The SL2S Galaxy-scale Lens Sample. III. Lens Models, Surface Photometry and Stellar Masses for the final sample

We present Hubble Space Telescope (HST) imaging data and CFHT Near IR ground-based images for the final sample of 56 candidate galaxy-scale lenses uncovered in the CFHT Legacy Survey as part of the Strong Lensing in the Legacy Survey (SL2S) project. The new images are used to perform lens modeling, measure surface photometry, and estimate stellar masses of the deflector early-type galaxies. Lens modeling is performed on the HST images (or CFHT when HST is not available) by fitting the spatially extended light distribution of the lensed features assuming a singular isothermal ellipsoid mass profile and by reconstructing the intrinsic source light distribution on a pixelized grid. Based on the analysis of systematic uncertainties and comparison with inference based on different methods we estimate that our Einstein Radii are accurate to \sim3%. HST imaging provides a much higher success rate in confirming gravitational lenses and measuring their Einstein radii than CFHT imaging does. Lens modeling with ground-based images however, when successful, yields Einstein radius measurements that are competitive with spaced-based images. Information from the lens models is used together with spectroscopic information from the companion paper IV to classify the systems, resulting in a final sample of 39 confirmed (grade-A) lenses and 17 promising candidates. The redshifts of the main deflector span a range 0.3<zd< 0.8, providing an excellent sample for the study of the cosmic evolution of the mass distribution of early-type galaxies over the second half of the history of the Universe.Comment: Submitted to The Astrophysical Journa

The mass profile of early-type galaxies in overdense environments: the case of the double source plane gravitational lens SL2SJ02176-0513

SL2SJ02176-0513 is a remarkable lens for the presence of two multiply-imaged systems at different redshifts lensed by a foreground massive galaxy at $z_{\rm lens}=0.656$: a bright cusp arc at $z_{\rm arc}=1.847$ and an additional double-image system at an estimated redshift of $z_{\rm dbl}\sim2.9$ based on photometry and lensing geometry. The system is located about 400 kpc away from the center of a massive group of galaxies. Mass estimates for the group are available from X-ray observations and satellite kinematics. Multicolor photometry provides an estimate of the stellar mass of the main lens galaxy. The lensing galaxy is modeled with two components (stars and dark matter), and we include the perturbing effect of the group environment, and all available constraints. We find that classic lensing degeneracies, e.g. between external convergence and mass density slope, are significantly reduced with respect to standard systems and infer tight constraints on the mass density profile: (i) the dark matter content of the main lens galaxy is in line with that of typical galaxies $f_{\rm dm}(<R_{\rm e})=0.41^{+0.09}_{-0.06}$; (ii) the required mass associated with the dark matter halo of the nearby group is consistent with X-ray and weak-lensing estimates ($\sigma_{\rm grp}=550^{+130}_{-240}$); (iii) accounting for the group contribution in the form of an external convergence, the slope of the mass density profile of the main lens galaxy alone is found to be $\alpha=-1.03^{+0.22}_{-0.16}$, consistent with the isothermal ($\alpha=-1$) slope. We demonstrate that multiple source plane systems together with good ancillary dataset can be used to disentangle local and environmental effects.Comment: 10 pages, 6 figures, submitted to A&

The SL2S Galaxy-scale Lens Sample. V. Dark Matter Halos and Stellar IMF of Massive Early-type Galaxies out to Redshift 0.8

We investigate the cosmic evolution of the internal structure of massive early-type galaxies over half of the age of the Universe. We perform a joint lensing and stellar dynamics analysis of a sample of 81 strong lenses from the SL2S and SLACS surveys and combine the results with a hierarchical Bayesian inference method to measure the distribution of dark matter mass and stellar IMF across the population of massive early-type galaxies. Lensing selection effects are taken into account. We find that the dark matter mass projected within the inner 5 kpc increases for increasing redshift, decreases for increasing stellar mass density, but is roughly constant along the evolutionary tracks of early-type galaxies. The average dark matter slope is consistent with that of an NFW profile, but is not well constrained. The stellar IMF normalization is close to a Salpeter IMF at $\log{M_*} = 11.5$ and scales strongly with increasing stellar mass. No dependence of the IMF on redshift or stellar mass density is detected. The anti-correlation between dark matter mass and stellar mass density supports the idea of mergers being more frequent in more massive dark matter halos.Comment: Accepted for publication on The Astrophysical Journal. Revised version. (25 pages, 18 figures

The SL2S Galaxy-scale Lens Sample. IV. The dependence of the total mass density profile of early-type galaxies on redshift, stellar mass, and size

