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DOE OSTI2017

Probabilistic Cosmological Mass Mapping from Weak Lensing Shear

We infer gravitational lensing shear and convergence fields from galaxy ellipticity catalogs under a spatial process prior for the lensing potential. We demonstrate the performance of our algorithm with simulated Gaussian-distributed cosmological lensing shear maps and a reconstruction of the mass distribution of the merging galaxy cluster Abell 781 using galaxy ellipticities measured with the Deep Lens Survey. Given interim posterior samples of lensing shear or convergence fields on the sky, we describe an algorithm to infer cosmological parameters via lens field marginalization. In the most general formulation of our algorithm we make no assumptions about weak shear or Gaussian-distributed shape noise or shears. Because we require solutions and matrix determinants of a linear system of dimension that scales with the number of galaxies, we expect our algorithm to require parallel high-performance computing resources for application to ongoing wide field lensing surveys.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

A Robust Mass Estimator for Dark Matter Subhalo Perturbations in Strong Gravitational Lenses

A few dark matter substructures have recently been detected in strong gravitational lenses through their perturbations of highly magnified images. We derive a characteristic scale for lensing perturbations and show that they are significantly larger than the perturber’s Einstein radius. We show that the perturber’s projected mass enclosed within this radius, scaled by the log-slope of the host galaxy’s density profile, can be robustly inferred even if the inferred density profile and tidal radius of the perturber are biased. We demonstrate the validity of our analytic derivation using several gravitational lens simulations where the tidal radii and the inner log-slopes of the density profile of the perturbing subhalo are allowed to vary. By modeling these simulated data, we find that our mass estimator, which we call the effective subhalo lensing mass, is accurate to within about 10% or smaller in each case, whereas the inferred total subhalo mass can potentially be biased by nearly an order of magnitude. We therefore recommend that the effective subhalo lensing mass be reported in future lensing reconstructions, as this will allow for a more accurate comparison with the results of dark matter simulations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

THE GINI COEFFICIENT AS A TOOL FOR IMAGE FAMILY IDENITIFICATION IN STRONG LENSING SYSTEMS WITH MULTIPLE IMAGES

The sample of cosmological strong lensing systems has been steadily growing in recent years and with the advent of the next generation of space-based survey telescopes, the sample will reach into the thousands. The accuracy of strong lens models relies on robust identification of multiple image families of lensed galaxies. For the most massive lenses, often more than one background galaxy is magnified and multiply imaged, and even in the cases of only a single lensed source, identification of counter images is not always robust. Recently, we have shown that the Gini coefficient in space-telescope-quality imaging is a measurement of galaxy morphology that is relatively well-preserved by strong gravitational lensing. Here, we investigate its usefulness as a diagnostic for the purposes of image family identification and show that it can remove some of the degeneracies encountered when using color as the sole diagnostic, and can do so without the need for additional observations since whenever a color is available, two Gini coefficients are as well.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Weak lensing by voids in modified lensing potentials

We study lensing by voids in Cubic Galileon and Nonlocal gravity cosmologies, which are examples of theories of gravity that modify the lensing potential. We find voids in the dark matter and halo density fields of N-body simulations and compute their lensing signal analytically from the void density profiles, which we show are well fit by a simple analytical formula. In the Cubic Galileon model, the modifications to gravity inside voids are not screened and they approximately double the size of the lensing effects compared to GR. The difference is largely determined by the direct effects of the fifth force on lensing and less so by the modified density profiles. For this model, we also discuss the subtle impact on the force and lensing calculations caused by the screening effects of haloes that exist in and around voids. In the Nonlocal model, the impact of the modified density profiles and the direct modifications to lensing are comparable, but they boost the lensing signal by only ≈ 10%, compared with that of GR. Overall, our results suggest that lensing by voids is a promising tool to test models of gravity that modify lensing.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Gravitational Lensing Formalism in a Curved Arc Basis: A Continuous Description of Observables and Degeneracies from the Weak to the Strong Lensing Regime

