Search

We present a new measurement of the dark and luminous matter distribution of massive elliptical galaxies, and their evolution with redshift, by combining strong lensing and dynamical observables. Our sample of 58 lens galaxies covers a redshift range of $0.090\leq z_{\rm l}\leq0.884$. By combining new Hubble Space Telescope imaging with previously observed velocity dispersion and line-of-sight measurements, we decompose the luminous matter profile from the dark matter profile and perform a Bayesian hierarchical analysis to constrain the population-level properties of both profiles. We find that the inner slope of the dark matter density profile ("cusp"; $\rho_{\rm DM}\propto r^{-\gamma_{\rm in}}$) is slightly steeper ($\mu_{\gamma_{\rm in}}=1.18^{+0.03}_{-0.03}$ at $z=0.35$ with $\leq0.16$ intrinsic scatter) than a standard Navarro$-$Frenk$-$White (NFW; $\gamma_{\rm in}=1$), with an appreciable evolution with redshift ($d\log(\gamma_{\rm in})/dz=-0.33\pm0.13$) and is consistent with NFW-like distributions at higher redshifts ($z\geq0.56$ for $\leq1\sigma$ consistency). Additionally, we find the stellar mass-to-light ratio at the population level consistent with that of a Salpeter initial mass function, a small stellar mass-to-light gradient ($\kappa_{*}(r)\propto r^{-\eta}$, with $\overline{\eta}\leq9.4\times10^{-3}$), and isotropic stellar orbits. Our averaged total mass density profile is consistent with a power-law profile within $0.25-4$ Einstein radii ($\overline{\gamma}=2.14\pm0.06$), with an internal mass-sheet transformation parameter $\overline{\lambda}=1.02\pm0.01$ consistent with no mass sheet. Our findings confirm the validity of the standard mass models used for time-delay cosmography. However, our results are in strong tension with predictions from hydrodynamical simulations such as IllustrisTNG, highlighting the need to better understand the formation of massive galaxies., Comment: 28 pages, 20 figures

Strong gravitational lensing observations can provide extremely valuable information on the structure of galaxies, but their interpretation is made difficult by selection effects, which, if not accounted for, introduce a bias between the properties of strong lens galaxies and those of the general population. A rigorous treatment of the strong lensing bias requires, in principle, to fully forward model the lens selection process. However, doing so for existing lens surveys is prohibitively difficult. With this work we propose a practical solution to the problem: using an empirical model to capture the most complex aspects of the lens finding process, and constraining it directly from the data together with the properties of the lens population. We applied this method to real data from the SLACS sample of strong lenses. Assuming a power-law density profile, we recovered the mass distribution of the parent population of galaxies from which the SLACS lenses were drawn. We found that early-type galaxies with a stellar mass of $\log{M_*/M_\odot}=11.3$ and average size have a median projected mass enclosed within a $5$~kpc aperture of $\log{M_5/M_\odot}=11.332\pm0.013$, and an average logarithmic density slope of $\gamma=1.99\pm0.03$. These values are respectively $0.02$~dex and $0.1$ lower than inferred when ignoring selection effects. According to our model, most of the bias is due to the prioritisation of SLACS follow-up observations based on the measured velocity dispersion. As a result, the strong lensing bias in $\gamma$ reduces to $\sim0.01$ when controlling for stellar velocity dispersion., Comment: Submitted to Astronomy & Astrophysics. A 2-minute summary video is available at this link: https://youtu.be/wtrMRereBwE

Quadruply-imaged strongly lensed quasars (quads) are routinely used for measurements of the expansion rate of the Universe with time delays. It has recently been suggested that any quad lens is subject to a Malmquist-like bias that causes the inferred area enclosed within the tangential caustic to be systematically underestimated, and that such a bias might translate into a corresponding bias on the expansion parameter. In this work we extended that analysis by also considering the effect of Eddington bias. We found that the sign and amplitude of the combined bias depend on the functional form of the caustic area distribution of the lens population and on the noise associated with the caustic area estimation process. Based on simulations, we estimated that the corresponding impact on $H_0$ is on the order of a percent or smaller. If the likelihood of the lensing data is known, then the bias can be accounted for when modelling the lens population. However, ignoring the criteria used to select a quad might lead to a bias at the lens modelling stage that causes the inferred caustic area to be overestimated. Such a bias disappears for lens models that are well constrained by the data., Comment: Accepted for publication on Astronomy & Astrophysics

The statistics of Einstein radii for a sample of strong lenses can provide valuable constraints on the underlying mass distribution. The correct interpretation, however, relies critically on the modelling of the selection of the sample, which has proven to be a limiting factor. This may change thanks to upcoming uniform high-resolution imaging surveys that cover a large fraction of the sky, because they can provide complete lens samples, with well understood selection criteria. To explore how the observed distribution of Einstein radii depends on the galaxy properties, we simulated a realistic complete sample of strong lenses, predicting a number density of lenses of about 2.5 deg$^{-2}$ for a \Euclid-like setup. Such data can break the degeneracy between the stellar initial mass function (IMF) and the inner slope of the density profile of dark matter, without having to rely on additional information from stellar dynamics. We found that a survey covering only 50 deg$^2$ can already provide tight constraints: assuming that the cosmology is known, the dark matter slope is recovered with an uncertainty of $3.5\%$, while the uncertainty in the ratio between the true stellar mass and that inferred from stellar population modelling was found to be $10\%$. These findings highlight the potential of this method when applied to samples of lenses with well-understood selection functions., Comment: Submitted to Astronomy & Astrophysics

