An HSC view of the CMASS galaxy sample. Halo mass as a function of stellar mass, size and S\'ersic index

Aims. We wish to determine the distribution of dark matter halo masses as a function of the stellar mass and the stellar mass profile, for massive galaxies in the BOSS CMASS sample. Methods. We use grizy photometry from HSC to obtain S\'ersic fits and stellar masses of CMASS galaxies for which HSC weak lensing data is available, visually selected to have spheroidal morphology. We apply a cut in stellar mass, $\log{M_*/M_\odot} > 11.0$,selecting $\sim$10, 000 objects. Using a Bayesian hierarchical inference method, we first investigate the distribution of S\'ersic index and size as a function of stellar mass. Then, making use of shear measurements from HSC, we measure the distribution of halo mass as a function of stellar mass, size and S\'ersic index. Results. Our data reveals a steep stellar mass-size relation $R_e \propto M_*^{\beta_R}$, with $\beta_R$ larger than unity, and a positive correlation between S\'ersic index and stellar mass: $n \propto M_*^{0.46}$. Halo mass scales approximately with the 1.7 power of the stellar mass. We do not find evidence for an additional dependence of halo mass on size or S\'ersic index at fixed stellar mass. Conclusions. Our results disfavour galaxy evolution models that predict significant differences in the size growth efficiency of galaxies living in low and high mass halos.Comment: Accepted for publication on Astronomy & Astrophysics. 18 pages, 15 figure

Statistical strong lensing. III. Inferences with complete samples of lenses

Context. Existing samples of strong lenses have been assembled by giving priority to sample size, at the cost of having a complex selection function. With the advent of the next generation of wide-field photometric surveys, however, it might become possible to identify subsets of the lens population with well-defined selection criteria, trading sample size for completeness. Aims. There are two main advantages of working with a complete sample of lenses. First, it is possible to recover the properties of the general population of galaxies, of which strong lenses are a biased subset. Second, the relative number of lenses and non-detections can be used to further constrain models of galaxy structure. This work illustrates how to carry out a statistical strong lensing analysis that takes advantage of these features. Methods. I introduced a general formalism for the statistical analysis of a sample of strong lenses with known selection function, then tested it on simulated data. The simulation consists of a population of $10^5$ galaxies with an axisymmetric power-law density profile, a population of background point sources, and a subset of $\sim10^3$ strong lenses, complete above an observational cut. Results. The method allows to recover the distribution in Einstein radius and mass density slope of the galaxy population in an unbiased way. The number of non-lenses helps to constrain the model when magnification data are not available. Conclusions. Complete samples of lenses are a powerful asset to turn precise strong lensing measurements into accurate statements on the properties of the general galaxy population.Comment: Submitted to Astronomy & Astrophysics. A 2-minute summary video is available at https://youtu.be/f6PziIr9US

A robust two-parameter description of the stellar profile of elliptical galaxies

The stellar density profile a galaxy is typically summarised with two numbers: total stellar mass and half-light radius. The total mass of a galaxy, however, is not a well-defined quantity, due to the finite depth of photometric observations and the arbitrariness of the distinction between galaxy and diffuse intra-group light. This limits our ability to make accurate comparisons between models and observations. I wish to provide a more robust two-parameter description of the stellar density distribution of elliptical galaxies, in terms of quantities that can be measured unambiguously. I propose to use the stellar mass enclosed within 10 kpc in projection, $M_{*,10}$, and the mass-weighted stellar density slope within the same aperture, $\Gamma_{*,10}$, for this purpose. I measured the distribution in $M_{*,10}$ and $\Gamma_{*,10}$ of a sample of elliptical galaxies from the Sloan Digital Sky Survey and the Galaxy And Mass Assembly survey, using photometry from the Hyper Suprime-Cam survey. The pair of values of $(M_{*,10},\Gamma_{*,10})$ can be used to predict the stellar density profile in the inner 10 kpc of a galaxy with better than 20% accuracy. Similarly, $M_{*,10}$ and $\Gamma_{*,10}$ can be combined to obtain a proxy for stellar velocity dispersion at least as good as the stellar mass fundamental plane. As a first application, I then compared the observed $M_{*,10}-\Gamma_{*,10}$ relation of elliptical galaxies with that of similarly selected galaxies in the EAGLE Reference simulation. Observed and simulated galaxies match at $M_{*,10}=10^{11}M_\odot$, but the EAGLE $M_{*,10}-\Gamma_{*,10}$ relation is shallower and has a larger intrinsic scatter compared to observations. This new parameterisation of the stellar density profile of massive elliptical galaxies provides a more robust way of comparing results from different photometric surveys and from hydrodynamical simulations.Comment: 13 pages, 13 figures, submitted to Astronomy & Astrophysic