Gravitationally lensed curved arcs provide a wealth of information about the underlying lensing distortions. Extracting precise lensing information from extended sources is a key component in many studies aiming to answer fundamental questions about the universe. To maintain accuracy with increased precision, it is of vital importance to characterize and understand the impact of degeneracies inherent in lensing observables. In this work, we present a formalism to describe the gravitational lensing distortion effects resulting in curved extended arcs based on the eigenvectors and eigenvalues of the local lensing Jacobian and their directional differentials. We identify a nonlocal and nonlinear extended deflector basis that inherits these local properties. Our parameterization is tightly linked to observable features in extended sources and allows one to accurately extract the lensing information of extended images without imposing an explicit global deflector model. We quantify what degeneracies can be broken based on specific assumptions about the local lensing nature and assumed intrinsic source shape. Our formalism is applicable from the weak linear regime to the semi-linear regime and all the way up to the highly nonlinear regime of highly magnified arcs of multiple images. Furthermore, the methodology and implementation presented in this work provides a framework to assessing systematics, to guide inference efforts in the right choices in complexity based on the data at hand, and to quantify the lensing information extracted in a model-independent way

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Joint analysis of Dark Energy Survey Year 3 data and CMB lensing from SPT and P l a n c k . II. Cross-correlation measurements and cosmological constraints

Cross-correlations of galaxy positions and galaxy shears with maps of gravitational lensing of the cosmic microwave background (CMB) are sensitive to the distribution of large-scale structure in the Universe. Such cross-correlations are also expected to be immune to some of the systematic effects that complicate correlation measurements internal to galaxy surveys. We present measurements and modeling of the cross-correlations between galaxy positions and galaxy lensing measured in the first three years of data from the Dark Energy Survey with CMB lensing maps derived from a combination of data from the 2500 deg 2 SPT-SZ survey conducted with the South Pole Telescope and full-sky data from the Planck satellite. The CMB lensing maps used in this analysis have been constructed in a way that minimizes biases from the thermal Sunyaev Zel’dovich effect, making them well suited for cross-correlation studies. The total signal-to-noise of the cross-correlation measurements is 23.9 (25.7) when using a choice of angular scales optimized for a linear (nonlinear) galaxy bias model. Here we use the cross-correlation measurements to obtain constraints on cosmological parameters. For our fiducial galaxy sample, which consist of four bins of magnitude-selected galaxies, we find constraints of Ω m =0.272$^{+0.032}_{-0.052}$ and S 8 ≡σ8$\sqrt{Ω_m/0.3}$=0.736$^{+0.032}_{-0.028}$ (Ω m =0.245$^{+0.026}_{-0.044}$ and S 8 =0.734$^{+0.035}_{-0.028}$) when assuming linear (nonlinear) galaxy bias in our modeling. Considering only the cross-correlation of galaxy shear with CMB lensing, we find Ω m =0.270$^{+0.043}_{-0.061}$ and S 8 =0.740$^{+0.034}_{-0.029}$. Our constraints on S8 are consistent with recent cosmic shear measurements, but lower than the values preferred by primary CMB measurements from Planck.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Measuring galaxy cluster masses with CMB lensing using a Maximum Likelihood estimator: statistical and systematic error budgets for future experiments

We develop a Maximum Likelihood estimator (MLE) to measure the masses of galaxy clusters through the impact of gravitational lensing on the temperature and polarization anisotropies of the cosmic microwave background (CMB). We show that, at low noise levels in temperature, this optimal estimator outperforms the standard quadratic estimator by a factor of two. For polarization, we show that the Stokes Q/U maps can be used instead of the traditional E- and B-mode maps without losing information. We test and quantify the bias in the recovered lensing mass for a comprehensive list of potential systematic errors. Using realistic simulations, we examine the cluster mass uncertainties from CMB-cluster lensing as a function of an experiment’s beam size and noise level. We predict the cluster mass uncertainties will be 3 - 6% for SPT-3G, AdvACT, and Simons Array experiments with 10,000 clusters and less than 1% for the CMB-S4 experiment with a sample containing 100,000 clusters. The mass constraints from CMB polarization are very sensitive to the experimental beam size and map noise level: for a factor of three reduction in either the beam size or noise level, the lensing signal-to-noise improves by roughly a factor of two.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Cluster Mass Calibration at High Redshift: HST Weak Lensing Analysis of 13 Distant Galaxy Clusters from the South Pole Telescope Sunyaev-Zel’dovich Survey

