from this study. Some of the objects feature duplicated +entries, some of which have conflicting Autoz outputs, which we +retain for examination and selection. +3.1 +Selection Criteria +Since the candidates that remain have already been identified and +vetted through machine learning methods, we adopt a more lenient +selection criterion from the same 𝜎2 − 𝑅 parameter space as that +utilized in Holwerda et al. (2015). From a first look at the data, +we select candidates with 𝑅 ≥ 1.2. This is sufficient for a first +selection and for characterizing the output of the Autoz algorithm +from already positively-identified candidates. We show the selection +in Figure 1. +From the 67 Autoz entries that pass the 𝑅 selection, we re- +move those with stellar template matches (i.e. not a galaxy spec- +trum) and retain all those with galaxy-galaxy template match +configurations regardless of the galaxy type. The distribution of +foreground+background (lens+source) template type (PG+ELG, +ELG+PG, ELG+ELG, PG+PG) is shown in the histogram of Fig- +ure 2. Note that the majority of lens foreground objects match +to passive galaxy templates, with the majority of background ob- +jects matching to emission line galaxy templates. This is expected. +Massive elliptical galaxies tend to be the most readily observable +strong lensing foreground objects, and bright emission lines from +the background source are the most easily detected behind a passive +galaxy continuum. This selection bias is further enhanced by the +MNRAS 000, 1–24 (2021) + +4 +S. Knabel +1.0 +1.2 +1.4 +1.6 +1.8 +2.0 +2.2 +2.4 +R = +2/ +( +3)2/2 + ( +4)2/2 +2 +3 +4 +5 +6 +7 +8 +9 +10 +2 +Selection Based on and R Values +R = 1.2 +Holwerda-15 Selection +LinKS in GAMA +LinKS from Knabel-2020 +Li in GAMA +Selected Candidates +Figure 1. Initial selection of candidates with Autoz second-redshift deter- +minations. The y-axis shows the 𝜎2 second cross-correlation peak, with +higher values indicating a stronger match to the second galaxy template. +The x-axis is the parameter R, given by Equation 1. Black markers indicate +348 LinKS Autoz entries (300 unique candidates), 51 of which are over- +plotted with green markers to indicate Autoz entres of the 47 unique LinKS +candidates as selected in Knabel et al. 2020. Orange markers indicate the +53 Autoz entries for the 32 unique Li-BG candidates. The dashed vertical +line shows 𝑅 = 1.2, and the dotted box encloses the area of parameter space +used by Holwerda et al. 2015. Red squares surround 59 LinKS and 8 Li- +BG entries that satisfy 𝑅 ≥ 1.2 and are followed with additional selection +criteria. See Section 3.1. +fact that the parent LinKS and Li-BG samples were both identified +by CNNs trained with large elliptical galaxies. Configurations with +foreground lens emission line galaxies are possible, though much +more difficult to detect. The reasons are: (i) emission line galaxies +are typically lower in mass, so the lensing is less pronounced, (ii) +lensed background sources are often bright emission line galaxies, +so the blue light of each can blur together, and (iii) emission line +galaxies can include complex morphologies that can be mistaken +for lens features. The majority of Li-BG candidates in the Autoz +catalog were matched to emission line galaxies in the foreground, +but further selection and assessment of the spectra showed this to be +a false trend. As in Knabel et al. (2020), we select candidates with +background source redshifts that are reasonably far away from the +foreground lens redshifts, as well as those whose Autoz foreground +redshifts are greater than 0.05. Autoz estimates the probability of +success of the primary redshift match, and one candidate is removed +due to its very low probability. +Described in more detail and discussed in the context of Kn- +abel et al. (2020) in Appendix E, our selection results in 42 lens +candidates (39 from LinKS and 3 from Li-BG) with second redshift +matches, which constitute the initial Autoz sample. In later work, it +may be worth exploring machine learning algorithms to find better +use of the parameter space for classification than our naive selection +criteria. +3.2 +AUTOZ Selection Quality Control +An initial modeling and analysis strategy utilizing the Autoz sam- +ple of 42 candidates and PyAutoLens revealed the need for fur- +ther quality control. This assessment addresses the validity of our +application of Autoz output parameters to select second-redshift +determinations for the use in strong lens modeling. We examined +PG + ELG +ELG + PG +ELG + ELG +PG + PG +Type +0 +5 +10 +15 +20 +25 +Count +Spectral Template Pair Types for R-Selected Candidates +Links in GAMA +Li in GAMA +LinKS from Knabel-2020 +Figure 2. Autoz galaxy template combinations of candidate subsamples, +listed as foreground+background. Black and orange refer to LinKS and Li- +BG candidates respectively and are stacked to show total counts of each +template combination. The green outline shows the subset of LinKS candi- +dates that were examined in Knabel et al. 2020. As expected, the majority +of lens foreground objects match to PG templates, while the majority of +background objects match to ELG templates. +the 42 candidate spectra to understand the evidence for a second +redshift match within each. We superimposed upon the candidate +spectra important emission and absorption features redshifted by the +lens and source redshifts determined by Autoz. For ELG template +matches, we inspected 𝐻𝛽, [O II]𝜆3727, and [O III]𝜆𝜆4959,5007 +emission lines. For PG template matches, we looked at Calcium H +and K, 𝐻𝛽, Mg, and Na absorption lines. This illuminated some +specific cases that pointed to dubious redshift matches. We identify +four such cases: +3.2.1 +When there are Overlapping Emission or Absorption +Lines... +Autoz template matches utilize strong absorption or emission fea- +tures to identify passive and star-forming galaxies. We discovered +a significant failure condition of our method that occurs when the +second redshift match is identified by an emission or absorption line +that is also attributed to the foreground lens galaxy redshift. This is +particularly obvious in cases where Autoz determined ELG+ELG +configurations (i.e. both redshifts are identified by emission lines), +in which many of the higher-redshift matches were determined by an +[O II]𝜆3727 line that overlapped with the [O III]𝜆𝜆4959,5007 lines +of the foreground lens galaxy. For configurations where both the lens +and source are the same template type (ie. PG+PG or ELG+ELG), +overlapping line features usually indicate a poor second-redshift +determination. +However, emission and absorption features are present in the +spectra of both PGs and ELGs. For example, Treu et al. (2002) found +that ∼ 10% of elliptical galaxies in the intermediate redshift range +where our lens candidates lie have strong [O II]𝜆3727 emission; +in fact, the emission of [O II]𝜆3727 is detectable in the spectra +14 of the passive galaxy matches in our sample, and absorption of +Calcium H and K lines (as well as some Na and Mg) are identifiable +in 15 of the ELG galaxy spectrum matches. In most cases, the +overlap of lines draws suspicion of the background source spectrum +match, not the foreground lens match, which is typically the primary +template match (𝜎1). In our sample, emission line overlaps occur +exclusively between the background source [O II]𝜆3727 and one +MNRAS 000, 1–24 (2021) + +5 +of the [O III]𝜆𝜆4959,5007 couplet of the foreground lens passive +galaxy. Absorption line overlaps are all between source H or K lines +and lens H𝛽, Na, or Mg lines. +3.2.2 +When the Lens is described as an Emission Line Galaxy... +As shown in Figure 2, several of the template matches selected +by the strategy described in Section 3.1 are configurations with +a foreground lens emission line galaxy (ELG+ELG or ELG+PG). +We reiterate that there is no physical reason to mistrust these red- +shift matches on this fact alone. In fact, given that several of the +ELG matches have strong absorption features at the same redshift, +these may very well be elliptical galaxies with strong oxygen emis- +sion lines. However, upon examination of candidate spectra and the +quality of initial models for these ELG+ lens configurations, we +found that several of these candidates included dubious template +matches and were removed. +The overlapping ELG+ELG emission lines have been dis- +cussed. In addition, some of the spectra of ELG+ configurations +included key emission line features that would have been observed +in wavelength ranges of high noise. Many of the GAMA spectra have +their most significant noise at the extremes of the wavelength range, +e.g. at wavelengths shorter than ∼4500Å. For lenses at redshifts +lower than ∼0.2, the [O II]𝜆3727Åemission line lies in this region, +which removes an important identifying emission line feature from +consideration. +3.2.3 +When Source Emission Lines are Redshifted Beyond +Observed Wavelength Range... +The cases where a background source emission line overlaps with +a foreground lens emission line often correlate with another case: +some of the background source emission lines have redshifted to +wavelengths beyond the observed wavelength range of the spectro- +scopic survey. For our purposes, this translates to upper limits of +background source redshifts beyond which the emission line will +not be present in the spectrum. For GAMA, which has an upper +limit of 8850Å, the emission lines we have discussed begin to dis- +appear around z∼0.77. SDSS-BOSS has an extended upper limit of +wavelength to 10400 Å (∼J-band), which corresponds to upper red- +shift limits of around z∼1 where we begin to see missing emission +lines. GAMA-DR3 SpecAll table contains SDSS-BOSS spectra +for several of the candidates, so we can look to these spectra for ev- +idence of lines that have redshifted beyond the GAMA upper limit. +The Autoz catalog includes only GAMA spectra, so the outputs we +use for selection would not benefit from the extended range of the +SDSS-BOSS spectra. +3.2.4 +When Primary Redshift is Background Source... +The primary redshift match corresponding to 𝜎1 is typically (but +not always) the foreground lens galaxy. The background source +redshift is the primary redshift match for 10 of the 42 Autoz sample +candidates. The results of the Autoz algorithm are largely flux- +weighted, and an especially bright background source (e.g. a strong +emission line) could be interpreted by the algorithm as the primary +redshift solution instead of the lower-redshift lens object. However, +8 of these 10 are ELG+PG template configurations, where a PG +template gives the primary redshift solution at higher redshift. The +case of a bright continuum at higher redshift overshadowing the +foreground emission line galaxy is unlikely. +All candidates in the Autoz sample were modeled and exam- +ined in the manner described in Sections 4-6 before these four cases +were identified. In Section 7 we discuss the results of modeling and +assessment in the context of the cases described in this section and +recommend alterations to the initial selection scheme. We note that +a poor redshift match does not remove/negate the validity of the lens +identification, nor does it question the accuracy of the uniform appli- +cation of Autoz to GAMA spectroscopic targets. These additional +selection decisions were instituted following critical assessment of +problems with our initial strategy that required time with human +eyes on the spectra. With reasonable background source redshift +determinations, modeling of the imaging data can yield meaningful +physical measurements. +4 +PYAUTOLENS +We use the open source lens modeling software PyAutoLens +(Nightingale et al. 2021b)3 to perform our analysis. The software is +described in Nightingale et al. (2018) and Nightingale et al. (2021b), +building on the works of Warren & Dye (2003), Suyu et al. (2006) +and Nightingale & Dye (2015). We refer readers to these works for +a full description of our approach to lens modeling. Section 4.1 +broadly describes the method as we apply it here, and a more tech- +nical description of the specifics of the implementation is given in +Appendices A and B. +4.1 +Lens Modeling with PyAutoLens +PyAutoLens models the foreground lens galaxy’s light and mass as +well as the background source galaxy’s light simultaneously. First, +PyAutoLens assumes a profile for the foreground lens’s light (e.g. a +Sérsic profile), producing a model image of the lens galaxy. A mass +model then ray-traces a grid of image-pixels from the image-plane to +the source-plane, with the source’s light evaluated on this deflected +grid via another light profile. This creates an image of the lensed +source, which is added to the lens galaxy image to create an overall +model image of the strong lens. This image is convolved with the +instrument PSF and compared to the data to evaluate the residuals +and likelihood of that lens model. To fit a lens model to imaging +data, PyAutoLens searches an N-dimensional parameter space so +as to minimize the residuals (and therefore maximize the likelihood) +between the model image and the observed image. The lens models +fitted in this work consist of 𝑁 = 7 − 14 parameters, corresponding +to the parameters of the light and mass profiles that represent the +lens and source galaxies. To sample parameter space, we use the +nested sampling algorithm Dynesty (Speagle et al. 2019), and we +detail its specific implementation below. +The parameter spaces of a strong lens model are challenging +to sample, and local maxima and unphyscial lens models are of- +ten inferred. Automating the model-fitting procedure is therefore +difficult, and PyAutoLens approaches automation via a technique +called non-linear search chaining. Here, a sequence of Dynesty +model-fits are performed