Efficient algorithms are being developed to search for strong gravitational lens systems owing to increasing large imaging surveys. Neural networks have been successfully used to discover galaxy-scale lens systems in imaging surveys such as the Kilo Degree Survey, Hyper-Suprime Cam (HSC) Survey and Dark Energy Survey over the last few years. Thus, it has become imperative to understand how some of these networks compare, their strengths and the role of the training datasets as most of the networks make use of supervised learning algorithms. In this work, we present the first-of-its-kind systematic comparison and benchmarking of networks from four teams that have analysed the HSC Survey data. Each team has designed their training samples and developed neural networks independently but coordinated apriori in reserving specific datasets strictly for test purposes. The test sample consists of mock lenses, real (candidate) lenses and real non-lenses gathered from various sources to benchmark and characterise the performance of each of the network. While each team's network performed much better on their own constructed test samples compared to those from others, all networks performed comparable on the test sample with real (candidate) lenses and non-lenses. We also investigate the impact of swapping the training samples amongst the teams while retaining the same network architecture. We find that this resulted in improved performance for some networks. These results have direct implications on measures to be taken for lens searches with upcoming imaging surveys such as the Rubin-Legacy Survey of Space and Time, Roman and Euclid., Comment: 13 pages, 8 figures

Empirical correlations connecting starlight to galaxy dynamics (e.g., the fundamental plane (FP) of elliptical/quiescent galaxies and the Tully--Fisher relation of spiral/star-forming galaxies) provide cosmology-independent distance estimation and are central to local Universe cosmology. In this work, we introduce the mass hyperplane (MH), which is the stellar-to-dynamical mass relation $(M_\star/M_\mathrm{dyn})$ recast as a linear distance indicator. Building on recent FP studies, we show that both star-forming and quiescent galaxies follow the same empirical MH, then use this to measure the peculiar velocities (PVs) for a sample of 2496 galaxies at $z<0.12$ from GAMA. The limiting precision of MH-derived distance/PV estimates is set by the intrinsic scatter in size, which we find to be $\approx$0.1~dex for both quiescent and star-forming galaxies (when modeled independently) and $\approx$0.11~dex when all galaxies are modeled together; showing that the MH is as good as the FP. To empirically validate our framework and distance/PV estimates, we compare the inferred distances to groups as derived using either quiescent or star-forming galaxies. A good agreement is obtained with no discernible bias or offset, having a scatter of $\approx$0.05~dex $\approx$12\% in distance. Further, we compare our PV measurements for the quiescent galaxies to the previous PV measurements of the galaxies in common between GAMA and the Sloan Digital Sky Survey (SDSS), which shows similarly good agreement. Finally, we provide comparisons of PV measurements made with the FP and the MH, then discuss possible improvements in the context of upcoming surveys such as the 4MOST Hemisphere Survey (4HS)., Comment: Accepted: 15th May 2024

Galaxies that cause the strong gravitational lensing of background galaxies provide us crucial information about the distribution of matter around them. Traditional modelling methods that analyse such strong lenses are both time and resource consuming, require sophisticated lensing codes and modelling expertise. To study the large lens population expected from imaging surveys such as LSST, we need fast and automated analysis methods. In this work, we build and train a simple convolutional neural network with an aim to rapidly predict model parameters of gravitational lenses. We focus on the most important lens mass model parameters, namely, the Einstein radius, the axis ratio and the position angle of the major axis of the mass distribution. The network is trained on a variety of simulated data with an increasing degree of realism and shows satisfactory performance on simulated test data. The trained network is then applied to the real sample of galaxy-scale candidate lenses from the Subaru HSC, a precursor survey to LSST. Unlike the simulated lenses, we do not have the ground truth for the real lenses. Therefore, we have compared our predictions with those from YattaLens, a lens modelling pipeline. Additionally, we also compare the parameter predictions for 10 HSC lenses that were also studied by other conventional modelling methods. These comparisons show a fair quantitative agreement on the Einstein radius, although the axis ratio and the position angle from the network as well as the individual modelling methods, seem to have systematic uncertainties beyond the quoted errors., Comment: 10 pages, 9 figures

The mass distribution in massive elliptical galaxies encodes their evolutionary history, thus providing an avenue to constrain the baryonic astrophysics in their evolution. The power-law assumption for the radial mass profile in ellipticals has been sufficient to describe several observables to the noise level, including strong lensing and stellar dynamics. In this paper, we quantitatively constrained any deviation, or the lack thereof, from the power-law mass profile in massive ellipticals through joint lensing-dynamics analysis of a large statistical sample with 77 galaxy-galaxy lens systems. We performed an improved and uniform lens modelling of these systems from archival Hubble Space Telescope imaging using the automated lens modelling pipeline dolphin. We combined the lens model posteriors with the stellar dynamics to constrain the deviation from the power law after accounting for the line-of-sight lensing effects, a first for analyses on galaxy-galaxy lenses. We find that the Sloan Lens ACS Survey (SLACS) lens galaxies with a mean redshift of 0.2 are consistent with the power-law profile within 1.1$\sigma$ (2.8$\sigma$) and the Strong Lensing Legacy Survey (SL2S) lens galaxies with a mean redshift of 0.6 are consistent within 0.8$\sigma$ (2.1$\sigma$), for a spatially constant (Osipkov-Merritt) stellar anisotropy profile. We adopted the spatially constant anisotropy profile as our baseline choice based on previous dynamical observables of local ellipticals. However, spatially resolved stellar kinematics of lens galaxies are necessary to differentiate between the two anisotropy models. Future studies will use our lens models to constrain the mass distribution individually in the dark matter and baryonic components., Comment: 31 pages, 20 figures, 9 tables. This version: accepted to MNRAS