We present an HST/Advanced Camera for Surveys (ACS) weak gravitational lensing analysis of 13 massive high-redshift (z(median) = 0.88) galaxy clusters discovered in the South Pole Telescope (SPT) Sunyaev-Zel'dovich Survey. This study is part of a larger campaign that aims to robustly calibrate mass-observable scaling relations over a wide range in redshift to enable improved cosmological constraints from the SPT cluster sample. We introduce new strategies to ensure that systematics in the lensing analysis do not degrade constraints on cluster scaling relations significantly. First, we efficiently remove cluster members from the source sample by selecting very blue galaxies in V - I colour. Our estimate of the source redshift distribution is based on Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS) data, where we carefully mimic the source selection criteria of the cluster fields. We apply a statistical correction for systematic photometric redshift errors as derived from Hubble Ultra Deep Field data and verified through spatial cross-correlations. We account for the impact of lensing magnification on the source redshift distribution, finding that this is particularly relevant for shallower surveys. Finally, we account for biases in the mass modelling caused by miscentring and uncertainties in the concentration-mass relation using simulations. In combination with temperature estimates from Chandra we constrain the normalization of the mass-temperature scaling relation ln (E(z) M-500c/10(14)M(circle dot)) = A + 1.5ln (kT/7.2 keV) to A = 1.81(-0.14)(+0.24)(stat.)+/- 0.09(sys.), consistent with self-similar redshift evolution when compared to lower redshift samples. Additionally, the lensing data constrain the average concentration of the clusters to c(200c) = 5.6(-1.8)(+3.7).

cosmology: observations↗
DOE OSTI2016

DETECTION OF LENSING SUBSTRUCTURE USING ALMA OBSERVATIONS OF THE DUSTY GALAXY SDP.81

We study the abundance of substructure in the matter density near galaxies using ALMA Science Verification observations of the strong lensing system SDP.81. We present a method to measure the abundance of subhalos around galaxies using interferometric observations of gravitational lenses. Using simulated ALMA observations we explore the effects of various systematics, including antenna phase errors and source priors, and show how such errors may be measured or marginalized. We apply our formalism to ALMA observations of SDP.81. We find evidence for the presence of a M = 10{sup 8.96±0.12} M {sub ⊙} subhalo near one of the images, with a significance of 6.9 σ in a joint fit to data from bands 6 and 7; the effect of the subhalo is also detected in both bands individually. We also derive constraints on the abundance of dark matter (DM) subhalos down to M ∼ 2 × 10{sup 7} M {sub ⊙}, pushing down to the mass regime of the smallest detected satellites in the Local Group, where there are significant discrepancies between the observed population of luminous galaxies and predicted DM subhalos. We find hints of additional substructure, warranting further study using the full SDP.81 data set (including, for example, the spectroscopic imaging of the lensed carbon monoxide emission). We compare the results of this search to the predictions of ΛCDM halos, and find that given current uncertainties in the host halo properties of SDP.81, our measurements of substructure are consistent with theoretical expectations. Observations of larger samples of gravitational lenses with ALMA should be able to improve the constraints on the abundance of galactic substructure.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

The STRong lensing Insights into the Dark Energy Survey (STRIDES) 2017/2018 follow-up campaign: discovery of 10 lensed quasars and 10 quasar pairs