that fit lens models of gradually increas- +ing complexity, whereby the results of the initial searches are used +to inform the search of more complex parameter spaces in the later +searches. Through experimentation, we have designed a pipeline +composed of a chain of three Dynesty searches that we use as a +3 https://github.com/Jammy2211/PyAutoLens +MNRAS 000, 1–24 (2021) + +6 +S. Knabel +template for fitting each lens. Our three-step pipeline consists of +three sequential model-fits: +(i) Search 1 - Lens Light: models only the foreground lens ellip- +tical light profile. +(ii) Search 2 - Lens Mass and Source Light: focuses on the back- +ground source light profile and lensing deflections. +(iii) Search 3 - Combined Lens and Source Models: models each +component in the system for parameter inference. +Between each search, various aspects of the fit can be altered +(e.g. a mask applied to the data can be customized to show only the +specific features of interest to each fit). This offers a more efficient +lens modeling procedure overall, as the parameter spaces of reduced +complexity are sampled faster. +Search chaining uses a technique called "prior passing" to ini- +tialize the regions of parameter space that are searched later in the +chain. Here, the models inferred in earlier non-linear searches ini- +tialize the priors of the more complex models fitted by the searches +later on. This ensures the non-linear search samples only the higher +likelihood regions of parameter space (see Nightingale et al. (2018)) +and therefore reduces the probability that a local maximum is in- +ferred. Prior passing sets the prior of each parameter as a Gaussian. +The mean is that parameter’s previous inferred median PDF value, +and the width is a value specific to each lens model and param- +eter. Prior widths have been carefully chosen to ensure they are +broad enough not to omit lens model solutions by trimming valid +solutions but sufficiently narrow to ensure the lens model does not +inadvertently infer local maxima. +The Dynesty nested sampling algorithm (Speagle et al. 2019) +can also balance efficiency in computation with how thoroughly +it explores parameter space. Initial model fits require only a rough +estimate of the lens model that provides a reasonably approximate fit +to the data. These searches therefore use faster Dynesty settings that +give a less thorough sampling of parameter space. Our final results +require accurate and robust parameter estimates with precise and +well-quantified errors. By Search 3, the priors are initialized such +that a deeper exploration of the parameter space can be performed +more efficiently, ensuring that Dynesty does not spend considerable +time in regions of parameter space that previous searches tell us do +not give a physical lens model. Some basic settings that can be varied +to affect the performance of the non-linear search are: (i) number of +live points, (ii) number of steps of random walks per iteration, (iii) +target acceptance fraction for random walks, (iv) Bayesian evidence +tolerance, (v) positions threshold, and (vi) sub-grid size. +The technical details of our modeling method, including data +preparation and pipeline, are described more fully for the interested +reader in Appendices A and B. The sequence of chained searches +and specific parameters that are set via prior passing are listed in Ta- +ble B1, and Dynesty settings are tabulated in Table B2. More details +on PyAutoLens’s use of Dynesty are provided in (Nightingale et +al. in prep). +4.2 +Physically Motivated Priors +Where possible, we calculate priors using photometric observations +from GAMA-DR3 preferentially over a universally applied "typical" +value. For either case, it is important not to fix the parameters too +restrictively to values from observations. +4.3 +Effective Radius +In Search 1, we initialize the effective radius parameter of the fore- +ground lens light profile with a Gaussian centered at the lesser of +two possible radii: (i) effective radius determined from photomet- +ric observations from GAMA-DR3 SersicCatSDSS v09 catalog +(Kelvin et al. 2012), or (ii) the median SLACS lens effective radius +and standard deviation from Auger et al. (2010) (7 ± 3.3kpc). We +expect the GAMA-DR3 observation to include extended blended +light from the source feature, which may result in a higher mea- +sured effective radius than would be measured from the foreground +galaxy if it were not lensing. In order to assist the search in the task +of deblending the lens and source light, we ensure that the prior is +not predisposed to unusually large effective radii. Another failure +state of early models resulted in unrealistically large source galaxy +effective radii. Instead of attributing the extended lens features to +lensing of a compact background object (which is most often the +case for strong lensing), the model makes up for that extra flux as +the physical extent of an extremely large, bright background source +galaxy at high redshift. This motivated an upper limit to the effective +radius of the source galaxy based on typical disk galaxy properties. +We take a rough value of 7.5 ± 2.5 kpc and upper limit of about 15 +kpc. +4.3.1 +Lens Mass-to-Light Ratio +Certain critical parameters are not easily approximated with typical +observations (and as such are the goal of the search), such as the +stellar mass-to-light ratio. This quantity can be inferred from stel- +lar population studies, but one of our goals is to illuminate mass +relations without the dependence on these assumptions. We want +the model to tell us about the stellar population as opposed to the +inverse. We want the algorithm to have the maximum freedom to +determine the best combination of stellar and dark mass profiles to +account for a gravitational potential that can describe the observed +lensing deflections. Our first attempts allowed for a wide uniform +prior distribution for the mass-to-light ratio of the stellar light-mass +profile. The resulting models showed higher values than expected, +some of which were unphysical in the context of predicted 𝑀∗/𝐿 +from stellar population models evolving with age. The population +would have to be older than the age of the Universe at the given +lens redshift for the model’s 𝑀∗/𝐿 to reconcile with our current +models of stellar populations and evolution. To approach this prob- +lem, we impose a minimum 𝑀∗/𝐿 of 1 (𝑀/𝐿)⊙ and a maximum +determined as a function of lens redshift. We assume a Salpeter +IMF and utilize stellar evolution models from (Bruzual & Charlot +2003) (updated 2016) based on the STELIB spectral library. We de- +termine the maximum possible restframe bandpass-specific 𝑀∗/𝐿 +corresponding to a formation time close to the beginning of the +Universe. Other libraries (BaSeL and Milessx) give almost identi- +cal values. Given a simple stellar population forming from a single +starburst at time 𝑡 = 0, Salpeter IMF, and solar metallicity (Z = Z⊙ += 0.02 , X = 0.7000, Y = 0.2800, [Fe/H] = +0.0932), we examine the +evolution of the stellar mass-to-light ratio with population age in r- +and g-bands sampled at unequally spaced time steps over 20 Gyr of +stellar evolution. In our adopted cosmology, the age of the Universe +in the redshift range of our sample (z∼0.07-0.45) is about 9-13 Gyrs. +At this late stage in stellar evolution, the stellar mass-to-light ratio +varies slowly and is reasonably approximated as a linear relation. +On the domain [9, 13 Gyrs], the constraint is a linear relation: +MNRAS 000, 1–24 (2021) + +7 +𝑀∗/𝐿𝑟 [𝑀⊙/𝐿⊙] < 0.466𝑡 + 0.719 +(2) +𝑀∗/𝐿𝑔[𝑀⊙/𝐿⊙] < 0.717𝑡 + 0.380 +(3) +where 𝑡 is the age of the Universe at the lens redshift in the adopted +model cosmology. +In order to be implemented as priors in the lens models, these +restframe constraints must be k-corrected, calibrated to the flux +units in which the observed data is given, and rewritten in the model +mass and intensity units. We use SED-calculated k-corrections from +GAMA-DR3 kcorr_auto_z00 v05 (Loveday et al. 2012) for each +lensing galaxy to constrain the prior in the observed bandpass. These +constraints are converted to angular mass units per eps (electrons per +second) with the gain and exposure time of the KiDS observation. +These constraints ensure that the model does not attribute mass to a +stellar population that is impossible within current stellar evolution +models. In cases where the maximum possible 𝑀∗/𝐿 is fit, the +maximum possible stellar mass has also been attributed. In these +cases, the model may end up having to compensate with very high +amounts of dark matter to account for the lensing potential. +4.3.2 +NFW Profile Scale Radius +The scale radius of a dark matter halo is one of the key parameters +of the NFW mass density profile for dark matter halos. Gavazzi +et al. (2007) modeled 22 SLACS lenses with strong and weak +lensing constraints and a two-component mass profile consisting +of a de Vaucouleurs stellar component and spherical NFW dark +matter component. We adopt their resulting mean scale radius of +𝑟𝑠 = 58 ± 8ℎ−1 kpc for our dark matter profile Gaussian prior dis- +tributions. These values are converted to arcseconds from angular +diameter distances in our assumed cosmology. +4.4 +Choice of Image Bandpass +KiDS observations of each object in different bandpasses are not +equal in exposure time, signal-to-noise quality, or PSF. KiDS r-band +imaging is the highest quality of the bandpasses, with an exposure +time of 1800 s and a mean PSF of 0.65 arcseconds. g-band exposure +times are 900 s. For each candidate and for each model search, we +select the better of r- or g-band images. Search 1 fits the r-band image +because it most clearly shows the foreground lens light. If the lens +and source are clearly distinguishable in the r-band, then the same +image is used for Searches 2 and 3. However, the g-band image often +most clearly shows the lensed features of the background source; +in these cases the g-band is preferable for Search 2. Since Search +3 models the entire system, the image that most clearly shows both +profiles is used. +Each search assists the subsequent searches to distinguish be- +tween the lens and source light, which is one of the more difficult +challenges of modeling lenses from images of the resolution and +S/N attainable by ground-based observatories. Two effective first +solutions are (i) separating the initial search of foreground lens and +background source light profiles by color-band and (ii) masking +specific regions of the image. In this case the sacrifice in quality be- +tween the r- and g-bands as a consequence of survey design presents +an additional challenge to the fitting process as well as in later analy- +sis. PyAutoLens uses units of electrons per second, so the effect of +the difference in exposure times and S/N between observations with +the two bandpasses is minimized. However, measurements taken +from models that fit images of the same bandpass are much easier +to compare. +5 +MODEL QUALITY ASSESSMENT AND GRADING +With models complete, we assess the highest-likelihood models for +each candidate. Ideally, a reliable objective figure of merit such as +image 𝜒2 or Bayesian evidence would sufficiently quantify the qual- +ity of each lens model fit. Forming robust quantitative goodness-of- +fit metrics is currently an open problem in automated lens modeling. +Etherington et al. (2022) explored this problem using PyAutoLens +with much higher resolution images and found that none did a par- +ticularly satisfactory job. We take the Bayesian evidence to be the +reference figure of merit and follow this with a blind visual inspec- +tion of the image, fit, and spectrum of each modeled candidate. We +inspect the images and spectrum separately in order to isolate some +of the failure states that occur for each and have a clear picture of +the factors limiting the precision of the models. Three collaborators +give a separate score between 0 and 4 for each of the image, fit, +and spectrum for each candidate, so that each of the candidates has +three scores out of 12 and a total possible score of 36. +The procedure for assigning quality scores is as follows: The +collaborator (the "scorer") is shown via a randomized selection +either the spectrum or a set of images (observed and model-fit) of +a randomly selected candidate. The spectrum and image set are not +shown sequentially in order to keep the scores unbiased by each. +The spectrum score is based on the detection of redshifted line +features that correspond to both the foreground and background +redshifts. Wavelength accuracy, strength, and number of detectable +line features are considered, in addition to template type and the +presence of overlapping line features. The image and fit are scored +simultaneously from the set of four observed and model fit images +because the fit score is informed by the image score. The image +score is based on two images — (i) the observed image and (ii) the +observed image with the model’s lens light Sérsic profile subtracted. +The scorer considers how well the two images appear to show a well- +defined structure outside the central foreground lens light-profile +that could be reasonably described as a lens feature. For the fit +score, the scorer compares the lens-subtracted model image to the +lens-subtracted observed image and examines model background +source-plane image. The fit score is influenced by the image score; +the fit score cannot be higher than the image score +1. This means +that a poor image that is fit perfectly should not get a high fit score, +and a good image that is fit poorly should reflect the failure of the +model to adequately attribute the image features to the lensing of a +background source. +Following the scoring exercise, we remove any candidate that +received a "0" for any of the image, fit, or spectrum scores by any +scorer. This removes catastrophic failures and ensures that the final +set is reliable for follow-up analysis. The 19 candidate models that +remain are assigned a letter grade of A, B, C, or D according to +the structure outlined in Table 1. There are 2 A, 3 B, 9 C, and 5 +D grades in the scored subsample, described in Table 2. 