A constant stellar mass-to-light ratio $M_\star/L$ has been widely-used in studies of galaxy dynamics and strong lensing, which aim at disentangling the mass distributions of dark matter and baryons. However, systematic biases arising from constant $M_\star/L$ assumption have not been fully quantified. In this work, we take massive early-type galaxies from the TNG100 simulation to investigate possible systematic biases in the inferences due to a constant $M_\star/L$ assumption. We construct two-component matter density models, where one component describes the dark matter, the other for the stars, which is made to follow the light profile by assuming a constant $M_\star/L$. We fit the two-component model directly to the {\it total} matter density distributions of simulated galaxies to eliminate systematics coming from other model assumptions. We find that galaxies generally have more centrally-concentrated stellar mass profile than their light distribution. Given the light profiles adopted (i.e., single- and double-S{\'e}rsic profiles), the assumption of a constant $M_\star/L$ would artificially break the model degeneracy {\it for non-constant} $M_\star/L$ systems. For such systems, without knowing the true $M_{\star}/L$ but assuming a constant ratio, the two-component modeling procedure tend to generally overestimate $M_{\star}/L$ by $30\%-50\%$, and underestimate the central dark matter fraction $f_{\rm DM}$ by $\sim 20\%$ on average., Comment: 18 pages, 10 figures, submitted to MNRAS

In this empirical work, we aim to quantify the systematic uncertainties in stellar mass $(M_\star)$ estimates made from spectral energy distribution (SED) fitting through stellar population synthesis (SPS), for galaxies in the local Universe, by using the dynamical mass $(M_\text{dyn})$ estimator as an SED-independent check on stellar mass. We first construct a statistical model of the high dimensional space of galaxy properties; size $(R_e)$, velocity dispersion $(\sigma_e)$, surface brightness $(I_e)$, mass-to-light ratio $(M_\star/L)$, rest-frame colour, S\'ersic index $(n)$ and dynamical mass $(M_\text{dyn})$; accounting for selection effects and covariant errors. We disentangle the correlations among galaxy properties and find that the variation in $M_\star/M_\text{dyn}$ is driven by $\sigma_e$, S\'ersic index and colour. We use these parameters to calibrate an SED-independent $M_\star$ estimator, $\hat{M}_\star$. We find the random scatter of the relation $M_\star-\hat{M}_\star$ to be $0.108\text{dex}$ and $0.147\text{dex}$ for quiescent and star-forming galaxies respectively. Finally, we inspect the residuals as a function of SPS parameters (dust, age, metallicity, star formation rate) and spectral indices (H$\alpha$, H$\delta$, $D_n4000)$. For quiescent galaxies, $\sim65\%$ of the scatter can be explained by the uncertainty in SPS parameters, with dust and age being the largest sources of uncertainty. For star-forming galaxies, while age and metallicity are the leading factors, SPS parameters account for only $\sim13\%$ of the scatter. These results leave us with remaining unmodelled scatters of $0.055\text{dex}$ and $0.122\text{dex}$ for quiescent and star-forming galaxies respectively. This can be interpreted as a conservative limit on the precision in $M_\star$ that can be achieved via simple SPS-modelling., Comment: Accepted for publication in the Astrophysical Journal on 14 June 2023

Context. Strong lenses are a biased subset of the general population of galaxies. Aims. The goal of this work is to quantify how lens galaxies and lensed sources differ from their parent distribution, namely the strong lensing bias. Methods. We first studied how the strong lensing cross-section varies as a function of lens and source properties. Then, we simulated strong lensing surveys with data similar to that expected for Euclid and measured the strong lensing bias in different scenarios. We focused particularly on two quantities: the stellar population synthesis mismatch parameter, $\alpha_{sps}$, defined as the ratio between the true stellar mass of a galaxy and the stellar mass obtained from photometry, and the central dark matter mass at fixed stellar mass and size. Results. Strong lens galaxies are biased towards larger stellar masses, smaller half-mass radii and larger dark matter masses. The amplitude of the bias depends on the intrinsic scatter in the mass-related parameters of the galaxy population and on the completeness in Einstein radius of the lens sample. For values of the scatter that are consistent with observed scaling relations and a minimum detectable Einstein radius of $0.5''$, the strong lensing bias in $\alpha_{sps}$ is $10\%$, while that in the central dark matter mass is $5\%$. The bias has little dependence on the properties of the source population: samples of galaxy-galaxy lenses and galaxy-quasar lenses that probe the same Einstein radius distribution are biased in a very similar way. Conclusions. Given current uncertainties, strong lensing observations can be used directly to improve our current knowledge of the inner structure of galaxies, without the need to correct for selection effects. Time-delay measurements of $H_0$ from lensed quasars can take advantage of prior information obtained from galaxy-galaxy lenses with similar Einstein radii., Comment: Published on Astronomy & Astrophysics. A two-minute summary video of this paper is available at https://youtu.be/UmS9jRHTmZU