Here, we report the results of the STRong lensing Insights into the Dark Energy Survey (STRIDES) follow-up campaign of the late 2017/early 2018 season. We obtained spectra of 65 lensed quasar candidates with ESO Faint Object Spectrograph and Camera 2 on the NTT and Echellette Spectrograph and Imager on Keck, confirming 10 new lensed quasars and 10 quasar pairs. Eight lensed quasars are doubly imaged with source redshifts between 0.99 and 2.90, one is triply imaged (DESJ0345-2545, z = 1.68), and one is quadruply imaged (quad: DESJ0053-2012, z = 3.8). Singular isothermal ellipsoid models for the doubles, based on high-resolution imaging from SAMI on Southern Astrophysical Research Telescope or Near InfraRed Camera 2 on Keck, give total magnifications between 3.2 and 5.6, and Einstein radii between 0.49 and 1.97 arcsec. After spectroscopic follow-up, we extract multi-epoch grizY photometry of confirmed lensed quasars and contaminant quasar + star pairs from DES data using parametric multiband modelling, and compare variability in each system’s components. By measuring the reduced χ 2 associated with fitting all epochs to the same magnitude, we find a simple cut on the less variable component that retains all confirmed lensed quasars, while removing 94 per cent of contaminant systems. Based on our spectroscopic follow-up, this variability information improves selection of lensed quasars and quasar pairs from 34-45 per cent to 51–70 per cent, with most remaining contaminants being star-forming galaxies. Using mock lensed quasar light curves we demonstrate that selection based only on variability will over-represent the quad fraction by 10 per cent over a complete DES magnitude-limited sample, explained by the magnification bias and hence lower luminosity/more variable sources in quads.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Finding high-redshift strong lenses in DES using convolutional neural networks

We search Dark Energy Survey (DES) Year 3 imaging data for galaxy-galaxy strong gravitational lenses using convolutional neural networks. We generate 250 000 simulated lenses at redshifts > 0.8 from which we create a data set for training the neural networks with realistic seeing, sky and shot noise. Using the simulations as a guide, we build a catalogue of 1.1 million DES sources with 1.8 < g - i < 5, 0.6 < g - r < 3, r_mag > 19, g_mag > 20, and i_mag > 18.2. We train two ensembles of neural networks on training sets consisting of simulated lenses, simulated non-lenses, and real sources. We use the neural networks to score images of each of the sources in our catalogue with a value from 0 to 1, and select those with scores greater than a chosen threshold for visual inspection, resulting in a candidate set of 7301 galaxies. During visual inspection, we rate 84 as 'probably' or 'definitely' lenses. Four of these are previously known lenses or lens candidates. We inspect a further 9428 candidates with a different score threshold, and identify four new candidates. We present 84 new strong lens candidates, selected after a few hours of visual inspection by astronomers. This catalogue contains a comparable number of high-redshift lenses to that predicted by simulations. Based on simulations, we estimate our sample to contain most discoverable lenses in this imaging and at this redshift range.

Jacobs, C.↗
DOE OSTI2021

Lensing without borders – I. A blind comparison of the amplitude of galaxy–galaxy lensing between independent imaging surveys

ABSTRACT Lensing without borders is a cross-survey collaboration created to assess the consistency of galaxy–galaxy lensing signals (ΔΣ) across different data sets and to carry out end-to-end tests of systematic errors. We perform a blind comparison of the amplitude of ΔΣ using lens samples from BOSS and six independent lensing surveys. We find good agreement between empirically estimated and reported systematic errors which agree to better than 2.3σ in four lens bins and three radial ranges. For lenses with zL > 0.43 and considering statistical errors, we detect a 3–4σ correlation between lensing amplitude and survey depth. This correlation could arise from the increasing impact at higher redshift of unrecognized galaxy blends on shear calibration and imperfections in photometric redshift calibration. At zL > 0.54, amplitudes may additionally correlate with foreground stellar density. The amplitude of these trends is within survey-defined systematic error budgets that are designed to include known shear and redshift calibration uncertainty. Using a fully empirical and conservative method, we do not find evidence for large unknown systematics. Systematic errors greater than 15 per cent (25 per cent) ruled out in three lens bins at 68 per cent (95 per cent) confidence at z < 0.54. Differences with respect to predictions based on clustering are observed to be at the 20–30 per cent level. Our results therefore suggest that lensing systematics alone are unlikely to fully explain the ‘lensing is low’ effect at z < 0.54. This analysis demonstrates the power of cross-survey comparisons and provides a promising path for identifying and reducing systematics in future lensing analyses.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Dark Energy Survey Year 1 Results: Tomographic cross-correlations between Dark Energy Survey galaxies and CMB lensing from South Pole Telescope +Planck