17 of the +graded models are candidates from the LinKS subsample. Two of the +three candidates from the "Li-BG" sample were modeled to a level +of success that justified presentation alongside the others, though +both models are given grades of D. One D-grade model (G419067) +with a negative likelihood was a result of high image residuals in +the very center of the lens light profile. Note the asterisk in the +𝑙𝑛(evidence) column of Table 2. This model scored well enough +for inclusion (spectrum score 4, total score 22) by the blind visual +inspection. However, the visual inspection may have removed this +candidate with the inclusion of a residual or 𝜒2 map in addition to +the model images. The Bayesian evidence is therefore a prudent first +cut of extremely poor models. Otherwise, as shown in Figure 3, we +MNRAS 000, 1–24 (2021) + +8 +S. Knabel +Grade +Total Score ≥ +Spectrum Score ≥ +# Models with Grade +A +30 +9 +2 +B +20 +6 +3 +C +16 +5 +9 +D +12 +4 +5 +Table 1. Grading scheme based on the total score and spectrum score for each candidate as described in Section 5. We give greater weight to spectrum score +because the quality of the Autoz redshift determination is essential to deriving meaningful physical results. All graded models have received no "0" scores for +any individual quality by any scorer, ensuring that the final set is clean. +GAMA ID +ID +RA +DEC +𝑧lens +𝑧source +Type +Scores: +Spectrum +Total +Grade +𝑙𝑛(evidence) +323152 +2967 +130.546 +1.643 +0.353 +0.722 +PG+ELG +12 +33 +A +7.10 +138582 +2828 +183.140 +-1.827 +0.325 +0.433 +ELG+ELG +11 +32 +A +7.47 +250289 +2730 +214.367 +1.993 +0.401 +0.720 +PG+ELG +8 +27 +B +6.28 +62734 +539 +213.562 +-0.242 +0.274 +0.597 +PG+ELG +6 +26 +B +4.50 +513159 +2123 +221.917 +-0.999 +0.289 +0.701 +PG+ELG +7 +23 +B +7.59 +3891172 +3056 +139.227 +-1.545 +0.340 +0.609 +PG+PG +5 +24 +C +6.43 +373093 +2897 +139.306 +1.198 +0.384 +0.837 +PG+ELG +5 +23 +C +7.31 +559216 +2507 +176.116 +-0.619 +0.250 +0.714 +PG+ELG +7 +19 +C +7.77 +3629152 +1933 +135.889 +-0.975 +0.407 +0.787 +PG+PG +5 +19 +C +7.36 +3896212 +1483 +129.806 +-0.830 +0.382 +0.848 +PG+PG +6 +18 +C +6.38 +342310 +2163 +215.081 +2.171 +0.380 +0.693 +PG+ELG +5 +18 +C +5.79 +272448 +2541 +179.420 +1.423 +0.272 +0.889 +PG+ELG +5 +17 +C +7.07 +262874 +26 +221.611 +2.224 +0.386 +0.859 +PG+PG +6 +16 +C +6.00 +387244 +1819 +135.569 +2.365 +0.218 +0.712 +PG+ELG +5 +16 +C +7.37 +569641 +BG3 +219.730 +-0.597 +0.360 +0.826 +ELG+ELG +4 +25 +D +7.27 +419067 +1179 +138.620 +2.635 +0.188 +0.764 +PG+ELG +4 +22 +D +* +16104 +BG1 +217.678 +0.745 +0.287 +0.849 +PG+ELG +4 +19 +D +7.08 +561058 +3349 +182.560 +-0.495 +0.320 +0.856 +PG+ELG +6 +14 +D +6.96 +262836 +1953 +221.405 +2.314 +0.144 +0.418 +ELG+PG +5 +13 +D +7.80 +Table 2. The 19 models with letter grades as selected in Section 5. The other 24 models were considered too poor for consideration here. ID refers to internal the +LinKS sample identifier or our labeling of Li-BG candidates that were modeled. Type refers to the configurations of foreground+background galaxy template +type. Scores are the sums of scores given by three individual scorers. Grades classify the quality according to the grading scheme shown in Table 1. 𝑙𝑛(evidence) +is the log of the Bayesian evidence reported by PyAutoLens. * G419067 had a negative evidence as a result of high image residuals in the center of the lens +light profile. +find that the quality of fit determined by careful visual inspection is +not correlated to the reported Bayesian evidence. +To the authors’ knowledge, none of these lens candidates +have been previously confirmed with high-resolution (HST-quality) +imaging or spectroscopy. G250289 was identified in HSC as +J083726+015639 by Sonnenfeld et al. (2019). Spectrum scores of +6 or better can be considered to be probable spectroscopic evidence +for the lens candidate, and the highest spectrum scores for the two +A grades can be considered spectroscopic confirmations. No ad- +ditional extensive efforts were made to identify another possible +background source redshift if the one determined by Autoz was +deemed unreliable. All scores can be considered useful follow-up +evidence for the quality of the candidates, in that the success of a +model lends additional confidence to the identifications. However, +Petrillo et al. (2019a) and Li et al. (2020) have already provided +extensive studies of the quality of their lens identifications, and our +image modeling is conducted on the same observations as their +analysis. Therefore, any poor model performance here does not +contradict a positive identification. +6 +MODEL RESULTS +6.1 +Extracting Best-Fit Parameters +For each lens model, the parameter space is sampled over tens +of thousands of iterations, estimating the log likelihood for each +sample fit and constructing a probability density function (PDF) +for each free parameter listed in Table B1 of the Appendix. Mass +and light profiles are fully described by the model-fit parameters. +The Einstein radius, total lensing "Einstein" mass, mass fractions, +luminosity, and mass-to-light ratios are calculated for each sample +from the model grid and integrated over the angular area enclosed +by the Einstein radius. +Parameters involving the luminosity require k-corrections to +restframe (see Section 4.3.1). Three of the four models used the +g-band image for Search 3, so they are easy to compare. Special +attention should be given to G250289, which was instead modeled +from its r-band image. In attempting to give the models the best +chance to succeed, we were inconsistent in the choice of bandpass +for modeling (see Section 4.4). Luminosity and mass-to-light ratios +for this model are corrected to the g-band after r-band restframe +k-correction. This is done by multiplying (or dividing) by an ad- +MNRAS 000, 1–24 (2021) + +9 +4.5 +5.0 +5.5 +6.0 +6.5 +7.0 +7.5 +8.0 +log evidence +10 +15 +20 +25 +30 +Total Score +Rejected Quality Scores +Accepted Quality Scores +Quality Scores vs. Log Evidence +Figure 3. Total score from visual quality inspection vs the natural log of +the Bayesian evidence from model fitting. X-markers are rejected based on +visual quality inspection. Square markers are accepted. There is very little +correlation between the visual inspection results and the objective quality- +of-fit metric. +ditional factor 10−0.4(𝑔−𝑟), where (𝑔 − 𝑟) ∼ 0.285 is the color +difference calculated by integrating the product of each bandpass +response function and a template elliptical galaxy spectrum from +Kinney et al. (1996) over the bandpass range. This has the effect +of scaling luminosity down and 𝑀/𝐿 up. Given our goal here, +which is to explore the methods, this is sufficient for characterizing +the differences between models in a consistent parameter space. +However, future efforts that intend to approach these measurements +more rigorously should approach the initial modeling with more +consistency. +We briefly present best-estimate results from the highest- +likelihood model fits for the four highest quality models in Table 3, +selected primarily by the blind quality scoring described in Section +5. Bayesian evidence reported by PyAutoLens and the subjective +reasonableness of the inferred quantities are also considered in the +selection of this small subsample. One B-grade model, G62734, is +not included because its central dark matter content is poorly con- +strained. This and the other 14 lower-grade models are considered +to be worth revisiting but were not successful enough to present +alongside the cleaner examples we present here. +To discuss inferred quantities, we estimate bivariate PDFs for +the quantities using a Gaussian kernel-density estimate from the +final 10000 iterations. The best estimate for each inferred quantity +listed in Table 3 is determined at the maximum of one of these +bivariate PDFs, where we use uncorrelated values as much as pos- +sible. We show the observed image, maximum likelihood model fit, +and spectrum for the highest scoring model in Figure 4. The other +three models listed in Table 3, as well as G62734, are shown and +discussed in more detail in Figures C1-C4 of Appendix C. +We are primarily interested in studying the stellar and dark +matter content in the central regions of the lens galaxies. Although +the mass and light profiles in the models are inferred to a larger +radius, mass measurements via strong lensing are the most precise +when considering only mass within the Einstein radius of the galaxy. +It is important to note that the Einstein radius is a feature individual +to each system, so the quantities are not calculated within a uniform +radius from the center of each galaxy. Values for each Einstein radius +can be found in Table 3. +6.2 +Comparing Highest-Quality Model Results +We show the four highest-quality models for comparison. Figures +5-7 show the four models in parameter space of interest to our study. +All of the plotted quantities are taken within the Einstein radius (see +Table 3). Each model identified with a different marker, and B-grade +group-member galaxy G250289 is indicated with a red marker to +remind the reader that the final model fit utilized the r-band. Green +and blue contours enclose 1𝜎 (39%) and 2𝜎 (86%) of the two- +dimensional PDF respectively. With the small sample size shown +here, we do not intend to address questions of assembly bias and +galaxy formation mechanisms. These plots are intended to discuss +the cleanest subset of our sample in the context of what can be +considered more thoroughly in future work. +Figure 5 shows the integrated stellar mass and dark mass en- +closed within the Einstein radius of the lens models. These are +obtained by integrating over the Sérsic stellar mass profile and el- +liptical NFW profile. The galaxies have total enclosed Einstein mass +values of order 𝑀𝐸 ∼ 3 − 8 × 1011 𝑀⊙, which is is expected since +lensing galaxies are typically quite massive. Assembly bias would +show itself here as a trend where group central galaxies tend to have +higher stellar mass than isolated galaxies at the same dark mat- +ter halo mass. The only group-member galaxy, G250289 (marked +with a red cross), lies in one of the smaller dark matter halos and +has the highest stellar mass. G323152 (marked with a black cir- +cle, not listed in GAMA GroupFinding catalog) has a similar dark +mass and about one-fifth of the stellar mass compared to G250289. +Conversely, the two isolated galaxies have the highest dark masses +and the lowest stellar masses. The higher stellar mass in G250289 +could have more to do with effects from the difference in r-band and +g-band S/N than a physical interpretation. With so few data, it is +difficult to determine how much of an effect this difference has on +the results of the models. +The total lensing (Einstein) mass enclosed within the Einstein +radius is generally well-constrained. We want our models to fur- +ther constrain the fraction of this lensing mass that is dark matter. +The fraction of dark matter is not directly constrained by a model +prior but is very sensitive to the assumed forms of mass and light +profiles and the constraints placed upon those. Figure 6 shows the +g-band integrated luminosity and dark matter fraction (both calcu- +lated within the Einstein radius) for each model. The uncertainties +in the fraction of dark matter along the x-axis are relatively small, +which is surprising given the inherent degeneracy of stellar and dark +mass in lens modeling. The small parameter space explored could +indicate a lack of flexibility of the models’ stellar and dark mass +profile priors, perhaps an excessive constraint or weighting toward +one mass component over the other. As discussed in Section 4.2, +the careful selection of priors can be challenging. Compare again +G250289 (red cross) and G323152 (black circle), which have simi- +lar enclosed dark masses. Even corrected (scaled down) from r-band +to g-band, the enclosed luminosity for G250289 is 2-4 times greater +than the other three, which could be why the model attributes a +higher fraction of the Einstein mass to the stellar component. These +models have relatively similar total Einstein masses enclosed within +similar Einstein radii around 1.2-1.7 arcsec. G250289 has an Ein- +stein radius of ∼ 1.5 arcsec that is typical and within the range of +the other model values, so additional luminosity and stellar mass is +not a result of an overextended radius of integration. +Figure 7 shows the g-band stellar mass-to-light ratio compared +to the enclosed dark mass. Dotted lines at the 2𝜎 contours indicate +upper constraints placed on the mass-to-light ratio. This figure com- +pletes our discussion of the degeneracy. In summary, the model has +MNRAS 000, 1–24 (2021) + +10 +S. Knabel +GAMA ID +𝑧lens +𝑧source +Type +𝑀∗/𝑀⊙ +𝑀𝐸/𝑀⊙ +𝑓𝐷𝑀 +𝜃𝐸 +𝜃𝑒 𝑓 𝑓 +𝑀∗/𝐿𝑔 +𝐿𝑔/𝐿⊙ +Grade +138582 +0.325 +0.433 +ELG+ELG +9.91e+10 +8.69e+11 +0.888 +1.20 +1.99 +7.70 +1.98e+10 +A +323152 +0.353 +0.722 +PG+ELG +1.31e+11 +4.65e+11 +0.717 +1.27 +2.78 +4.98 +2.69e+10 +A +513159 +0.289 +0.701 +PG+ELG +7.31e+10 +7.29e+11 +0.900 +1.72 +2.44 +4.85 +1.52+10 +B +250289 +0.401 +0.720 +PG+ELG +5.47e+11 +8.82e+11 +0.375 +1.55 +2.44 +8.92 (6.86 r) +6.11e+10 (7.95e+10 r) +B +Table 3. Results of 4 highest scoring models. 𝑧𝑙𝑒𝑛𝑠 and 𝑧𝑠𝑜𝑢𝑟𝑐𝑒 are the redshifts of the foreground deflector and background source. Type refers to the +configuration of foreground+background template types. 𝜃𝐸 is the Einstein radius calculated from the model mass distribution and lensing distances. Remaining +quantities are integrated within 𝜃𝐸. 