We compare stellar mass surface density, metallicity, age, and line-of-sight velocity dispersion profiles in massive ($M_*\geq10^{10.5}\,\mathrm{M_\odot}$) present-day early-type galaxies (ETGs) from the MaNGA survey with simulated galaxies from the TNG100 simulation of the IllustrisTNG suite. We find an excellent agreement between the stellar mass surface density profiles of MaNGA and TNG100 ETGs, both in shape and normalisation. Moreover, TNG100 reproduces the shapes of the profiles of stellar metallicity and age, as well as the normalisation of velocity dispersion distributions of MaNGA ETGs. We generally also find good agreement when comparing the stellar profiles of central and satellite galaxies between MaNGA and TNG100. An exception is the velocity dispersion profiles of very massive ($M_*\gtrsim10^{11.5}\,\mathrm{M_\odot}$) central galaxies, which, on average, are significantly higher in TNG100 than in MaNGA ($\approx50\,\mathrm{km\,s^{-1}}$). We study the radial profiles of $\mathit{in}$-$\mathit{situ}$ and $\mathit{ex}$-$\mathit{situ}$ stars in TNG100 and discuss the extent to which each population contributes to the observed MaNGA profiles. Our analysis lends significant support to the idea that high-mass ($M_*\gtrsim10^{11}\,\mathrm{M_\odot}$) ETGs in the present-day Universe are the result of a merger-driven evolution marked by major mergers that tend to homogenise the stellar populations of the progenitors in the merger remnant., Comment: 22 pages, 9 figures, accepted for publication in MNRAS

Around $10^5$ strongly lensed galaxies are expected to be discovered with Euclid and the LSST. Utilising these large samples to study the inner structure of lens galaxies requires source redshifts, to turn lens models into mass measurements. However, obtaining spectroscopic source redshifts for large lens samples is prohibitive with the capacity of spectroscopic facilities. Alternatively, we study the possibility of obtaining source photometric redshifts (photo-zs) for large lens samples. Our strategy consists of deblending the source and lens light by simultaneously modelling the lens and background source in all available photometric bands, and feeding the derived source colours to a template-fitting photo-z algorithm. We describe the lens and source light with a Sersic profile, and the lens mass with a Singular Isothermal Ellipsoid. We test our approach on a simulated and a real sample of lenses, both in broad-band photometry of the Hyper Suprime-Cam survey. We identify the deviations of the lens light from a Sersic profile and the contrast between the lens and source image as the main drivers of the source colour measurement error. We split the real sample based on the ratio $\Lambda$ of the lens to source surface brightness measured at the image locations. In the $\Lambda<1$ regime, the photo-z outlier fraction is $20\%$, and the accuracy of photo-z estimation is limited by the performance of template-fitting process. In the opposite regime, the photo-z outlier fraction is $75\%$, and the errors from the source colour measurements dominate the photo-z uncertainty. Measuring source photo-zs for lenses with $\Lambda<1$ poses no particular challenges, compared to isolated galaxies. For systems with significant lens light contamination, however, improving the description of the surface brightness distribution of the lens is required: a single Sersic model is not sufficiently accurate., Comment: 15 pages, 13 figures, Accepted for Publication in A&A

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 the total flux and half-light radius of a galaxy with spiral arms can 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: Published on Astronomy & Astrophysics. A 2-minute summary video is available at https://youtu.be/y5ffIZP9XHY

Context. The assembly history of the stellar component of a massive elliptical galaxy is closely related to that of its dark matter halo. Measuring how the properties of galaxies correlate with their halo mass can help understand their evolution. Aims. We investigate how the dark matter halo mass of elliptical galaxies varies as a function of their properties, using weak gravitational lensing observations. To minimise the chances of biases, we focus on galaxy properties that can be determined robustly: the surface brightness profile and the colour. Methods. We selected 2409 central massive elliptical galaxies from the SDSS spectroscopic sample. We first measured their surface brightness profile and colours by fitting Sersic models to photometric data from the Kilo-Degree Survey (KiDS). We fitted their halo mass distribution as a function of redshift, rest-frame $r-$band luminosity, half-light radius and rest-frame $u-g$ colour, using KiDS weak lensing data and a Bayesian hierarchical approach. For the sake of robustness to assumptions on the large-radii behaviour of the surface brightness, we repeated the analysis replacing total luminosity and half-light radius with the luminosity within a 10~kpc aperture, $L_{r,10}$, and the light-weighted surface brightness slope, $\Gamma_{10}$. Results. We did not detect any correlation between halo mass and either half-light radius or colour, at fixed redshift and luminosity. Conclusions. Our results indicate that the average star formation efficiency of massive elliptical galaxies has little dependence on their final size or colour. This suggests that the origin of the diversity in the size and colour distribution of these objects lies with properties other than halo mass., Comment: In press on Astronomy & Astrophysics. A short summary video is available at https://youtu.be/LlvwQNjLT7k

Context. Strong lensing mass measurements require the knowledge of the redshift of both the lens and the source galaxy. Traditionally, spectroscopic redshifts are used for this purpose. Upcoming surveys, however, will lead to the discovery of $\sim10^5$ strong lenses, and it will be very difficult to obtain spectroscopic redshifts for most of them. Photometric redshift measurements will also be very challenging, due to the blending between lens and source light. Aims. The goal of this work is to demonstrate how to carry out an inference of the structural properties of the galaxy population from the analysis of a set of strong lenses with no individual source redshift measurements, and to assess the loss in precision compared to the case in which spectroscopic redshifts are available. Methods. Building on the formalism introduced in Paper III, I developed a method that allows to carry out a statistical strong lensing inference while marginalising over the source redshifts. This method, which relies on the knowledge of the properties of the unlensed background source population and of the selection function of the survey, generalises an approach known as photogeometric redshift, originally introduced by the Strong Lensing Legacy Survey collaboration. I tested the method on simulated data consisting of a subset of 137 strong lenses that is complete above a cut in observational space. Results. The method recovers the properties of the galaxy population, with a precision that is comparable to that attainable in the case in which individual source redshifts are known. Conclusions. The photogeometric redshift method is a viable approach for the analysis of large sets of strong lenses, provided that the background source population properties and lens selection function are well-known., Comment: Published on Astronomy & Astrophysics. A 2-minute summary video is available at https://youtu.be/bNleRlWA_PE