We measure the cross-correlation between redMaGiC galaxies selected from the Dark Energy Survey (DES) year 1 data and gravitational lensing of the cosmic microwave background (CMB) reconstructed from South Pole Telescope (SPT) and Planck data over 1289 deg2 . When combining measurements across multiple galaxy redshift bins spanning the redshift range of 0.15 <z <0.90 , we reject the hypothesis of no correlation at 19.9 σ significance. When removing small-scale data points where thermal Sunyaev-Zel'dovich signal and nonlinear galaxy bias could potentially bias our results, the detection significance is reduced to 9.9 σ . We perform a joint analysis of galaxy-CMB lensing cross-correlations and galaxy clustering to constrain cosmology, finding Ωm=0.27 6-0.030+0.029 and S8=σ8√{Ωm/0.3 }=0.80 0-0.094+0.090 . We also perform two alternate analyses aimed at constraining only the growth rate of cosmic structure as a function of redshift, finding consistency with predictions from the concordance Λ CDM model. The measurements presented here are part of a joint cosmological analysis that combines galaxy clustering, galaxy lensing and CMB lensing using data from DES, SPT and Planck.

Omori, Y.↗
DOE OSTI2022

Dark Energy Survey Year 3 results: Cosmology from combined galaxy clustering and lensing validation on cosmological simulations

In this work, we present a validation of the Dark Energy Survey Year 3 (DES Y3) 3×2-point analysis choices by testing them on Buzzard2.0, a new suite of cosmological simulations that is tailored for the testing and validation of combined galaxy clustering and weak-lensing analyses. We show that the buzzard2.0 simulations accurately reproduce many important aspects of the DES Y3 data, including photometric redshift and magnitude distributions, and the relevant set of two-point clustering and weak-lensing statistics. We then show that our model for the 3×2-point data vector is accurate enough to recover the true cosmology in simulated surveys assuming the true redshift distributions for our source and lens samples, demonstrating robustness to uncertainties in the modeling of the nonlinear matter power spectrum, nonlinear galaxy bias, and higher-order lensing corrections. Additionally, we demonstrate for the first time that our photometric redshift calibration methodology, including information from photometry, spectroscopy, clustering cross-correlations, and galaxy–galaxy lensing ratios, is accurate enough to recover the true cosmology in simulated surveys in the presence of realistic photometric redshift uncertainties.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Lensing covariance on cut sky and SPT - P l a n c k lensing tensions

We investigate correlations induced by gravitational lensing on simulated cosmic microwave background data of experiments with an incomplete sky coverage and their effect on inferences from the South Pole Telescope (SPT) data. These correlations agree well with the theoretical expectations, given by the sum of supersample and intrasample lensing terms, with only a typically negligible ~5 % discrepancy in the amplitude of the supersample lensing effect. Including these effects we find that lensing constraints are in 3.0 σ or 2.1 σ tension between the SPT polarization measurements and Planck temperature or lensing reconstruction constraints respectively. If the lensing-induced covariance effects are neglected, the significance of these tensions increases to 3.5 σ or 2.5 σ . Using the standard scaling parameter AL substantially underestimates the significance of the tension once other parameters are marginalized over. By parameterizing the supersample lensing through the mean convergence in the SPT footprint, we find a hint of underdensity in the SPT region. We also constrain extra sharpening of the cosmic microwave background acoustic peaks due to missing smoothing of the peaks by supersample lenses at a level that is much smaller than the lens sample variance. Finally, we extend the usual “shift in the means” statistic for evaluating tensions to non-Gaussian posteriors, generalize an approach to extract correlation modes from noisy simulated covariance matrices, and present a treatment of correlation modes not as data covariances but as auxiliary model parameters.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