The effect of spiral arms on the S\'ersic photometry of galaxies

Context. The S\'ersic profile is a widely-used model to describe the surface brightness distribution of galaxies. Spiral galaxies, however, are qualitatively different from a S\'ersic model. Aims. The goal of this study is to assess how accurately can the total flux and half-light radius of a galaxy with spiral arms be recovered, when fitted with a S\'ersic profile. Methods. I selected a sample of bulge-dominated galaxies with spiral arms. Using photometric data from the Hyper Suprime-Cam survey, I estimated the contribution of the spiral arms to their total flux. Then I generated simulated images of galaxies with similar characteristics, fitted them with a S\'ersic model and quantified the error on the determination of the total flux and half-light radius. Results. Spiral arms can introduce biases on the photometry of galaxies, in a way that depends on the underlying smooth surface brightness profile, the location of the arms, and the depth of the photometric data. A set of spiral arms accounting for 10% of the flux of a bulge-dominated galaxy typically causes the total flux and the half-light radius to be overestimated by 15% and 30%, respectively. This bias, however, is much smaller if the galaxy is disk-dominated. Conclusions. Galaxies with a prominent bulge and a non-zero contribution from spiral arms are the most susceptible to biases in the total flux and half-light radius, when fitted with a S\'ersic profile. If photometric measurements with high accuracy are required, then measurements over finite apertures are to be preferred over global estimates of the flux.Comment: Submitted to Astronomy & Astrophysics. A 2-minute summary video is available at https://youtu.be/y5ffIZP9XH

Statistical strong lensing. I. Constraints on the inner structure of galaxies from samples of a thousand lenses

Context: The number of known strong gravitational lenses is expected to grow substantially in the next few years. The statistical combination of large samples of lenses has the potential of providing strong constraints on the inner structure of galaxies. Aims: We investigate to what extent we can calibrate stellar mass measurements and constrain the average dark matter density profile of galaxies by statistically combining strong lensing data from thousands of lenses. Methods: We generate mock samples of axisymmetric lenses. We assume that, for each lens, we have measurements of two image positions of a strongly lensed background source, as well as magnification information from full surface brightness modelling, and a stellar population synthesis-based estimate of the lens stellar mass. We then fit models describing the distribution of the stellar population synthesis mismatch parameter $\alpha_{sps}$ (the ratio between the true stellar mass and the stellar population synthesis-based estimate) and dark matter density profile of the population of lenses to an ensemble of 1000 mock lenses. Results: The average $\alpha_{sps}$, projected dark matter mass and dark matter density slope can be obtained with great precision and accuracy, compared with current constraints. A flexible model and the knowledge of the lens detection efficiency as a function of image configuration are required in order to avoid a biased inference. Conclusions: Statistical strong lensing inferences from upcoming surveys have the potential to calibrate stellar mass measurements and to constrain the inner dark matter density profile of massive galaxies.Comment: Published on Astronomy & Astrophysics. A 2-minute summary video can be found at this link: https://youtu.be/En0-uJobqE

RingFinder: automated detection of galaxy-scale gravitational lenses in ground-based multi-filter imaging data

We present RingFinder, a tool for finding galaxy-scale strong gravitational lenses in multiband imaging data. By construction, the method is sensitive to configurations involving a massive foreground early-type galaxy and a faint, background, blue source. RingFinder detects the presence of blue residuals embedded in an otherwise smooth red light distribution by difference imaging in two bands. The method is automated for efficient application to current and future surveys, having originally been designed for the 150-deg2 Canada France Hawaii Telescope Legacy Survey (CFHTLS). We describe each of the steps of RingFinder. We then carry out extensive simulations to assess completeness and purity. For sources with magnification mu>4, RingFinder reaches 42% (resp. 25%) completeness and 29% (resp. 86%) purity before (resp. after) visual inspection. The completeness of RingFinder is substantially improved in the particular range of Einstein radii 0.8 < REin < 2. and lensed images brighter than g = 22.5, where it can be as high as 70%. RingFinder does not introduce any significant bias in the source or deflector population. We conclude by presenting the final catalog of RingFinder CFHTLS galaxy-scale strong lens candidates. Additional information obtained with Hubble Space Telescope and Keck Adaptive Optics high resolution imaging, and with Keck and Very Large Telescope spectroscopy, is used to assess the validity of our classification, and measure the redshift of the foreground and the background objects. From an initial sample of 640,000 early type galaxies, RingFinder returns 2500 candidates, which we further reduce by visual inspection to 330 candidates. We confirm 33 new gravitational lenses from the main sample of candidates, plus an additional 16 systems taken from earlier versions of RingFinder. First applications are presented in the SL2S galaxy-scale Lens Sample paper series.Comment: 32 pages (aastex 2col format), 6 figs, ApJ Accepte