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. Mandatory. 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: Published on Astronomy & Astrophysics. A 2-minute summary video is available at https://youtu.be/f6PziIr9USE

Context. Time delay lensing is a powerful tool to measure the Hubble constant $H_0$. In order to obtain an accurate estimate of $H_0$ from a sample of time delay strong lenses, however, it is necessary to have a very good knowledge of the mass structure of the lens galaxies. Strong lensing data on their own are not sufficient to break the degeneracy between $H_0$ and the lens model parameters, on a single object basis. Aims. The goal of this study is to determine whether it is possible to break the $H_0$-lens structure degeneracy with the statistical combination of a large sample of time-delay lenses, relying purely on strong lensing data (that is, with no stellar kinematics information). Methods. I simulated a set of 100 lenses with doubly imaged quasars and related time delay measurements. I fitted these data with a Bayesian hierarchical method and a flexible model for the lens population, emulating the lens modelling step. Results. The sample of 100 lenses, on its own, provides a measurement of $H_0$ with $3\%$ precision, but with a $-4\%$ bias. However, the addition of prior information on the lens structural parameters from a large sample of lenses with no time delays, such as that considered in Paper I, allows for a $1\%$-level inference. Moreover, the 100 lenses allow for a $0.03$~dex calibration of galaxy stellar masses, regardless of the level of prior knowledge of the Hubble constant. Conclusions. Breaking the $H_0$-lens model degeneracy with lensing data alone is possible, but $1\%$ measurements of $H_0$ require either a number of time delay lenses much larger than 100, or the knowledge of the structural parameter distribution of the lens population from a separate sample of lenses., Comment: Published on Astronomy & Astrophysics. A 2-minute summary video is available at https://youtu.be/EBiWvKCL6yk

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-uJobqE4

The stellar initial mass function (IMF) is believed to be non-universal among early-type galaxies (ETGs). Parameterizing the IMF with the so-called IMF mismatch parameter $\alpha_{\rm IMF}$, which is a measure of the stellar mass-to-light ratio of an ensemble of stars and thus of the 'heaviness' of its IMF, one finds that for ETGs $\alpha_{\rm e}$ (i.e. $\alpha_{\rm IMF}$ integrated within the effective radius $R_{\rm e}$) increases with $\sigma_{\rm e}$ (the line-of-sight velocity dispersion $\sigma_{\rm los}$ integrated within $R_{\rm e}$) and that, within the same ETG, $\alpha_{\rm IMF}$ tends to decrease outwards. We study the effect of dissipationless (dry) mergers on the distribution of the IMF mismatch parameter $\alpha_{\rm IMF}$ in ETGs using the results of binary major and minor merging simulations. We find that dry mergers tend to make the $\alpha_{\rm IMF}$ profiles of ETGs shallower, but do not alter significantly the shape of the distributions in the spatially resolved $\sigma_{\rm los}\alpha_{\rm IMF}$ space. Individual galaxies undergoing dry mergers tend to decrease their $\alpha_{\rm e}$, due to erosion of $\alpha_{\rm IMF}$ gradients and mixing with stellar populations with lighter IMF. Their $\sigma_{\rm e}$ can either decrease or increase, depending on the merging orbital parameters and mass ratio, but tends to decrease for cosmologically motivated merging histories. The $\alpha_{\rm e}$-$\sigma_{\rm e}$ relation can vary with redshift as a consequence of the evolution of individual ETGs: based on a simple dry-merging model, ETGs of given $\sigma_{\rm e}$ are expected to have higher $\alpha_{\rm e}$ at higher redshift, unless the accreted satellites are so diffuse that they contribute negligibly to the inner stellar distribution of the merger remnant., Comment: 15 pages, 13 figures, accepted for publication in MNRAS

We investigate the internal structure of elliptical galaxies at $z\sim 0.2$ from a joint lensing-dynamics analysis. We model Hubble Space Telescope images of a sample of 23 galaxy-galaxy lenses selected from the Sloan Lens ACS (SLACS) survey. Whereas the original SLACS analysis estimated the logarithmic slopes by combining the kinematics with the imaging data, we estimate the logarithmic slopes only from the imaging data. We find that the distribution of the lensing-only logarithmic slopes has a median $2.08\pm0.03$ and intrinsic scatter $0.13 \pm 0.02$, consistent with the original SLACS analysis. We combine the lensing constraints with the stellar kinematics and weak lensing measurements, and constrain the amount of adiabatic contraction in the dark matter (DM) halos. We find that the DM halos are well described by a standard Navarro-Frenk-White halo with no contraction on average for both of a constant stellar mass-to-light ratio ($M/L$) model and a stellar $M/L$ gradient model. For the $M/L$ gradient model, we find that most galaxies are consistent with no $M/L$ gradient. Comparison of our inferred stellar masses with those obtained from the stellar population synthesis method supports a heavy initial mass function (IMF) such as the Salpeter IMF. We discuss our results in the context of previous observations and simulations, and argue that our result is consistent with a scenario in which active galactic nucleus feedback counteracts the baryonic-cooling-driven contraction in the DM halos., Comment: 26 pages, 19 figures, 3 tables. This version: accepted to MNRAS