𝑀𝐸 is the total enclosed Einstein mass. 𝑓𝐷𝑀 is the enclosed dark matter fraction. L is the enclosed luminosity in the +r-band enclosed. 𝑀∗/𝐿 is the enclosed stellar mass-to-light ratio. Grade is an evaluation of the quality of the fit to the image according to the scheme outlined +in Table 1. +4000 +5000 +6000 +7000 +8000 +Wavelength (A) +0.0 +2.5 +5.0 +7.5 +10.0 +12.5 +15.0 +17.5 +20.0 +Flux (10 +17 erg/s/cm2/A) +G323152_2967 GAMA Spectrum - Lens and Source Type and Redshifts (PG + ELG; 0.353, 0.722) +Spectrum +Error +CaH +CaK +Hb +Mg5175 +Na5892 +Hb +OII +OIII4959 +OIII5007 +Figure 4. G323152. A-Grade. Upper left: The observed image shows an apparent arc feature above the central lens galaxy light-profile. Upper right: The model +image captures the extra light reasonably, though without the exact shape. This could be a result of internal substructure or the impact of shear along the line of +sight, both of which are unaccounted for in the model. Lower: The GAMA spectrum shows strong line features at the redshiftsat of 0.353 and 0.722 identified +by Autoz. Dotted lines identify foreground lens galaxy absorption features (H, K, H𝛽, Mg, and Na) at 𝑧 = 0.353, and dashed lines show background source +emission features (H𝛽, [O II], [O III]) at 𝑧 = 0.722. +two options for attributing the lensing mass: (i) To favor the stellar +component, a higher stellar mass can be the result of a heavier stellar +population, and (ii) conversely, a very large, centrally concentrated +dark matter halo can make up for a lower stellar mass and lumi- +nosity. This is all expected. Bounds of integration for luminosity, +stellar mass, and dark mass are all dependent on the measure of the +Einstein radius, which is in turn dependent on the total mass which +the model is attempting to parse into stellar and dark components. +It is a complex problem with degenerate variables that is only con- +strained by meaningful priors. In our cleanest subsample, the most +identifiable differences occur for the candidate that was modeled +from a different photometric bandpass. This is another experimen- +tal design decision based on limitations of the data that significantly +affected our ability to analyze the resulting models. Thus, even our +best models suffer. +MNRAS 000, 1–24 (2021) + +G323152KiDSImage +4.0 +0.8 +2.0 +0.6 +(eps) +arcsec +0.0 +Intensity +0.4 +-2.0 +0.2 +0.0 +-4.0 +-4.0 +-2.0 +0.0 +2.0 +4.0 +arcsecG323152Model Image +4.0 +0.8 +2.0 +0.6 +Intensity (eps) +arcsec +0.0 +0.4 +-2.0 +0.2 +-4.0 +0.0 +-4.0 +-2.0 +0.0 +2.0 +4.0 +arcsec11 +2 +3 +4 +5 +6 +7 +8 +9 +10 +Dark Mass - (MD/1011M ) +0 +1 +2 +3 +4 +5 +6 +Stellar Mass - (M * /1011M ) +Stellar Mass vs Dark Mass +G138582 - A - Isolated - g-band +G323152 - A - N/A - g-band +G513159 - B - Isolated - g-band +G250289 - B - Group - r-band +Figure 5. Mass components integrated within the Einstein radius of each +of the four best-fit models described in Section 6 and Table 3. The legend +shows the GAMA identifier, quality grade, environment classification, and +the SDSS bandpass used for the final model fitting. Green and blue contours +about each point enclose 1𝜎 (39%) and 2𝜎 (86%) of the two-dimensional +PDF respectively. +0.3 +0.4 +0.5 +0.6 +0.7 +0.8 +0.9 +1.0 +Dark Fraction +1 +2 +3 +4 +5 +6 +7 +Luminosity - (Lg/1010L ) +Luminosity vs Dark Fraction +G138582 - A - Isolated - g-band +G323152 - A - N/A - g-band +G513159 - B - Isolated - g-band +G250289 - B - Group - r-band +Figure 6. SDSS g-band luminosity and dark matter fraction integrated within +the Einstein radius of each of the four best-fit models described in Section 6 +and Table 3. Legend and marker information are the same as in Figure 5. +7 +AUTOZ CONSIDERATIONS POST-MODELING +Here we summarize the results of our quality control procedure de- +scribed in Section 5 and give several recommendations for removing +contaminants. Appendix D gives a more detailed breakdown of the +candidates and models in the context of the cases discussed in Sec- +tion 3.2. +We discovered some failure modes for our method of utilizing +the Autoz algorithm for background source redshift determina- +tion. Revisions to our initial procedure removed about half of the +candidates. Few single cases should be excluded without consid- +eration; for example, some redshift determinations were kept even +though there appeared to potentially be a falsely attributed line. +However, absorption and emission lines must both be checked for +overlap regardless of the template configuration type, and template +type should be questioned with this information. Several of the lens +ELG galaxies turned out to have prominent absorption features at +2 +3 +4 +5 +6 +7 +8 +9 +10 +Dark Mass - (MD/1011M ) +1 +2 +3 +4 +5 +6 +7 +8 +9 +10 +M * /Lg - (M /L ) +Stellar Mass-to-Light Ratio vs Dark Mass +G138582 - A - Isolated - g-band +G323152 - A - N/A - g-band +G513159 - B - Isolated - g-band +G250289 - B - Group - r-band +Figure 7. Stellar mass-to-light ratio (𝑀∗/𝐿𝑔) in g-band and dark mass +integrated within the Einstein radius of each of the four best-fit models +described in Section 6 and Table 3. Dashed lines at the 2𝜎 contours indicate +boundaries corresponding to upper constraints placed on the mass-to-light +ratio of the models (see Section 4.2). Legend and marker information are +the same as in Figure 5. +the same redshift. The binary identification of PG and ELG, as +we have done here, is an oversimplification that hinders both our +classification and understanding of the spectra and expected galaxy +properties. +The two A-grade candidate models were acquired with Autoz +redshift matches that we consider to be cases that deserve extra +care (where the foreground galaxy is best matched with an ELG +template). This is interesting because one may be tempted to cut +these cases entirely in order to obtain a clean and fairly homogeneous +sample (i.e. large elliptical galaxy lensing a bright emission line +galaxy, PG+ELG). We find the more careful consideration of other +possible cases to be fruitful. If we had adopted a selection that +focused only on configurations where the primary template matched +a passive lensing galaxy, then ∼ 20% of our final selection, including +the two highest-scoring models, would have never been considered. +Care should be taken in order to reap the benefits of this expanded +population while minimizing contamination. +In the big picture, the improvement of spectral quality in wide- +field surveys is essential for making this work in an automated way +over large sample sizes, but an automated redshift algorithm like +Autoz could be optimized for background source redshift determi- +nation. Our subjective quality scores show little correlation to the +Autoz output parameters that we used for the initial selection, as +shown in Figure 8. The two axes show the Autoz selection param- +eter space, composed of the second cross-correlation peak 𝜎2 and +the 𝑅 parameter. Three of the candidates with the highest 𝜎2 show +very poor spectrum scores because they are instances of overlap- +ping emission lines. This suggests that a higher threshold for 𝜎2 +may not actually yield higher-quality background source redshift +matches. We now introduce other options for maintaining a clean +sample selection with Autoz while expanding the sample size in +future works. +MNRAS 000, 1–24 (2021) + +12 +S. Knabel +3 +4 +5 +6 +7 +2 +1.2 +1.4 +1.6 +1.8 +2.0 +R +3 +4 +5 +6 +7 +2 +Rejected Quality Scores +Accepted Quality Scores +0 +2 +4 +6 +8 +10 +12 +Spectrum Score +0 +5 +10 +15 +20 +25 +30 +35 +Total Score +Quality Scores vs. AUTOZ Selection Criteria +Figure 8. Upper: Spectrum quality scores and Lower: total score shown as +scatter plot color variations scaled with the colorbar on the right of each plot. +The axes of the scatter plot are the selection criteria from Figure 1. Vertical +axes are the second-highest cross-correlation peak 𝜎2, and horizontal axes +are the 𝑅 parameter. Dark purple colors indicate poor scores, with higher +scores at orange and yellow. Little correlation can be seen between these +parameters and the results of the models or their subjective spectrum scores. +In the upper plot, four low-scoring spectra with high 𝜎2 correspond to +overlapping emission lines. +7.1 +Recommendations to Remove Contaminants from +AUTOZ Selection +One could quite easily remove contaminants during the automated +selection. Each of these recommendations pays particular attention +to the redshifts of emission line galaxies in both the foreground +lens and background source positions. The two most convincing +(A-grade) spectra and models were cases of ELG+, so we want to re- +move as many contaminants as possible without the blanket removal +of either of these cases. In order to maintain the applicability of this +procedure to an even larger set of data than is considered here, we +recommend the following selection criteria be implemented when +adopting automated redshift determinations: +(i) Remove ELG+ELG and PG+PG matches where emission +or absorption lines redshift to overlapping wavelengths between +foreground lens and background source. One can calculate lens +and source redshift combinations that result in overlapping observed +emission lines similarly to the procedure described in Holwerda +et al. (2015). The following equation defines a region of parameter +space between a lower and upper linear function of (1 + 𝑧source) to +(1 + 𝑧lens). Within this region, an overlap will occur for a given pair +of restframe emission line wavelengths: +���� +1 + 𝑧source +1 + 𝑧lens +− 𝜆𝑟,lens +𝜆𝑟,source +���� < 𝐴 +𝑅 +(4) +where 𝑧source and 𝑧lens are the source and lens redshifts, 𝜆𝑟,lens and +𝜆𝑟,source are the restframe wavelengths of emission lines from lens +and source, 𝑅 is the spectral resolution of the instrument, and A is a +coefficient that widens the range of exclusion for potential overlap- +ping features. The equation implicitly accounts for the dependence +of resolution on observed wavelength. Figure 9 shows the regions +where a redshift combination of foreground lens and background +source results in overlapping lines given GAMA’s spectral resolu- +tion of 𝑅 ∼ 1300 and 𝐴 = 4 (i.e. overlapping emission lines are +closer than 4 times the smallest resolvable wavelength difference). +This prescription identifies most of the cases of overlap that were +flagged by direct visual inspection of the spectra. We retained one +of them with the lowest possible D-grade because its SDSS-BOSS +spectrum showed fairly reasonable source H𝛽 and [O III] couplet +lines at higher-wavelength that were not in the range of the GAMA +spectrum. +(ii) Remove +ELG configurations where H𝛽 and [O III] cou- +plet emission lines are redshifted beyond the wavelength range +of the observation. Table 4 and Figure 10 show the redshift lim- +its beyond which H𝛽 and [O III]𝜆𝜆4959,5007 lines will be above +the survey upper wavelength limit for several optical spectroscopic +surveys. Spectroscopy in the 1-𝜇m range is necessary in order to +detect the emission lines from sources at z∼1 and will become more +important for modeling lenses with foreground lens redshifts higher +than z∼0.5. DESI and the upcoming 4MOST have higher resolu- +tion and cover extended optical wavelength ranges that correspond +to these redshifts, which will reduce the significance of this prob- +lem. Background source redshifts could also be assessed by looking +for emission lines in very near-infrared (e.g. MOSFIRE Y-band, +0.97-1.12 𝜇m) spectra, where possible. In principle, template-based +automated redshift identification could be run for each separately, +which would negate some of the difficulties inherent to identifying +the two distinct signals within the single observation. The obvious +negative to this option is the need for additional observations. +(iii) Remove ELG+ matches with any of the following charac- +teristics: (a) low foreground lens redshift (less than z∼0.2 for our +sample), (b) ELG+PG configuration, and (c) primary redshift +match to the background source. ELG+ configurations with low +foreground lens redshifts suffered from several failure conditions in +addition to being a less-likely configuration than PG+. For GAMA, +the noisy short-wavelength end of the observed spectral range cor- +responds to emission lines with 𝑧lens less than ∼0.2, leading to +mistaken classification of noise peaks as emission lines. While this +is specific in part to GAMA’s wavelength-specific spectral perfor- +mance, several of these low-redshift foreground lens matches are +also ELG+PG configurations, of which almost all were removed +in quality scoring. The one remaining candidate had the lowest +score of all those accepted. Perhaps even more condemning is the +fact that many of these low-redshift ELG+ foreground lens matches +were also cases where the background source was assigned the pri- +mary redshift. This trio of doubtful cases coincided for several of +the candidates that were removed from our sample during quality +scoring. +8 +DISCUSSION +8.1 +GAMA Environment +The sample of 42 KiDS lens candidates and the subsample of 19 +with accepted grade A-D models are both close to evenly split be- +tween group-member and isolated galaxies according to the GAMA +GroupFinding metrics. 