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

Luminous and dark matter in early-type galaxies

Three open problems in our understanding of early-type galaxies are 1) identifying theprocess(es) responsible for their rapid size evolution, 2) accurately constraining the stellarIMF and its variations in the population, 3) measuring the density profile of their darkmatter halo. We use strong lensing as the main diagnostic tool to address these issues.We first dissected a massive elliptical galaxy in its stellar and dark matter components,measuring both its IMF and the inner slope of the dark matter halo. We then collecteda sample of 45 strong lenses in the redshift interval 0.2 &lt; z &lt; 0.8 and used them, incombination with lenses from other surveys, to measure the slope of the total densityprofile, the stellar IMF and the dark matter mass in the population of massive early-typegalaxies, and their time evolution. Finally, we used our measurements of the evolution ofthe density slope to test a galaxy growth scenario based on purely dissipationless mergers.Our main results are: the stellar IMF of massive early-type galaxies is significantly heavierthan that of the Milky Way and correlates with galaxy mass; the dark matter halo hasa steep slope in at least one system; more compact galaxies have less dark matter thantheir extended counterparts at fixed redshift and stellar mass; early-type galaxies evolvewhile keeping the slope of their total density profile approximately constant. This last result cannot be reproduced with purely dissipationless mergers, therefore a little amountof dissipation is required

The cosmic evolution of the stellar mass−-velocity dispersion relation of early-type galaxies

We study the evolution of the observed correlation between central stellar velocity dispersion $\sigma_\mathrm{e}$ and stellar mass $M_*$ of massive ($M_*\gtrsim 3\times 10^{10}\,\mathrm{M_\odot}$) early-type galaxies (ETGs) out to redshift $z\approx 2.5$, exploiting a Bayesian hierarchical inference formalism. Collecting ETGs from state-of-the-art literature samples, we build a $fiducial$ sample ($0\lesssim z\lesssim 1$), which is obtained with homogeneous selection criteria, but also a less homogeneous $extended$ sample ($0\lesssim z\lesssim 2.5$). Based on the fiducial sample, we find that the $M_*$-$\sigma_\mathrm{e}$ relation is well represented by $\sigma_\mathrm{e}\propto M_*^{\beta}(1+z)^{\zeta}$, with $\beta\simeq 0.18$ independent of redshift and $\zeta\simeq 0.4$ (at given $M_*$, $\sigma_\mathrm{e}$ decreases for decreasing $z$, for instance by a factor of $\approx1.3$ from $z=1$ to $z=0$). When the slope $\beta$ is allowed to evolve, we find it increasing with redshift: $\beta(z)\simeq 0.16+0.26\log(1+z)$ describes the data as well as constant $\beta\simeq 0.18$. The intrinsic scatter of the $M_*$-$\sigma_\mathrm{e}$ relation is $\simeq0.08$ dex in $\sigma_\mathrm{e}$ at given $M_*$, independent of redshift. Our results suggest that, on average, the velocity dispersion of $individual$ massive ($M_*\gtrsim 3\times 10^{11}\,M_\odot$) ETGs decreases with time while they evolve from $z\approx 1$ to $z\approx 0$. The analysis of the extended sample leads to results similar to that of the fiducial sample, with slightly stronger redshift dependence of the normalisation ($\zeta\simeq 0.5$) and weaker redshift dependence of the slope (${\rm d} \beta/{\rm d} \log (1+z)\simeq 0.18$) when $\beta$ varies with time. At $z=2$ ETGs with $M_*\approx 10^{11}\,M_\odot$ have, on average, $\approx1.7$ higher $\sigma_\mathrm{e}$ than ETGs of similar stellar mass at $z=0$.Comment: 26 pages, 15 figures, accepted for publication in MNRA