We present spectroscopic confirmation of three new two-image gravitationally lensed quasars, compiled from existing strong lens and X-ray catalogs. Images of HSC J091843.27$-$022007.5 show a red galaxy with two blue point sources at either side, separated by 2.26 arcsec. This system has a source and a lens redshifts $z_s=0.804$ and $z_{\ell}=0.459$, respectively, as obtained by our follow-up spectroscopic data. CXCO J100201.50$+$020330.0 shows two point sources separated by 0.85 arcsec on either side of an early-type galaxy. The follow-up spectroscopic data confirm the fainter quasar has the same redshift with the brighter quasar from the SDSS fiber spectrum at $z_s=2.016$. The deflecting foreground galaxy is a typical early-type galaxy at a redshift of $z_{\ell}=0.439$. SDSS J135944.21$+$012809.8 has two point sources with quasar spectra at the same redshift $z_s=1.096$, separated by 1.05 arcsec, and fits to the HSC images confirm the presence of a galaxy between these. These discoveries demonstrate the power of the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP)'s deep imaging and wide sky coverage. Combined with existing X-ray source catalogues and follow-up spectroscopy, the HSC-SSP provides us unique opportunities to find multiple-image quasars lensed by a foreground galaxy., Comment: Accepted for publication in MNRAS, 7 pages, 3 figures (add credit to Claude Cornen)

We use KiDS weak lensing data to measure variations in mean halo mass as a function of several key galaxy properties (namely: stellar colour, specific star formation rate, Sersic index, and effective radius) for a volume-limited sample of GAMA galaxies in a narrow stellar mass range ($M_* \sim 2$--$5 \times 10^{10}$ Msol). This mass range is particularly interesting, inasmuch as it is where bimodalities in galaxy properties are most pronounced, and near to the break in both the galaxy stellar mass function and the stellar-to-halo mass relation (SHMR). In this narrow mass range, we find that both size and Sersic index are better predictors of halo mass than either colour or SSFR, with the data showing a slight preference for Sersic index. In other words, we find that mean halo mass is more tightly correlated with galaxy structure than either past star formation history or current star formation rate. Our results lead to an approximate lower bound on the dispersion in halo masses among $\log M_* \approx {10.5}$ galaxies: we find that the dispersion is $\gtrsim 0.3$ dex. This would imply either that offsets from the mean SHMR are closely coupled to size/structure, or that the dispersion in the SHMR is larger than past results have suggested. Our results thus provide new empirical constraints on the relationship between stellar and halo mass assembly at this particularly interesting mass range., Comment: 16 pages, 7 figures; submitted to MNRAS; updated to reflect accepted version

The evolution of the structural and kinematic properties of early-type galaxies (ETGs), their scaling relations, as well as their stellar metallicity and age contain precious information on the assembly history of these systems. We present results on the evolution of the stellar mass-velocity dispersion relation of ETGs, focusing in particular on the effects of some selection criteria used to define ETGs. We also try to shed light on the role that in-situ and ex-situ stellar populations have in massive ETGs, providing a possible explanation of the observed metallicity distributions., Comment: 5 pages, 2 figures. To appear in Proceedings of IAU Symposium 359 (T. Storchi-Bergmann, R. Overzier, W. Forman & R. Riffel, eds.)

Strong lenses are extremely useful probes of the distribution of matter on galaxy and cluster scales at cosmological distances, but are rare and difficult to find. The number of currently known lenses is on the order of 1,000. We wish to use crowdsourcing to carry out a lens search targeting massive galaxies selected from over 442 square degrees of photometric data from the Hyper Suprime-Cam (HSC) survey. We selected a sample of $\sim300,000$ galaxies with photometric redshifts in the range $0.2 < z_{phot} < 1.2$ and photometrically inferred stellar masses $\log{M_*} > 11.2$. We crowdsourced lens finding on this sample of galaxies on the Zooniverse platform, as part of the Space Warps project. The sample was complemented by a large set of simulated lenses and visually selected non-lenses, for training purposes. Nearly 6,000 citizen volunteers participated in the experiment. In parallel, we used YattaLens, an automated lens finding algorithm, to look for lenses in the same sample of galaxies. Based on a statistical analysis of classification data from the volunteers, we selected a sample of the most promising $\sim1,500$ candidates which we then visually inspected: half of them turned out to be possible (grade C) lenses or better. Including lenses found by YattaLens or serendipitously noticed in the discussion section of the Space Warps website, we were able to find 14 definite lenses, 129 probable lenses and 581 possible lenses. YattaLens found half the number of lenses discovered via crowdsourcing. Crowdsourcing is able to produce samples of lens candidates with high completeness and purity, compared to currently available automated algorithms. A hybrid approach, in which the visual inspection of samples of lens candidates pre-selected by discovery algorithms and/or coupled to machine learning is crowdsourced, will be a viable option for lens finding in the 2020s., Comment: Published version