22 (8 graded) are associated with groups +and 19 (9 graded) are isolated. (G323152) is not represented in +GAMA group catalogs. +We note that most strong lensing galaxies should be the most +MNRAS 000, 1–24 (2021) + +13 +Survey +𝜆𝑙𝑖𝑚 (Å) +𝑧source +H𝛽 +[O III]𝜆4959 +[O III]𝜆5007 +AAT (GAMA/DEVILS) +8850 +0.821 +0.785 +0.768 +SDSS (original) +9200 +0.893 +0.855 +0.837 +4MOST (lo-res) +9500 +0.954 +0.916 +0.897 +DESI +9800 +1.016 +0.976 +0.957 +SDSS-BOSS +10400 +1.139 +1.097 +1.077 +Table 4. Five spectroscopic surveys and their upper wavelength limits limits. The right three columns show the source redshift at which the given emission line +will be redshifted beyond the upper wavelength limit of the observation. +GAMA ID +𝑧lens +𝑧source +𝜎lens +𝜎source +Type +Grade +323152 +0.353 +0.722 +7.52 +11.32 +PG+ELG +A +262836 +0.418 +0.144 +3.87 +10.23 +ELG+PG +D +Table 5. Two models with Autoz primary redshift template match to the background source and secondary match to the foreground lens (𝜎lens < 𝜎source). +Type refers to the foreground+background configuration of galaxy templates. Grade is an evaluation of the quality of the fit to the image according to the +scheme outlined in Table 1. G323152 is one of the highest scoring models in this study. +1.0 +1.1 +1.2 +1.3 +1.4 +1.5 +1 + zlens +1.3 +1.4 +1.5 +1.6 +1.7 +1.8 +1.9 +2.0 +1 + zsource +Redshift Combinations with Line Overlaps +CaH - H +CaH - Mg5175 +CaH - Na5892 +CaK - H +CaK - Mg5175 +CaK - Na5892 +H - Mg5175 +H - Na5892 +Mg5175 Na5892 +O[II] - H +O[II] - O[III]4959 +O[II] - O[III]5007 +H - O[III]4959 +H - O[III]5007 +Candidates +Figure 9. Combinations of foregrounds len and background source redshift +that result in overlapping important emission or absorption line features. +Colored line-regions are calculated with Equation 4 and indicate parameter +space where the labeled line features will overlap. Each is labeled in the +legend as "source feature - lens feature". Using these functions identifies 19 +of the 20 overlaps in the 42 candidates and all 6 that made the final selection +of 19. The region in the lower right between the solid and dashed black lines +shows the selection criterion utilized in the initial Autoz selection, which +removed candidates where the source redshift was within 0.1 of the lens +redshift. +massive galaxies in their halo, either in a group or in isolation. +Figure 12 shows the rank of the proximity of the object to the +center of mass of the group relative to other group members, with 1 +indicating the closest or center-most galaxy. Most of the candidates +shown here are group central galaxies, but our models failed for +11 of those. On the other hand, 4 of the 5 candidates that are not +8000 +8500 +9000 +9500 +10000 +10500 +11000 +Wavelength (Å) +0.6 +0.7 +0.8 +0.9 +1.0 +1.1 +1.2 +1.3 +Redshift +GAMA +0.768 +SDSS +0.837 +4MOST +0.897 +DESI +0.957 +SDSS-BOSS +1.077 +MOSFIRE Y +Redshift of Emission Lines Exceeding Spectrum Range +H +O[III]4959 +O[III]5007 +lim +Figure 10. Blue, green, and purple lines show the redshift of restframe H𝛽 +and [O III]𝜆𝜆4959,5007. Dotted vertical lines show the upper wavelength +limit of various spectroscopic surveys, and the overlaid arrows point to the +redshift at which the first of these three lines will disappear in the survey +observations. The red shaded region indicates the very near-IR coverage +of MOSFIRE Y-band (0.97-1.12 𝜇m) that could also potentially reveal +background source emission lines at around z∼1 and greater. +the central galaxy of their group were accepted and given grades, +comprising 40% of the graded group-galaxy members. Low scores +for group member galaxies could mean that their identification as +lenses is a false-positive given their proximity to other significantly +large galaxies. Alternatively, if these are lenses, the modeled mass +structure of the lensing galaxy as a single light-mass component +and assumption of its presence in the center of the dark matter halo +may not be accurate enough to reproduce the lensing observables. +If this were the case, one might expect the group centrals to be more +easily modeled than the subdominant or "satellite" galaxies with +ranks of 2 or greater, which is not apparent in Figure 12. The two +B-grade group galaxies are ranked 1 and 2, indicating that one of +them is a central while the other has at least one companion that is +competing for dominance in the group. The rank 2 group member +MNRAS 000, 1–24 (2021) + +14 +S. Knabel +is G62734, which was removed from the final selection because its +dark matter content was poorly constrained. This could be a result +of this galaxy’s distance from the center of the group mass. +Compared with the SLACS study in Treu et al. (2009), in which +12 of 70 (17%) were associated with groups, our KiDS/GAMA +strong lens candidate sample and selected subsample of 19 models +is more highly represented by group-member galaxies. Definitions +of group membership based on environmental parameters are not +the same between these studies. The nearly 50/50 split between +group-member and isolated galaxies in our sample does not neces- +sarily support or dispute a preference for overdense environments +by lensing (and all massive) elliptical galaxies. However, the high +completeness of GAMA compared with SDSS may instead suggest +that our sample minimizes the apparent environmental preference. +The distinction of group association here could be affected by se- +lection bias, as those designated as isolated could in fact be groups +with satellite members beyond the GAMA flux limit. If this were +the case, there should be a systematic bias in isolated galaxies to- +ward higher redshift. Figure 11 shows that neither subsample of +group member or isolated candidates is significantly distinguished +in redshift or stellar mass. +With more data and better measurements than we have ac- +complished here, one may be able to compare observations to the +scatter in the upper plot of Figure 9 of Zehavi et al. (2018), where +for fixed dark halo mass, higher stellar-mass galaxies tend to exist +in denser environments. Note that the modeled mass components +here are calculated within the Einstein radius and not the full ex- +tent of the galaxy. The majority of the dark halo component should +extend well beyond the stellar halo, and these high-mass lensing +galaxies are more likely to exist in more massive dark matter haloes +(log(𝑀ℎ/ℎ−1𝑀⊙) ∼ 12 − 14) where the suggested environmen- +tal trend is less supported. The precision and numbers required +to test assembly bias will require more refinement of the methods +discussed in this study as well as the power of more sophisticated +surveys to come. +8.2 +Future Work: a Place for Ground-Based Observations +Realistic lens modeling by fitting mass and light profile parameters +is a complex problem with a large number of parameters. With even +the highest-quality ground-based imaging offered by the likes of the +Kilo-Degree Survey, the angular resolution is insufficient to con- +strain the individual model solutions to levels where one can make +strong inferences about the individual lens galaxies. There are sim- +ply too many solutions that fit the image to a high probability, which +inflates the uncertainty to levels that make it difficult for one to draw +conclusions from the inferred quantities. These uncertainties on a +single lens can be significantly constrained with the level of imag- +ing afforded by AO or space-based instruments. Figure 13 shows a +model solution for one of the lens models after being simulated with +the optics for three observatories: (i) VLT Survey Telescope (VST) +used for KiDS, which was the instrument that collected the original +image, (ii) LSST at the Vera Rubin Observatory (VRO) represent- +ing the next generation of ground-based observatories, and (iii) +Advanced Camera for Surveys (ACS) on the Hubble Space Tele- +scope. The same model-fitting procedure applied to HST images or +observations with adaptive optics (AO) of the same lensing galaxies +would result in error estimates an order of magnitude better than +the results we achieve here. Alternatively, future systematic mod- +eling of orders of magnitude more ground-based, lower-resolution +observations (as we expect to achieve with observatories like the +VRO) can result in similar precision. Constraints at the population +11.0 +11.2 +11.4 +11.6 +11.8 +12.0 +Stellar Mass log(M * /M +) +0.0 +0.1 +0.2 +0.3 +0.4 +0.5 +Redshift (z) +Isolated Galaxies +Group Galaxies +0.0 +2.5 +5.0 +7.5 +0 +5 +Figure 11. Redshifts and stellar masses of Autoz sample from GAMA-DR3 +StellarMassesLambdar v20 (Taylor et al. 2016) determined by stellar +population and separated by group-member and isolated galaxies according +to GAMA team internal GroupFinding catalogs (Robotham et al. 2011). +There is no clear distinction between the subsamples in either observable. +Figure 12. Stacked histogram. Quality scores for 41 of 42 candidates in +reference to data from GAMA GroupFinding catalogs (one candidate does +not have environment data). Location on the x-axis distinguishes "Isolated" +from group member galaxies, which are further separated by the rank in +projected distance from the center of mass of the group. A rank of 1 indicates +that the lens candidate is the central galaxy of the associated group. Colors +indicate the quality grade of models, with no color indicating models that +were not accepted. +level (made possible with these larger sample sizes) can enhance +higher-resolution individual measurements through Bayesian hier- +archical frameworks. Our work demonstrates the value of wide-field, +lower-resolution surveys as a complementary tool to the expensive +and hyper-competitive observing campaigns that are the default for +strong lens studies. +The next generation of spectroscopic surveys is already under- +way, e.g. the DEVILS deep survey on the AAT (Holwerda et al. +2021; Davies et al. 2018) and the DESI redshift survey. One can +MNRAS 000, 1–24 (2021) + +Rank in Projected Distance from Group Center +24 +A +B +16 +I D +Failed +12 +8 +0 +solated1 +2 +3 +4 +Fank15 +expect increased numbers of spectroscopic lensing candidates as +well as opportunities to identify the redshift of the potential back- +ground source. More comprehensive spectroscopic surveys are be- +ing planned with the 4MOST instrument (de Jong et al. 2012; De- +pagne & 4MOST consortium 2014). These planned surveys include +extra-galactic ones such as the two-tiered Wide Area Vista Extra- +galactic Survey (WAVES, Driver et al. 2019), the Optical, Radio +Continuum and HI Deep Spectroscopic Survey (ORCHIDSS, Dun- +can et al. in prep.), and a cosmological low-S/N wide-area survey +(CRS, Richard et al. 2019). These 4MOST surveys are expected to +achieve high completeness in their target fields and yield a boon of +spectroscopically confirmed strong lensing systems with the same +advantages exploited by the procedure outlined here at better spec- +tral resolution and wider fields. +Identifications of strong gravitational lenses through imaging +are also expected to increase in the near future with observations +by the likes of the Vera Rubin Observatory, Euclid, and the Roman +Space Telescope, in addition to improved machine learning tech- +niques. Following the discussion in Knabel et al. (2020), one ex- +pects the selection functions of the spectroscopic surveys and these +optical and near-infrared imaging surveys to show a limited im- +provement in overlap. The analysis presented here, however, shows +that in the overlap a useful subset of strong lenses can be utilized +for modeling by imaging and spectroscopy combined. +The lenses discussed here, and in future similar ground-based +efforts, are also ideal candidates for deeper follow-up observation +with higher-resolution imaging and spectroscopy. These follow-up +observations could include Integral Field Unit (IFU) observations +to measure the stellar population characteristics across the ellipti- +cal, chart the foreground lens galaxy kinematics, as well as study +the background source light and stellar population characteristics. +These considerations are more aligned with and have been suffi- +ciently described in the existing literature and will not be discussed +further here. +9 +CONCLUSIONS +We arrive at the following conclusions from our analysis of strong +lens candidates in the Kilo-Degree Survey using Autoz and PyAu- +toLens: +(i) Meaningful strong-lens studies can be conducted by applying +lens-modeling methods such as those we have outlined here to large +imaging and spectroscopic surveys. +(ii) Automated template-matching redshift algorithms like Au- +toz can be utilized to determine reliable background source red- +shifts required for lens modeling. Careful consideration should be +taken in cleaning the algorithm’s selection, following the recom- +mendations outlined in Section 7.1. +(iii) Limits of optical resolution in large ground-based surveys +present significant challenges to the uniqueness of solutions in our +Bayesian modeling of individual strong lenses. +(iv) As sample sizes grow, refinements to these techniques can +produce lensing measurements in quantities that will offer consider- +able statistical power. This approach is complementary to the more +detailed modeling of individual lenses that is possible with deeper +and higher resolution observations. +10 +ACKNOWLEDGEMENTS +SK acknowledges NASA Kentucky, National Science Foundation +(NSF), University of Louisville, and University of California, Los +Angeles, for financial and technical support. The material of this +work is based upon work supported by NASA Kentucky under +NASA award No: 80NSSC20M0047. This material is based upon +work supported by the National Science Foundation Graduate Re- +search Fellowship Program under Grant No. 2021325146. Any opin- +ions, findings, and conclusions or recommendations expressed in +this material are those of the author(s) and do not necessarily reflect +the views of the National Science Foundation. +DATA AVAILABILITY +KiDS +images +and +data +used +in +this +paper +are +avail- +able +from +the +Astro-WISE +Database +Viewer +Web +Ser- +vice (dbview.astro-wise.org). LinKS-specific data can be +found at the LinKS website (https://www.astro.rug.nl/ +lensesinkids/). The GAMA Autoz catalog is available from +GAMA-DR3 website (http://www.gama-survey.org/dr3/, +AATSpecAutozAll, SpecAll, LamdarStellarMasses, Sersic- +CatSDSS, and kcorr_auto_z00 catalogs) and the