We present optical and near infrared spectroscopy obtained at Keck, VLT, and Gemini for a sample of 36 secure strong gravitational lens systems and 17 candidates identified as part of the SL2S survey. The deflectors are massive early-type galaxies in the redshift range z_d=0.2-0.8, while the lensed sources are at z_s=1-3.5. We combine this data with photometric and lensing measurements presented in the companion paper III and with lenses from the SLACS and LSD surveys to investigate the cosmic evolution of the internal structure of massive early-type galaxies over half the age of the universe. We study the dependence of the slope of the total mass density profile \gamma' (\rho(r)\propto r^{-\gamma'}) on stellar mass, size, and redshift. We find that two parameters are sufficent to determine \gamma' with less than 6% residual scatter. At fixed redshift, \gamma' depends solely on the surface stellar mass density \partial \gamma'/ \partial \Sigma_*=0.38\pm 0.07, i.e. galaxies with denser stars also have steeper slopes. At fixed M_* and R_{eff}, \gamma' depends on redshift, in the sense that galaxies at a lower redshift have steeper slopes (\partial \gamma' / \partial z = -0.31\pm 0.10). However, the mean redshift evolution of \gamma' for an individual galaxy is consistent with zero d\gamma'/dz=-0.10\pm0.12. This result is obtained by combining our measured dependencies of \gamma' on z,M_*,R_{eff} with the evolution of the R_{eff}-M_* taken from the literature, and is broadly consistent with current models of the formation and evolution of massive early-type galaxies. Detailed quantitative comparisons of our results with theory will provide qualitatively new information on the detailed physical processes at work.Comment: Submitted to The Astrophysical Journa

Too Much SALT? The Nuanced Impact of the State and Local Tax Deduction Cap on Pass-Through Business Taxpayers

Perhaps the most controversial provision of the Tax Cuts and Jobs Act of 2017 is the state and local tax deduction limitation (or SALT cap), partic¬ularly with respect to how the cap impacts pass-through entities in high-tax states. This particular provision of the tax law has been criticized by opponents as deliberately punitive to small businesses in blue states, while proponents maintain that eliminating the SALT cap would primar¬ily benefit high income taxpayers. Politicians from blue states have called for the repeal of the SALT cap, and some states have enacted various workarounds with questionable prospects of success. Still, many taxpay¬ers will not benefit from a SALT deduction irrespective of the SALT cap, particularly taxpayers that either take the standard deduction or are subject to the alternative minimum tax (AMT). We examine the developing law around the SALT cap and provide descriptive empirical evidence of its disparate impact on closely held business taxpayers. Consistent with prior economics literature, we find that the impact is indeed most pro¬nounced among high-income taxpayers in blue states. However, we note that the impact is substantially less than the furor over the limitation would suggest because many high-income taxpayers are subject to the AMT and so are not significantly affected by the limitation. These findings suggest two underemphasized points. First, the imposition of the SALT cap was not the drastic financial hit to blue state taxpayers that policy makers and commentators have suggested. Second, with a new adminis¬tration that favors eliminating the SALT cap, Congress could consider whether the repeal of the cap alone is enough because further changes would be needed to return the SALT deduction to its earlier prominence

Testing the Evolution of the Correlations between Supermassive Black Holes and their Host Galaxies using Eight Strongly Lensed Quasars

One of the main challenges in using high redshift active galactic nuclei to study the correlations between the mass of the supermassive Black Hole (MBH) and the properties of their active host galaxies is instrumental resolution. Strong lensing magnification effectively increases instrumental resolution and thus helps to address this challenge. In this work, we study eight strongly lensed active galactic nuclei (AGN) with deep Hubble Space Telescope imaging, using the lens modelling code Lenstronomy to reconstruct the image of the source. Using the reconstructed brightness of the host galaxy, we infer the host galaxy stellar mass based on stellar population models. MBH are estimated from broad emission lines using standard methods. Our results are in good agreement with recent work based on non-lensed AGN, demonstrating the potential of using strongly lensed AGNs to extend the study of the correlations to higher redshifts. At the moment, the sample size of lensed AGN is small and thus they provide mostly a consistency check on systematic errors related to resolution for the non-lensed AGN. However, the number of known lensed AGN is expected to increase dramatically in the next few years, through dedicated searches in ground and space based wide field surveys, and they may become a key diagnostic of black hole and galaxy co-evolution.Comment: 12 pages, 4 figures, 3 tables. MNRAS in press. Comments welcom

Probing dark matter substructure in the gravitational lens HE0435-1223 with the WFC3 grism

Strong gravitational lensing provides a powerful test of Cold Dark Matter (CDM) as it enables the detection and mass measurement of low mass haloes even if they do not contain baryons. Compact lensed sources such as Active Galactic Nuclei (AGN) are particularly sensitive to perturbing subhalos, but their use as a test of CDM has been limited by the small number of systems which have significant radio emission which is extended enough avoid significant lensing by stars in the plane of the lens galaxy, and red enough to be minimally affected by differential dust extinction. Narrow-line emission is a promising alternative as it is also extended and, unlike radio, detectable in virtually all optically selected AGN lenses. We present first results from a WFC3 grism narrow-line survey of lensed quasars, for the quadruply lensed AGN HE0435-1223. Using a forward modelling pipeline which enables us to robustly account for spatial blending, we measure the [OIII] 5007 \AA~ flux ratios of the four images. We find that the [OIII] fluxes and positions are well fit by a simple smooth mass model for the main lens. Our data rule out a $M_{600}>10^{8} (10^{7.2}) M_\odot$ NFW perturber projected within $\sim$1\farcs0 (0\farcs1) arcseconds of each of the lensed images, where $M_{600}$ is the perturber mass within its central 600 pc. The non-detection is broadly consistent with the expectations of $\Lambda$CDM for a single system. The sensitivity achieved demonstrates that powerful limits on the nature of dark matter can be obtained with the analysis of $\sim20$ narrow-line lenses.Comment: Accepted for publication in MNRAS, 15 pages, 8 figure