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 & Astrophysics

We report the largest sample of candidate strong gravitational lenses belonging to the Survey of Gravitationally-lensed Objects in HSC Imaging for group-to-cluster scale (SuGOHI-c) systems. These candidates are compiled from the S18A data release of the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) Survey. We visually inspect $\sim39,500$ galaxy clusters, selected from several catalogs, overlapping with the Wide, Deep, and UltraDeep fields, spanning the cluster redshift range $0.05

A double source plane (DSP) system is a precious probe for the density profile of distant galaxies and cosmological parameters. However, these measurements could be affected by the surrounding environment of the lens galaxy. Thus, it is important to evaluate the cluster-scale mass for detailed mass modeling. We observed the {\it Eye of Horus}, a DSP system discovered by the Subaru HSC--SSP, with XMM--Newton. We detected two X-ray extended emissions, originating from two clusters, one centered at the {\it Eye of Horus}, and the other located $\sim100$ arcsec northeast to the {\it Eye of Horus}. We determined the dynamical mass assuming hydrostatic equilibrium, and evaluated their contributions to the lens mass interior of the Einstein radius. The contribution of the former cluster is $1.1^{+1.2}_{-0.5}\times10^{12}~M_{\odot}$, which is $21-76\%$ of the total mass within the Einstein radius. The discrepancy is likely due to the complex gravitational structure along the line of sight. On the other hand, the contribution of the latter cluster is only $\sim2\%$ on the {\it Eye of Horus}. Therefore, the influence associated with this cluster can be ignored., Comment: 8 pages, 6 figures

Strong gravitationally lensed quasars provide powerful means to study galaxy evolution and cosmology. We use Chitah to hunt for new lens systems in the Hyper Suprime$-$Cam Subaru Strategic Program (HSC SSP) S16A. We present 46 lens candidates, of which 3 are previously known. Including 2 additional lenses found by YattaLens, we obtain X-shooter spectra of 6 promising candidates for lens confirmation and redshift measurements. We report new spectroscopic redshift measurements for both the lens and source galaxies in 4 lens systems. We apply the lens modeling software Glee to model our 6 X-shooter lenses uniformly. Through our analysis of the HSC images, we find that HSCJ022622$-$042522, HSCJ115252$+$004733, and HSCJ141136$-$010216 have point-like lensed images, and that the lens light distribution is well aligned with mass distribution within 6 deg. Thanks to the X-shooter spectra, we estimate fluxes on the Baldwin- Phillips-Terlevich (BPT) diagram, and find that HSCJ022622$-$042522 has a probable quasar source, based on the upper limit of the Nii flux intensity. We also measure the FWHM of Ly$\alpha$ emission of HSCJ141136$-$010216 to be $\sim$254 km/s, showing that it is a probable Lyman-$\alpha$ emitter., Comment: 13 pages, 7 figures

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 MNRAS

We report the serendipitous discovery of HSC J0904$-$0102, a quadruply-lensed Lyman break galaxy (LBG) in the Survey of Gravitationally-lensed Objects in Hyper Suprime-Cam Imaging (SuGOHI). Owing to its point-like appearance, the source was thought to be a lensed active galactic nucleus. We obtained follow-up spectroscopic data with the Gemini Multi-Object Spectrographs on the Gemini South Telescope, which confirmed this to be a lens system. The deflecting foreground galaxy is a typical early-type galaxy at a high redshift of $z_{\ell} = 0.957$ with stellar velocity dispersion $\sigma_v=259\pm56$ km~s$^{-1}$. The lensed source is identified as an LBG at $z_{\rm s} = 3.403$, based on the sharp drop bluewards of Ly$\alpha$ and other absorption features. A simple lens mass model for the system, assuming a singular isothermal ellipsoid, yields an Einstein radius of $\theta_{\rm Ein} = 1. 23^{\prime\prime}$ and a total mass within the Einstein radius of $M_{\rm Ein} = (5.55\pm 0.24) \times 10^{11}M_{\odot}$ corresponding to a velocity dispersion of $\sigma_{\rm SIE}= 283\pm 3$ km~s$^{-1}$, which is in good agreement with the value derived spectroscopically. The most isolated lensed LBG image has a magnification of $\sim 6.5$. In comparison with other lensed LBGs and typical $z\sim4$ LBG populations, HSC J0904$-$0102 is unusually compact, an outlier at $>2\sigma$ confidence. Together with a previously discovered SuGOHI lens, HSC J1152$+$0047, that is similarly compact, we believe that the HSC Survey is extending LBG studies down to smaller galaxy sizes., Comment: Accepted for publication on MNRAS, 10 pages, 6 figures

We present a measurement of the Hubble constant ($H_{0}$) and other cosmological parameters from a joint analysis of six gravitationally lensed quasars with measured time delays. All lenses except the first are analyzed blindly with respect to the cosmological parameters. In a flat $\Lambda$CDM cosmology, we find $H_{0} = 73.3_{-1.8}^{+1.7}$, a 2.4% precision measurement, in agreement with local measurements of $H_{0}$ from type Ia supernovae calibrated by the distance ladder, but in $3.1\sigma$ tension with $Planck$ observations of the cosmic microwave background (CMB). This method is completely independent of both the supernovae and CMB analyses. A combination of time-delay cosmography and the distance ladder results is in $5.3\sigma$ tension with $Planck$ CMB determinations of $H_{0}$ in flat $\Lambda$CDM. We compute Bayes factors to verify that all lenses give statistically consistent results, showing that we are not underestimating our uncertainties and are able to control our systematics. We explore extensions to flat $\Lambda$CDM using constraints from time-delay cosmography alone, as well as combinations with other cosmological probes, including CMB observations from $Planck$, baryon acoustic oscillations, and type Ia supernovae. Time-delay cosmography improves the precision of the other probes, demonstrating the strong complementarity. Allowing for spatial curvature does not resolve the tension with $Planck$. Using the distance constraints from time-delay cosmography to anchor the type Ia supernova distance scale, we reduce the sensitivity of our $H_0$ inference to cosmological model assumptions. For six different cosmological models, our combined inference on $H_{0}$ ranges from $\sim73$-$78~\mathrm{km~s^{-1}~Mpc^{-1}}$, which is consistent with the local distance ladder constraints., Comment: Accepted for publication in MNRAS; 23 pages, 13 figures, 8 tables