team internal +GroupFinding catalog for the full GAMA fields will be made avail- +able in GAMA-DR4 (Driver et al. in preparation). +SOFTWARE CITATIONS +This work uses the following software packages: +• Astropy (Astropy Collaboration et al. 2013; Price-Whelan +et al. 2018) +• Colossus (Diemer 2018) +• corner.py (Foreman-Mackey 2016) +• dynesty (Speagle 2020) +• matplotlib (Hunter 2007) +• numba (Lam et al. 2015) +• NumPy (van der Walt et al. 2011) +• PyAutoFit (Nightingale et al. 2021a) +• PyAutoLens (Nightingale & Dye 2015; Nightingale et al. +2018, 2021b) +• Python (Van Rossum & Drake 2009) +• scikit-image (Van der Walt et al. 2014) +• scikit-learn (Pedregosa et al. 2011) +• Scipy (Virtanen et al. 2020) +REFERENCES +Alpaslan M., et al., 2014, MNRAS, 440, L106 +Alpaslan M., et al., 2015, MNRAS, 451, 3249 +Artale M. C., Zehavi I., Contreras S., Norberg P., 2018, MNRAS, 480, 3978 +Astropy Collaboration et al., 2013, A&A, 558, A33 +Auger M. W., Treu T., Bolton A. S., Gavazzi R., Koopmans L. V. E., Marshall +P. J., Bundy K., Moustakas L. A., 2009a, ApJ, 705, 1099 +Auger M. W., Treu T., Bolton A. S., Gavazzi R., Koopmans L. V. E., Marshall +P. J., Bundy K., Moustakas L. A., 2009b, ApJ, 705, 1099 +Auger M. W., Treu T., Bolton A. S., Gavazzi R., Koopmans L. V. E., Marshall +P. J., Moustakas L. A., Burles S., 2010, ApJ, 724, 511 +Baldry I. K., et al., 2014, MNRAS, 441, 2440 +Behroozi P. S., Conroy C., Wechsler R. H., 2010, ApJ, 717, 379 +Behroozi P., et al., 2020, arXiv e-prints, p. arXiv:2007.04988 +MNRAS 000, 1–24 (2021) + +16 +S. Knabel +Figure 13. Upper left: Maximum log-likelihood model for G3629152 shown with pixel-scale 0.2 arcsec/pixel. Other images are simulated with identical +background sky and convolved with optics of upper right: VST (r-band PSF 0.65 arcsec, pixel scale 0.2), lower left: LSST at Rubin (PSF 0.5, pixel scale 0.2), +and lower right: ACS on HST (PSF 0.1, pixel scale 0.05). Imaging from space-based observatories or AO would allow for better model-fitting and tighter +uncertainties for future efforts. +Bolton A. S., Burles S., Koopmans L. V. E., Treu T., Moustakas L. A., 2006, +ApJ, 638, 703 +Brough S., 2011, preprint +Bruzual G., Charlot S., 2003, MNRAS, 344, 1000 +Chaves-Montero J., Angulo R. E., Schaye J., Schaller M., Crain R. A., +Furlong M., Theuns T., 2016, MNRAS, 460, 3100 +Contreras S., Zehavi I., Padilla N., Baugh C. M., Jiménez E., Lacerna I., +2019, MNRAS, 484, 1133 +Contreras S., Chaves-Montero J., Zennaro M., Angulo R. E., 2021, arXiv +e-prints, p. arXiv:2105.05854 +Cui W., Davé R., Peacock J. A., Anglés-Alcázar D., Yang X., 2021, Nature +Astronomy, 5, 1069 +Davies L. J. M., et al., 2018, MNRAS +Depagne E., 4MOST consortium t., 2014, preprint +Diemer B., 2018, The Astrophysical Journal Supplement Series, 239, 35 +Driver S. P., et al., 2009, Astronomy and Geophysics, 50, 050000 +Driver S. P., et al., 2011, MNRAS, 413, 971 +Driver S. P., et al., 2019, The Messenger, 175, 46 +Eisenstein D. J., et al., 2001, AJ, 122, 2267 +Etherington A., et al., 2022, MNRAS, 517, 3275 +Foreman-Mackey D., 2016, The Journal of Open Source Software, 1, 24 +Gavazzi R., Treu T., Rhodes J. D., Koopmans L. V. E., Bolton A. S., Burles +S., Massey R. J., Moustakas L. A., 2007, ApJ, 667, 176 +Hearin A. P., Watson D. F., van den Bosch F. C., 2015, MNRAS, 452, 1958 +Hearin A. P., Zentner A. R., van den Bosch F. C., Campbell D., Tollerud E., +2016, MNRAS, 460, 2552 +Holwerda B. W., et al., 2015, MNRAS, 449, 4277 +Holwerda B. W., et al., 2019, AJ, 158, 103 +Holwerda B. W., Knabel S., Steele R. C., Strolger L., Kielkopf J., Jacques +A., Roemer W., 2021, arXiv e-prints, p. arXiv:2104.11654 +Hopkins A. M., 2018, Publ. Astron. Soc. Australia, 35, 39 +Huang Y., Li Q., Zhang H., Li X., Sun W., Chang J., Dong X., Liu X., 2020, +arXiv e-prints, p. arXiv:2012.09338 +Hunter J. D., 2007, Computing in Science & Engineering, 9, 90 +Jacobs C., et al., 2019, ApJS, 243, 17 +Kelvin L. S., et al., 2012, MNRAS, 421, 1007 +Kinney A. L., Calzetti D., Bohlin R. C., McQuade K., Storchi-Bergmann T., +Schmitt H. R., 1996, ApJ, 467, 38 +Knabel S., et al., 2020, AJ, 160, 223 +Kuijken K., et al., 2019, A&A, 625, A2 +Lam S. K., Pitrou A., Seibert S., 2015, Proceedings of the Second Workshop +on the LLVM Compiler Infrastructure in HPC - LLVM ’15, pp 1–6 +Li R., et al., 2020, ApJ, 899, 30 +Lin L., Li C., He Y., Xiao T., Wang E., 2016, preprint +MNRAS 000, 1–24 (2021) + +SimulatedModel +10.0 +8.0 + 1.4 +6.0 +1.2 +4.0 + 1.0 +Intensity (eps) +2.0 +arcsec +0.8 +0.0 +-2.0 +0.6 +-4.0 +0.4 +-6.0 + 0.2 +-8.0 +-10.0 +-10.0-8.0-6.0-4.0-2.00.0 +2.0 +4.0 +6.0 +8.0 10.0 +arcsecSimulatedwithVSTOptics +10.0 +8.0 + 0.3 +6.0 +4.0 +2.0 +0.2 +Intensity (eps) +arcsec +0.0 +-2.0 +0.1 +-4.0 +-6.0 +0.0 +-8.0 +-10.0 +-10.0-8.0-6.0-4.0-2.00.02.04.0 +6.0 +8.010.0 +arcsecSimulatedwithVROOptics +10.0 +8.0 +0.4 +6.0 +4.0 +0.3 +2.0 +Intensity (eps) +arcsec +0.2 +0.0 +-2.0 +0.1 +-4.0 +-6.0 +0.0 +-8.0 +-10.0 +-10.0-8.0-6.0-4.0-2.00.02.04.06.0 +8.010.0 +arcsecSimulatedwithHSTOptics +10.0 +1.6 +8.0 +1.4 +6.0 +1.2 +4.0 +2.0 +arcsec +0.0 +-2.0 +0.6 +-4.0 +0.4 +-6.0 +0.2 +-8.0 +0.0 +-10.0 +-10.0-8.0-6.0-4.0-2.0 0.02.0 +4.0 +6.0 +8.0 10.0 +arcsec17 +Liske J., et al., 2015, MNRAS, 452, 2087 +Loveday J., et al., 2012, MNRAS, 420, 1239 +Mandelbaum R., Slosar A., Baldauf T., Seljak U., Hirata C. M., Nakajima +R., Reyes R., Smith R. E., 2013, MNRAS, 432, 1544 +Matthee J., Schaye J., Crain R. A., Schaller M., Bower R., Theuns T., 2017, +MNRAS, 465, 2381 +McCarthy K. S., Zheng Z., Guo H., Luo W., Lin Y.-T., 2021, arXiv e-prints, +p. arXiv:2104.13379 +Nightingale J. W., Dye S., 2015, Monthly Notices of the Royal Astronomical +Society, 452, 2940 +Nightingale J. W., Dye S., Massey R. J., 2018, Monthly Notices of the Royal +Astronomical Society, 478, 4738 +Nightingale J. W., Hayes R. G., Griffiths M., 2021a, Journal of Open Source +Software, 6, 2550 +Nightingale J. W., et al., 2021b, Journal of Open Source Software, 6, 2825 +Pedregosa F., et al., 2011, Journal of Machine Learning Research, 12, 2825 +Petrillo C. E., et al., 2017, MNRAS, 472, 1129 +Petrillo C. E., et al., 2019a, MNRAS, 482, 807 +Petrillo C. E., et al., 2019b, MNRAS, 484, 3879 +Planck Collaboration 2015, preprint +Posti L., Fall S. M., 2021, arXiv e-prints, p. arXiv:2102.11282 +Price-Whelan A. M., et al., 2018, AJ, 156, 123 +Richard J., et al., 2019, The Messenger, 175, 50 +Robotham A. S. G., et al., 2011, MNRAS, 416, 2640 +Sérsic J. L., 1968, Atlas de galaxias australes. Observatorio Astronomico, +Universidad de Cordoba, Argentina +Somerville R. S., Popping G., Trager S. C., 2015, preprint +Sonnenfeld A., Jaelani A. T., Chan J., More A., Suyu S. H., Wong K. C., +Oguri M., Lee C.-H., 2019, A&A, 630, A71 +Speagle J. S., 2020, Monthly Notices of the Royal Astronomical Society, +493, 3132 +Speagle J. S., et al., 2019, MNRAS, 490, 5658 +Suyu S. H., Marshall P. J., Hobson M. P., Blandford R. D., 2006, Monthly +Notices of the Royal Astronomical Society, 371, 983 +Taylor R., Davies J. I., Jachym P., Keenan O., Minchin R. F., Palous J., Smith +R., Wunsch R., 2016, preprint +Treu T., Stiavelli M., Casertano S., Møller P., Bertin G., 2002, ApJ, 564, +L13 +Treu T., Gavazzi R., Gorecki A., Marshall P. J., Koopmans L. V. E., Bolton +A. S., Moustakas L. A., Burles S., 2009, ApJ, 690, 670 +Treu T., Auger M. W., Koopmans L. V. E., Gavazzi R., Marshall P. J., Bolton +A. S., 2010, ApJ, 709, 1195 +Van Rossum G., Drake F. L., 2009, Python 3 Reference Manual. CreateS- +pace, Scotts Valley, CA +Van der Walt S., Schönberger J. L., Nunez-Iglesias J., Boulogne F., Warner +J. D., Yager N., Gouillart E., Yu T., 2014, PeerJ, 2, e453 +Velander M., et al., 2014, MNRAS, 437, 2111 +Virtanen P., et al., 2020, Nature Methods, 17, 261 +Warren S. J., Dye S., 2003, The Astrophysical Journal, 590, 673 +Zehavi I., Contreras S., Padilla N., Smith N. J., Baugh C. M., Norberg P., +2018, ApJ, 853, 84 +Zehavi I., Kerby S. E., Contreras S., Jiménez E., Padilla N., Baugh C. M., +2019, ApJ, 887, 17 +Zentner A. R., Hearin A. P., van den Bosch F. C., 2014, MNRAS, 443, 3044 +de Jong R. S., et al., 2012, preprint +de Jong J. T. A., Verdoes Kleijn G. A., Kuijken K. H., Valentijn E. A., 2013, +Experimental Astronomy, 35, 25 +de Jong J. T. A., et al., 2015, A&A, 582, A62 +de Jong J. T. A., et al., 2017, A&A, 604, A134 +van der Walt S., Colbert S. C., Varoquaux G., 2011, Computing in Science +Engineering, 13, 22 +APPENDIX A: PREPARING DATA FOR MODELING +Images and weight maps are 101 × 101 pixel (∼ 20 × 20 𝑎𝑟𝑐𝑠𝑒𝑐2) +cutouts from coadded images of KiDS tile observations acquired +from the publicly available Astro-WISE Database Viewer Web Ser- +vice4. g- and r-band images are cut out centered on the object’s +RA and DEC, recentered to the brightest pixel in the central (lens) +galaxy light profile, and converted to eps (electrons per second) for +modeling. KiDS image pixel values in the Astro-WISE Database +are given in calibrated flux units relative to the flux corresponding +to magnitude 0 and are converted to "brightness" units of electron +counts by multiplying by the tile’s average gain, which includes +additional factors necessary for this conversion. PyAutoLens is by +default set to be optimally utilized with units of electrons per sec- +ond (eps), which is acquired by dividing by the exposure time (1800 +seconds for r-band, 900 for g-band). +PyAutoLens requires input of the PSF and noise map for each +image. The inverse square root of the weight map corresponding to +the cutout image gives the rms noise, which is converted to electron +counts and squared to recreate the background sky. We then add this +image to the corresponding cutout image and take the square root +to give the noise map, after which we convert to eps. We generate +a Gaussian PSF for each image from the average FWHM PSF for +each image. +We next mark pixel-positions of the distorted images of the +lensed background source in each image, when visible, using a +GUI distributed with PyAutoLens. During a lens model fit, PyAu- +toLens casts aside all mass models where these image-pixel posi- +tions do not trace within a designated threshold of one another in the +source plane. This narrows the parameter space that is searched and +ensures that the model fits the observed image features of interest. +We generate three masks for the three searches with each can- +didate: (i) lens mask — a circular aperture tailored to show only the +lens galaxy (on the order of but usually slightly less the effective +radius, typically around 1-1.3 arcseconds); (ii) source mask — a +circular annular aperture showing only the light we determine to +be the lensed background source features (with inner radius about +the size of the circular lens mask and outer radius around 3 arcsec- +onds); and (iii) full mask — a circular aperture of typically around 3 +arcseconds that includes most of the light from the lens and source +features and masks as many peripheral contaminants as possible. +APPENDIX B: LENS MODELING PIPELINE +This section details continues the description of our lens modeling +methods summarized in Section 4.1. Through experimentation, we +have designed a pipeline composed of a chain of three Dynesty +searches that we use as a template for fitting each lens. The variety +of lensing configurations, image quality, etc. force us to tailor aspects +of each model-fit individually, in particular alternating the masks +that segment the foreground lens light and distorted background +source light. In order to institute the least bias possible, we allow +the models to probe a wide range of possible solutions for each +parameter. The shape of the prior distribution has significant effects +on the performance of the search. We use uniform, log uniform, and +Gaussian functions depending on the parameter and informative +auxiliary observations. In the following sections, we describe this +three-step automated pipeline, where from here on we refer to a +"search" as a model-fit performed by the non-linear search Dynesty. +Each subsequent search in the chain has more complexity in the +form of additional parameters, which we balance in computational +4 dbview.astro-wise.org +MNRAS 000, 1–24 (2021) + +18 +S. Knabel +time by passing priors from previous search outputs. For each non- +leanear search in the chain, the priors are described in Table B1, +and the Dynesty settings are given in Table B2. +B1 +Search 1 — Lens Light +Search 1 is the simplest and quickest of the three searches and +focuses on returning an accurate lens light profile. The subtraction +of this modeled light from the observed image should then show +the lensed features of the background source. This search fits an +elliptical Sérsic profile (Sérsic 1968), +𝐼(𝑅) = 𝐼𝑒𝑒−𝑏𝑛 [( 𝑅 +𝑅𝑒 )1/𝑛−1] +(B1) +where 𝑅 is angular radius from the center of the profile, 𝐼𝑒 is +the intensity at the effective radius 𝑅𝑒, 𝑏𝑛 ≈ 2𝑛 − 0.327, and 𝑛 +is the Sérsic index. PyAutoLens generates an image from these +parameters in the image-plane and fits to the observed r-band image. +The purpose of this search is to infer a high likelihood Sérsic lens +light model, which serves two purposes for Search 2: (i) it provides a +lens-light subtracted image and; (ii) it provides lens light priors that +are passed to subsequent searches. Because the image is centered +during pre-processing, the distribution can be initialized with fairly +tight constraints. Elliptical components, 𝜖1 and 𝜖2, are defined as +𝜖1 = 𝜖𝑦 = 1 + 𝑏/𝑎 +1 − 𝑏/𝑎 sin 2𝛼 +(B2) +𝜖2 = 𝜖𝑥 = 1 + 𝑏/𝑎 +1 − 𝑏/𝑎 cos 2𝛼 +(B3) +where b and a are the semi-major and -minor axes of the ellipse, +and 𝛼 is the position angle. The intensity is parametrized according +to electrons per second and therefore takes a wide log-uniform dis- +tribution. The Sérsic index prior covers a wide range of reasonable +values with a uniform distribution. +For the r-band images, many of the lensed background source’s +features are positioned within