The effect of weak lensing on distance estimates from supernovae

Using a sample of 608 Type Ia supernovae from the SDSS-II and BOSS surveys, combined with a sample of foreground galaxies from SDSS-II, we estimate the weak lensing convergence for each supernova line of sight. We find that the correlation between this measurement and the Hubble residuals is consistent with the prediction from lensing (at a significance of 1.7σ). Strong correlations are also found between the residuals and supernova nuisance parameters after a linear correction is applied. When these other correlations are taken into account, the lensing signal is detected at 1.4σ. We show, for the first time, that distance estimates from supernovae can be improved when lensing is incorporated, by including a new parameter in the SALT2 methodology for determining distance moduli. The recovered value of the new parameter is consistent with the lensing prediction. Using cosmic microwave background data from WMAP7, H {sub 0} data from Hubble Space Telescope and Sloan Digital Sky Survey (SDSS) Baryon acoustic oscillations measurements, we find the best-fit value of the new lensing parameter and show that the central values and uncertainties on Ω {sub m} and w are unaffected. The lensing of supernovae, while only seen at marginal significance in this low-redshift sample, will be of vital importance for the next generation of surveys, such as DES and LSST, which will be systematics-dominated.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Cosmological constraints from galaxy–lensing cross-correlations using BOSS galaxies with SDSS and CMB lensing

ABSTRACT We present cosmological parameter constraints based on a joint modelling of galaxy–lensing cross-correlations and galaxy clustering measurements in the SDSS, marginalizing over small-scale modelling uncertainties using mock galaxy catalogues, without explicit modelling of galaxy bias. We show that our modelling method is robust to the impact of different choices for how galaxies occupy dark matter haloes and to the impact of baryonic physics (at the $\sim 2{{\ \rm per\ cent}}$ level in cosmological parameters) and test for the impact of covariance on the likelihood analysis and of the survey window function on the theory computations. Applying our results to the measurements using galaxy samples from BOSS and lensing measurements using shear from SDSS galaxies and CMB lensing from Planck, with conservative scale cuts, we obtain $S_8\equiv \left(\frac{\sigma _8}{0.8228}\right)^{0.8}\left(\frac{\Omega _\mathrm{ m}}{0.307}\right)^{0.6}=0.85\pm 0.05$ (stat.) using LOWZ × SDSS galaxy lensing, and S8 = 0.91 ± 0.1 (stat.) using combination of LOWZ and CMASS × Planck CMB lensing. We estimate the systematic uncertainty in the galaxy–galaxy lensing measurements to be $\sim 6{{\ \rm per\ cent}}$ (dominated by photometric redshift uncertainties) and in the galaxy–CMB lensing measurements to be $\sim 3{{\ \rm per\ cent}}$, from small-scale modelling uncertainties including baryonic physics.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2017

The Initial Mass Function in the Nearest Strong Lenses from SNELLS: Assessing the Consistency of Lensing, Dynamical, and Spectroscopic Constraints

We present new observations of the three nearest early-type galaxy (ETG) strong lenses discovered in the SINFONI Nearby Elliptical Lens Locator Survey (SNELLS). Based on their lensing masses, these ETGs were inferred to have a stellar initial mass function (IMF) consistent with that of the Milky Way, not the bottom-heavy IMF that has been reported as typical for high- σ ETGs based on lensing, dynamical, and stellar population synthesis techniques. We use these unique systems to test the consistency of IMF estimates derived from different methods. We first estimate the stellar M {sub *}/ L using lensing and stellar dynamics. We then fit high-quality optical spectra of the lenses using an updated version of the stellar population synthesis models developed by Conroy and van Dokkum. When examined individually, we find good agreement among these methods for one galaxy. The other two galaxies show 2–3 σ tension with lensing estimates, depending on the dark matter contribution, when considering IMFs that extend to 0.08 M {sub ⊙}. Allowing a variable low-mass cutoff or a nonparametric form of the IMF reduces the tension among the IMF estimates to <2 σ . There is moderate evidence for a reduced number of low-mass stars in the SNELLS spectra, but no such evidence in a composite spectrum of matched- σ ETGs drawn from the SDSS. Such variation in the form of the IMF at low stellar masses ( m ≲ 0.3 M {sub ⊙}), if present, could reconcile lensing/dynamical and spectroscopic IMF estimates for the SNELLS lenses and account for their lighter M {sub *}/ L relative to the mean matched- σ ETG. We provide the spectra used in this study to facilitate future comparisons.

79 ASTRONOMY AND ASTROPHYSICS↗