the lens galaxy’s effective radius. +Search 1 therefore struggles to deblend the lens and source light, +and the distorted arcs of background source light are attributed to the +foreground lens galaxy. In some cases, this leads to a model solution +that describes a lens light profile that is very large and very elliptical. +To mitigate this systematic effect, we use the aforementioned lens +mask for Search 1 and constraints on the effective radius to assist +the search to focus on fitting the lens light and not the source light. +The residuals and uncertainties of this search therefore tend to be +quite high. In fact, the residuals often outline the lensed images of +the source itself, and the resulting maximum log-likelihood is lower +than the value inferred in the second and third searches. +B2 +Search 2 — Lens Mass and Source Light +Search 2 focuses on the light from the background source. This +component is modeled as a spherical exponential light profile in +the source plane defined at the source redshift. The exponential +light profile corresponds to the simple 𝑛 = 1 case of Equation +B1 and is parameterized using its (source-plane) center, effective +radius, and intensity. With higher-resolution imaging data, the back- +ground source light profile could be fit with a more detailed model. +The background source center coordinates are initialized to values +within 2 arcseconds of the line of sight of the foreground lens center. +The intensity of the background source light is again set to a wide +log-uniform prior distribution, as for the lens light in Search 1. The +source effective radius is initialized with a Gaussian distribution +around a typical disk galaxy size, as discussed in Section 4.2. To +map coordinates to the source plane, the lens galaxy’s total mass is +modeled as a singular isothermal elliptical (SIE) profile. The mass +profile’s Einstein radius prior is a wide Gaussian distribution cen- +tered at 1.0 arcsecond with a hard upper limit of 2.5 arcseconds. The +center and elliptical components of the SIE are paired with the light +profile with the assumption that the ellipses will be aligned. The +lens light profile takes prior distributions passed from the results +of Search 1. By fixing the center of the lens profiles to the results +of Search 1, the lens model in this search is reduced to 10 free pa- +rameters. This, in addition to taking informed Gaussian priors from +Search 1 for the lens light, helps the model to focus on solutions that +fit the source-light instead of systematic solutions that fit artefacts in +the data. We use the annular source mask that removes the lens light +from the observed image and therefore further focuses the model +on fitting the source light. We also utilize PyAutoLens’s position +resampling functionality, whereby the brightest pixels in the lensed +source are marked (via a GUI). Again, the results of this search are +passed as priors to Search 3. +B3 +Search 3 — Combined Lens and Source Models +Search 3 fits every component of the system. To model the fore- +ground lens, we use a combined elliptical Sérsic mass-light profile +for the stellar component and an elliptical NFW profile for the dark +matter halo. Background source light is modeled again as a spheri- +cal exponential profile. Priors are passed from Search 2 (see Table +B1), except for the dark matter halo profile and stellar mass-to-light +ratio. The prior distributions for these crucial parameters are de- +termined by calculating central and limiting values according to a +more careful process, as described in Section 4.2. The full mask +including all the lens and source features is used to remove back- +ground features and other contaminants that exist in the periphery, +which saves computational time. Lensed image positions are again +used to discard unphysical mass models. This final search produces +a reasonable fit to the complexities introduced by each component +and gives uncertainties on each of the inferred quantities. Additional +disk and bulge components, cores, and multiple galaxies at different +planes along the line of sight can be fitted and would allow more +precise and realistic models. These improvements to realism are +unhelpful here given the quality of imaging available for the objects +in question but would be simply applied in future studies following +the same principles outlined in our strategy. +APPENDIX C: HIGHEST-QUALITY MODEL RESULTS +Figures C1-C4 show the observed image, model image, and spectra +for some of the most successful models. +APPENDIX D: SPECTRUM QUALITY CONTROL +We return to the specific cases described in Section 3.2 to see how +they affected our final quality scoring and subsample selection in +the interest of retaining the most true positives while minimizing +the inclusion of false positives. +MNRAS 000, 1–24 (2021) + +19 +# Free +Search +Parameters +Fit +Profile +Prior +Probability Density Function +1 +7 +Lens Light +Elliptical Sérsic +Center (y, x) +Uniform (-0.3 - 0.3 arcsec) +Elliptical Comps (𝜖1, 𝜖2) +Gaussian (mean = 0.0, 𝜎 = 0.3) +Intensity +Log Uniform (10−6 - 106 eps) +Effective Radius +Gaussian (GAMA-DR3 r mean and 𝜎 +arcsec or SLACS 7 kpc ± 3.3 at lens +distance, upper limit = mean + 3𝜎 ) +Sérsic Index +Uniform (0.5 - 8.0) +2 +10 +Lens Light +Elliptical Sérsic +Center (y, x) +Prior Passed from Search 1 (fixed) +Elliptical Comps (𝜖1, 𝜖2) +Prior Passed from Search 1 (Gaussian) +Intensity +Prior Passed from Search 1 (Gaussian) +Effective Radius +Prior Passed from Search 1 (Gaussian) +Sérsic Index +Prior Passed from Search 1 (Gaussian) +Lens Stellar Mass +Elliptical Isothermal +Center (y, x) +Paired to Lens Light Prior (fixed) +Elliptical Comps (𝜖1, 𝜖2) +Paired to Lens Light Prior (Gaussian) +Einstein Radius +Gaussian (mean = 1.0, 𝜎 = 0.5, +limit = 0 - 2.5 arcsec) +Source Light +Spherical Exponential +Center (y, x) +Uniform (-2.0 - 2.0 arcsec) +Intensity +Log Uniform (10−6 - 106 eps) +Effective Radius +Gaussian (7.5 kpc ±2.5 at source +distance, upper limit = mean + 3𝜎) +3 +14 +Lens Stellar Light +Elliptical Sérsic +Center (y, x) +Prior Passed from Search 2 (fixed) +and Mass +Elliptical Comps (𝜖1, 𝜖2) +Prior Passed from Search 1 (Gaussian) +Intensity +Prior Passed from Search 2 (Gaussian) +Effective Radius +Prior Passed from Search 2 (Gaussian) +Sérsic Index +Prior Passed from Search 2 (Gaussian) +Mass-to-Light Ratio +Log Uniform (Limits calculated) +Lens Dark Mass +Elliptical NFW +Center (y, x) +Paired to Stellar Mass prior (fixed) +Elliptical Comps (𝜖1, 𝜖2) +Gaussian (mean = 0.0, 𝜎 = 0.3) +𝜅𝑠 +Uniform (0.0 - 1.0) +Scale Radius +Gaussian (calculated from SLACS-IV +mean and 𝜎) +Source Light +Spherical Exponential +Center (y, x) +Prior Passed from Search 2 (Gaussian) +Intensity +Prior Passed from Search 2 (Gaussian) +Effective Radius +Prior Passed from Search 2 (Gaussian) +Table B1. Details about model searches and priors for three-step lens model-fitting with PyAutoLens. Each phase fits a number of free parameters that model +light and mass profiles of the lens and source galaxies by exploring the parameter space according to the prior’s probability density function. Parameters fit in +Searches 1 and 2 are input as Gaussian or fixed priors for subsequent searches. "Elliptical Components" are related to the axis ratio and position angle as in +Equations B2 and B3. See Sections B and 4.2 for more details about searches, profiles, and priors. +Search +n live points +Evidence Tolerance +Steps per Walk +Acceptance Fraction +Positions Threshold +Sub-Grid Size +1 +200 +0.5 +10 +0.3 +N/A +2×2 sub-pixels +2 +300 +0.25 +10 +0.3 +1.5 arcsec +2×2 sub-pixels +3 +500 +0.25 +10 +0.3 +1.5 arcsec +2×2 sub-pixels +Table B2. Dynesty non-linear search settings for each of the three searches of model-fitting. These settings balance computational cost with a thorough +exploration of parameter space. Relaxed settings (e.g. low n live points and high evidence tolerance) are useful for expediting initial fits that inform later fits. +The trade-off is less well-defined uncertainty and a chance that the global maximum likelihood fit has been missed in favor of a local one. See Section 4.1 for a +thorough description of PyAutoLens and Dynesty search settings. +D1 +When there are Overlapping Emission or Absorption +Lines... +Almost half of the candidates (20 of 42) we selected initially by +Autoz output had overlapping line features of some kind in their +spectrum. 12 of these were overlapping absorption features; 8 were +emission features. 6 of the 19 candidates that were accepted follow- +ing critical quality control had overlaps. The presence of an overlap +affected the scoring of the individual spectrum, which was accepted +only if the other background source line features were well-shown. +We classify the cases of overlap as "on-template" or "off-template" +in reference to the background source template. "Off-template" over- +laps are cases when the overlapping line is an emission or absorption +feature for a background source PG or ELG respectively, as opposed +to "on-template" overlaps, where the overlap is emission or absorp- +tion for ELG or PG respectively. 9 of the 20 cases of overlap were +MNRAS 000, 1–24 (2021) + +20 +S. Knabel +4000 +5000 +6000 +7000 +8000 +Wavelength (A) +0.0 +2.5 +5.0 +7.5 +10.0 +12.5 +15.0 +17.5 +20.0 +Flux (10 +17 erg/s/cm2/A) +G138582_2828 GAMA Spectrum - Lens and Source Type and Redshifts (ELG + ELG; 0.325, 0.433) +Spectrum +Error +Hb +OII +OIII4959 +OIII5007 +Hb +OII +OIII4959 +OIII5007 +4000 +5000 +6000 +7000 +8000 +9000 +10000 +Wavelength (A) +0 +2 +4 +6 +8 +Flux (10 +17 erg/s/cm2/A) +G138582_2828 SDSS Spectrum - Lens and Source Type and Redshifts (ELG + ELG; 0.325, 0.433) +Figure C1. G138582. A-Grade. Upper left: The observed image shows a single bright elongated feature in the lower left of the foreground lens galaxy profile +with a tail in the upper part of the feature. Upper right: The model image correctly captures the shape of the image with lensing characteristics. Lower: The +GAMA and SDSS spectra both show reasonably strong emission lines (H𝛽, [O II], [O III]) for the foreground lens galaxy at 𝑧 = 0.325 (dotted) and the +background source galaxy at 𝑧 = 0.433 (dashed). Foreground lens CaH&K absorption lines are also easily identified but are left ummarked here to show the +presence of emission lines for this spectrum’s ELG+ELG AUTOZ template match. +"on-template". The other 11 were "off-template". The 6 overlapping +cases that were retained in the final subsample of 19 graded models +consisted of 1 on-template and 5 off-template overlaps. +7 of the 8 candidates with overlapping emission features in- +clude background source ELGs (3 PG+ELG and 4 ELG+ELG), and +one is a background source PG (ELG+PG). Two of these are retained +in the 19 graded models. Recall from Section 3.2 that all emission +line overlaps are between the lens [O III]𝜆𝜆4959,5007 couplet and +the source [O II]𝜆3727. It appears that these emission lines can have +a significant effect even when one of the templates is a PG. Of the 12 +absorption feature overlaps, 8 were PG+ELG, 2 were ELG+ELG, +and 2 were PG+PG. 5 of these off-template PG+ELG absorption +line overlaps make our final selection of 19 candidates, with a grade +B, two C’s, and two D’s. One of the highest-scoring candidates +MNRAS 000, 1–24 (2021) + +G138582KiDSImage +4.0 +1.0 +2.0 +0.8 +arcsec +Intensity +0.0 +0.4 +-2.0 +0.2 +0.0 +-4.0 +-4.0 +-2.0 +0.0 +2.0 +4.0 +arcsecG138582Model lmage +4.0 +0.8 +2.0 +arcsec +0.0 +0.4 +-2.0 +0.2 +-4.0 +-4.0 +0.0 +-2.0 +0.0 +2.0 +4.0 +arcsec21 +4000 +5000 +6000 +7000 +8000 +Wavelength (A) +0 +2 +4 +6 +8 +10 +12 +Flux (10 +17 erg/s/cm2/A) +G250289_2730 GAMA Spectrum - Lens and Source Type and Redshifts (PG + ELG; 0.401, 0.720) +Spectrum +Error +CaH +CaK +Hb +Mg5175 +Na5892 +Hb +OII +OIII4959 +OIII5007 +4000 +5000 +6000 +7000 +8000 +9000 +10000 +Wavelength (A) +0 +1 +2 +3 +4 +Flux (10 +17 erg/s/cm2/A) +G250289_2730 SDSS Spectrum - Lens and Source Type and Redshifts (PG + ELG; 0.401, 0.720) +Figure C2. G250289. B-Grade. Upper left: The observed image shows a doubly imaged source with a near-elliptical shape in the upper left with respect to the +foreground lens and an arc mirrored across the lens to the lower right that blends somewhat with the foreground lens light. Upper right: The model reconstructs +the locations of both images, but the mirrored image in the lower right lacks the stretched elongated shape, which may be an effect of internal structure that +is unaccounted for in the model. Lower: The absorption features shown with dotted lines (CaH, CaK, H𝛽, Mg, and Na) of the foreground lens galaxy at 𝑧 = +0.401 are particularly strong. Emission of [O II] from the source galaxy at 𝑧 = 0.720 appears in both spectra with dashed lines, as well as weaker features from +H𝛽 and [O III]. However, the SDSS spectrum appears to show a stronger [O III]𝜆4959 than [O III]𝜆5007, which should not be the case. The weak background +source-flux could be because much of the the upper left source feature in the observed image is outside the 1- and 1.5-arcsecond GAMA and SDSS apertures. +(G250289, PG+ELG) had an overlap of foreground-lens H𝛽 and +background-source CaK absorption features, but the emission lines +from the background source were well-defined and gave confidence +to the redshift determination. This case is a bit odd considering the +background galaxy was fit to an ELG template and would presum- +ably be most heavily weighted by emission features. None of the +ELG+ELG or PG+PG configurations with overlaps were accepted. +One of the two candidates noted in Section 3 that were removed +from the Holwerda et al. (2015) sample had overlapping features. +The other had a reasonable spectrum and failed for other reasons. +MNRAS 000, 1–24 (2021) + +4.0 +G250289KiDSImage +2.0 +arcsec +0.0 +-2.0 +-4.0 +-4.0 +-2.0 +0.0 +2.0 +4.0 +arcsec4.0 +G250289ModelImage +4 +2.0 +arcsec +0.0 +-2.0 +1 +4.0 +-4.0 +-2.0 +0.0 +2.0 +4.0 +arcsec22 +S. Knabel +4000 +5000 +6000 +7000 +8000 +Wavelength (A) +0 +5 +10 +15 +20 +25 +Flux (10 +17 erg/s/cm2/A) +G62734_539 GAMA Spectrum - Lens and Source Type and Redshifts (PG + ELG; 0.274, 0.597) +Spectrum +Error +CaH +CaK +Hb +Mg5175 +Na5892 +Hb +OII +OIII4959 +OIII5007 +Figure C3. G62734. B-Grade. Dark mass poorly constrained, so not included in further analysis alongside the other A- and B-grade models. Upper +left: The observed image shows an image in the lower right with respect to the foreground lens profile. Upper right: The shape and location of the lensed +source feature in the lower right are well-fit in the model image, but there is some extra light surrounding the lensed source feature that may be due to the +less-sophisticated spherical exponential light profile that we use to model the source light. The exact reconstruction of the source light profile is not the main +goal of this exercise, though higher resolution imaging would make it worth further constraining with more flexible priors. Lower: Foreground lens absorption +features (CaH, CaK, H𝛽, Mg, and Na) are clearly shown with dotted lines at 𝑧 = 0.274, and weak emission features can be identified with dashed lines at 𝑧 = +0.597. +D2 +When the Lens is described as an Emission Line Galaxy... +As discussed in Section 3.2, the case of an emission line galaxy +acting as the foreground lens is less likely than a case where a +passive galaxy acts as the lens. Only 3 ELG+ configurations were +retained in the graded subsample of 19 candidates, two of which +were low-scoring D-grades. Only one of the ELG+PG configu- +rations was accepted and given a D-grade. Figure D1 shows the +foreground+background configurations for the 21 candidates in the +final selection in the same manner shown in Figure 2, now with +quality grades. A, B, C, and D grades are blue, green, purple, and +red respectively. Interestingly, one of the highest scoring (A-grade +candidate G138582) candidates was one of the ELG+ELG matches. +As shown in Appendix Figure C1, the emission lines from lens and +source are clearly determined, and the resulting model was one of +the most successful of this study. This example highlights the poten- +tial value of including (though with critical evaluation) the ELG+ +foreground lens template configurations in the selection. Still, the +template configurations shown in Figure D1 mostly reaffirm the +validity of the assumption that passive large elliptical galaxies pro- +vide the clearest and most usable foreground lenses. Further, since +more background source +ELG template configurations have higher +scores relative to +PG configurations, this again shows that the flux +from strong emission lines in the background source is more de- +tectable than the continuum and absorption features of a passive +galaxy. +D3 +When Source Emission Lines are Redshifted Beyond +Observed Wavelength Range... +27 of the initial 42 Autoz spectra had +ELG configurations (i.e. +background source is an emission line galaxy), 8 of which had +H𝛽 and [O III]𝜆𝜆4959,5007 emission lines redshifted beyond the +GAMA upper wavelength limit of 8850Å. These features would be +present in the longer-wavelength upper range of the SDSS-BOSS +spectrum for all 27 +ELG candidates, but not all were measured in +SDSS-BOSS. 3 of the 19 candidates had all three above line features +redshifted beyond the survey upper wavelength limit. Because these +3 objects were also measured with SDSS-BOSS spectroscopy and +MNRAS 000, 1–24 (2021) + +G62734KiDSImage +4.0 +8 +2.0 +7 +arcsec +0.0 +中 +Intensity +4 +m +-2.0 +2 +-4.0 +-4.0 +-2.0 +0.0 +2.0 +4.0 +arcsecG62734Model Image +4.0 +2.0 +6 +arcsec +0.0 +1 +-2.0 +2 +-4.0 +-4.0 +-2.0 +0.0 +2.0 +4.0 +arcsec23 +4000 +5000 +6000 +7000 +8000 +Wavelength (A) +0 +2 +4 +6 +8 +10 +12 +Flux (10 +17 erg/s/cm2/A) +G513159_2123 GAMA Spectrum - Lens and Source Type and Redshifts (PG + ELG; 0.289, 0.701) +Spectrum +Error +CaH +CaK +Hb +Mg5175 +Na5892 +Hb +OII +OIII4959 +OIII5007 +Figure C4. G513159. B-Grade. Upper left: The observed image shows a feature around 3 arcseconds away from the central foreground lens profile that may be +a lensed source feature. Upper right: The model successfully accounts for the position and flux of the extra light through lensing. Lower: The GAMA spectrum +shows strong CaH and CaK features with dotted lines for the foreground lens galaxy at 𝑧 = 0.289 and possible emission line features ([O II] and [O III]) with +dashed lines at 𝑧 = 0.701. Some expected features are plotted but not well-defined in the spectrum. +Figure D1. Stacked histogram of the four possible configurations of PG and +ELG, written as foreground+background, separated by their quality grade +(A, B, C, D) as described in Section 5. The large majority of successful +models were composed of a passive foreground lens galaxy and emission +line background source galaxy, which is expected. Other configurations are +less likely, but one of the two A-grade models came from an ELG+ELG +configuration. +included in GAMA-DR3 SpecAll, their emission lines redshifted +beyond 8850Å were detectable, but the AUTOZ match did not have +access to those wavelengths. These were 2 C-grades and a D-grade. +D4 +When Primary Redshift is Background Source... +10 of the initial 42 Autoz spectra featured higher cross-correlation +peaks to the background source than to the foreground lens (i.e. +𝜎1 is the match to the background source). 2 of those are included +in the final graded 19 models. These two cases are shown in Ta- +ble 5. One of these is one of the two highest-scoring candidates +(A-grade, candidate G323152, PG+ELG). G323152 represents the +case described in the section 3.2 where very strong emission lines +from the background source are interpreted as the primary redshift +match instead of the lower redshift passive continuum. The other +candidate with 𝜎1 assigned to the background source flux is a D- +grade with ELG+PG configuration. As mentioned before, we expect +this configuration with the primary match to the background source +redshift to be far less likely. Still, as with the ELG+ELG matches +discussed in the previous section, the A-grade example of this case +reinforces the value of including the Autoz configurations where +𝜎1 is at higher redshift than 𝜎2. +MNRAS 000, 1–24 (2021) + +G513159KiDSImage +4.0 +0.8 +2.0 +0.6 +(eps) +arcsec +0.0 +Intensity +0.4 +0.2 +-2.0 +0.0 +-4.0 +-4.0 +-2.0 +0.0 +2.0 +4.0 +arcsecG513159Model lmage +4.0 +8°0 +2.0 +0.6 +Intensity (eps) +arcsec +0.0 +0.4 +-2.0 +0.2 +-4.0 +-2.0 +0.0 +2.0 +4.0 +0.0 +-4.0 +arcsecSpectal Template Pair Types by Grade +12 +A +-B +14 +90 +6 +0 +PG + ELG +PG + PG +ELG + ELG +ELG + PG +cace24 +S. Knabel +GAMA ID +Type +𝑧1 +𝑧2 +𝜎1 +𝜎2 +R +G544226 +PG+ELG +0.227 +0.650 +9.393 +7.240 +2.122 +PG+ELG +0.650 +0.227 +6.294 +6.410 +0.650 +G262874 +ELG+ELG +0.386 +0.859 +6.222 +3.422 +1.217 +ELG+PG +0.386 +0.195 +9.339 +4.817 +1.416 +Table E1. Duplicate Autoz entries for LinKS lens candidates. Boldface text +indicates the selected entry. Type refers to foreground+background template +matches. 𝑧1 and 𝑧2 refer to redshift matches corresponding to Autoz cross- +correlation peaks 𝜎1 and 𝜎2. R is a parameter that weights 𝜎2 to third and +fourth matches. +D5 +Additional Curiosities, Overlaps, Failures of our +Utilization of AUTOZ +Two of the ELG+PG configurations show the lens [O III]𝜆4959 +line straddled by the H and K lines of the background source PG. +This is a case where a "peak" between the two absorption valleys +can be mistakenly considered an emission line feature. These are 2 +of 4 foreground lens redshift matches below z∼0.1. The other two +have overlaps between lens [O III]𝜆5007 and source [O II]𝜆3727. +A revision of the initial selection strategy could have extended the +redshift cutoff to z∼0.1 with no change to the sample. Two others +appear to have emission lines fairly close to absorption lines, which +might also give the impression of a peak or valley where it actually +does not exist. One of these was accepted in the 19 and was given a +grade of D. +APPENDIX E: SUBSAMPLE SELECTION AND CONTEXT +We find that the majority of machine learning candidates did not +pass our selection criteria covering Autoz output parameters. This +is predictable in light of the results of Knabel et al. (2020). +From the 421 LinKS candidates in the GAMA equatorial re- +gions, there are 348 matching Autoz entries (including duplicates) +for 300 unique LinKS candidates. 59 of these entries pass the +𝑅 ≥ 1.2 criterion, and 56 of these have galaxy-galaxy template +matches. Four of those entries are duplicates, leaving 52 candi- +dates (including 6 from Knabel et al. 2020). We remove 12 of these +through our redshift criteria, which leaves 42 (40 unique) LinKS +Autoz foreground+background redshift matches. The two dupli- +cates are shown in Table E1, with the accepted matches in bold text. +For G544226, both entries show a PG template match at redshift +𝑧 = 0.227 with an ELG at redshift 𝑧 = 0.650. The accepted entry +shows higher 𝜎1, 𝜎2, and R, and it attributes the primary redshift +match to the foreground lens galaxy. The other entry is an example +where 𝜎1 can refer to the background source galaxy and 𝜎2 to the +foreground lens galaxy, effectively reversing which shows "better" +match while still identifying the redshifts and type correctly. Note +that 𝜎1 and 𝜎2 for the rejected entry are quite close (6.294 and 6.410 +respectively). Both entries for the other duplicate candidate show +the same primary match. The entry that is rejected has a secondary +match to an ELG template at much closer redshift, which is most +likely a false match. We remove the one LinKS candidate with a +low redshift success probability and are left with 39 LinKS Autoz- +selected candidates, six of which were included in the final LinKS +candidate selection of Knabel et al. (2020). +32 of 48 Li-BG candidates in the GAMA equatorial fields +have a match in Autoz, with 53 entries including duplicates. 8 +candidates (with no duplicates) are selected by the 𝑅 criterion. 5 +of those 8 candidates are removed by our redshift criteria, leaving +3 unique candidates for analysis. One GalaxyZoo candidate has a +match in the Autoz catalog, but it does not pass selection criteria +for followup. +In order to briefly contextualize this selection in reference to +some of the results and conclusions drawn in Knabel et al. (2020), +we show the Autoz sample of 42 candidates selected in this work +in Figure E1 with circular markers in comparison with the candi- +dates discussed in Knabel et al. (2020) shown in the background +with X’s. Stellar mass estimates and lens redshifts shown here are +from GAMA-DR3 StellarMassesLambdar catalog. The Autoz +sample is slightly lower in stellar mass on average than the LinKS +subsample as selected in Knabel et al. (2020), with a mean and +median log 𝑀∗ of (11.50, 11.51) compared to (11.61, 11.67). A +Kolmogorov-Smirnov test of the stellar masses between the LinKS +Autoz subsample and the LinKS subsample as selected in Knabel +et al. (2020) results in a KS-metric of 0.352 with a p-value of 0.007, +indicating a statistically significant disparity between the masses +of the two selections. In fact, when compared to the GAMA spec- +troscopy subsample as selected in Knabel et al. (2020), the KS-test +results are almost identical (metric 0.353, p-value 0.007). The bulk +of Autoz candidates hovers in the parameter space overlapping the +upper mass end of the GAMA spectroscopic candidates and the +lower mass end of the LinKS from Knabel et al. (2020) candidates, +which is reasonable if they are to be large enough to have dis- +tinguishable features for identification by machine learning while +being small enough to have a higher chance of flux from the lensing +features being collected in the 1-arcsecond GAMA spectroscopic +fiber aperture. +Two candidates in the Autoz sample have 𝜎2 and R values that +would place them in the selection space defined for the Holwerda +et al. (2015) blended spectra candidates. One of them (G184530) +was not selected in that study because it is an ELG+PG configu- +ration (i.e. the emission line match is at closer redshift). The other +(G544226) was removed because Holwerda et al. (2015) removed +candidates near the alias of (1 + 𝑧1)/(1 + 𝑧2) = 1.343 ± 0.002, +corresponding to an overlap between redshifted [O II]𝜆3727 and +[O III]𝜆5007 emission lines. G544226 then would have been the +one overlap between the GAMA spectroscopic and LinKS machine +learning catalogs in Knabel et al. (2020) if it had not been removed. +G544226 made the selection for high-quality candidates in Knabel +et al. (2020). With a redshift of 𝑧 = 0.227 and log 𝑀∗ = 11.29, +it existed squarely in the overlap of parameters space between the +GAMA spectroscopy and LinKS machine learning candidates. +This paper has been typeset from a TEX/LATEX file prepared by the author. +MNRAS 000, 1–24 (2021) + +25 +9.5 +10.0 +10.5 +11.0 +11.5 +12.0 +Stellar Mass log(M * /M +) +0.0 +0.1 +0.2 +0.3 +0.4 +0.5 +0.6 +Redshift (z) +GAMA Spectroscopy (Knabel-2020) +LinKS (Knabel-2020) +GalaxyZoo (Knabel-2020) +Li+2020 (Full Sample) +LinKS AUTOZ Sample +LinKS (Knabel-2020) AUTOZ Sample +Li+2020 AUTOZ Sample +0 +10 +20 +0 +10 +Figure E1. Stellar masses and redshifts of the Autoz sample with deeper +colored circular markers shown against the candidates discussed in Knabel +et al. 2020 with faded X’s for context. LinKS candidates (shown in green +for the LinKS subsample selected in Knabel et al. 2020 and black for those +that were not) and "bright galaxy" candidates from Li et al. 2020 (orange) +have high stellar masses at intermediate redshift 𝑙𝑜𝑔(𝑀∗/𝑀⊙) ∼11-11.75 +at 𝑧 ∼0.2-0.5. Blue and yellow X’s are spectroscopy and citizen-science +candidates selected in Knabel et al. 2020. +MNRAS 000, 1–24 (2021) +