We present the measurement of the Hubble Constant, $H_0$, with three strong gravitational lens systems. We describe a blind analysis of both PG1115+080 and HE0435-1223 as well as an extension of our previous analysis of RXJ1131-1231. For each lens, we combine new adaptive optics (AO) imaging from the Keck Telescope, obtained as part of the SHARP AO effort, with Hubble Space Telescope (HST) imaging, velocity dispersion measurements, and a description of the line-of-sight mass distribution to build an accurate and precise lens mass model. This mass model is then combined with the COSMOGRAIL measured time delays in these systems to determine $H_{0}$. We do both an AO-only and an AO+HST analysis of the systems and find that AO and HST results are consistent. After unblinding, the AO-only analysis gives $H_{0}=82.8^{+9.4}_{-8.3}~\rm km\,s^{-1}\,Mpc^{-1}$ for PG1115+080, $H_{0}=70.1^{+5.3}_{-4.5}~\rm km\,s^{-1}\,Mpc^{-1}$ for HE0435-1223, and $H_{0}=77.0^{+4.0}_{-4.6}~\rm km\,s^{-1}\,Mpc^{-1}$ for RXJ1131-1231. The joint AO-only result for the three lenses is $H_{0}=75.6^{+3.2}_{-3.3}~\rm km\,s^{-1}\,Mpc^{-1}$. The joint result of the AO+HST analysis for the three lenses is $H_{0}=76.8^{+2.6}_{-2.6}~\rm km\,s^{-1}\,Mpc^{-1}$. All of the above results assume a flat $\Lambda$ cold dark matter cosmology with a uniform prior on $\Omega_{\textrm{m}}$ in [0.05, 0.5] and $H_{0}$ in [0, 150] $\rm km\,s^{-1}\,Mpc^{-1}$. This work is a collaboration of the SHARP and H0LiCOW teams, and shows that AO data can be used as the high-resolution imaging component in lens-based measurements of $H_0$. The full time-delay cosmography results from a total of six strongly lensed systems are presented in a companion paper., Comment: 33 pages, 23 figures

We present the lens mass model of the quadruply-imaged gravitationally lensed quasar WFI2033-4723, and perform a blind cosmographical analysis based on this system. Our analysis combines (1) time-delay measurements from 14 years of data obtained by the COSmological MOnitoring of GRAvItational Lenses (COSMOGRAIL) collaboration, (2) high-resolution $\textit{Hubble Space Telescope}$ imaging, (3) a measurement of the velocity dispersion of the lens galaxy based on ESO-MUSE data, and (4) multi-band, wide-field imaging and spectroscopy characterizing the lens environment. We account for all known sources of systematics, including the influence of nearby perturbers and complex line-of-sight structure, as well as the parametrization of the light and mass profiles of the lensing galaxy. After unblinding, we determine the effective time-delay distance to be $4784_{-248}^{+399}~\mathrm{Mpc}$, an average precision of $6.6\%$. This translates to a Hubble constant $H_{0} = 71.6_{-4.9}^{+3.8}~\mathrm{km~s^{-1}~Mpc^{-1}}$, assuming a flat $\Lambda$CDM cosmology with a uniform prior on $\Omega_\mathrm{m}$ in the range [0.05, 0.5]. This work is part of the $H_0$ Lenses in COSMOGRAIL's Wellspring (H0LiCOW) collaboration, and the full time-delay cosmography results from a total of six strongly lensed systems are presented in a companion paper (H0LiCOW XIII)., Comment: Version accepted by MNRAS. 29 pages including appendix, 17 figures, 6 tables. arXiv admin note: text overlap with arXiv:1607.01403

Context: The determination of the stellar initial mass function (IMF) of massive galaxies is one of the open problems in cosmology. Strong gravitational lensing is one of the few methods that allow us to constrain the IMF outside of the Local Group. Aims: The goal of this study is to statistically constrain the distribution in the IMF mismatch parameter, defined as the ratio between the true stellar mass of a galaxy and that inferred assuming a reference IMF, of massive galaxies from the BOSS CMASS sample. Methods: We take 23 strong lenses drawn from the CMASS sample, measure their Einstein radii and stellar masses using multi-band photometry from the Hyper Suprime-Cam survey, then fit a model distribution for the IMF mismatch parameter and dark matter halo mass to the whole sample. We use a prior on halo mass from weak lensing measurements and account for strong lensing selection effects in our model. Results: Assuming an NFW density profile for the dark matter distribution, we infer a value $\mu_{\mathrm{IMF}} = -0.04\pm0.11$ for the average base-10 logarithm of the IMF mismatch parameter, defined with respect to a Chabrier IMF. A Salpeter IMF is in tension with our measurements. Conclusions: Our results are consistent with a scenario in which the region of massive galaxies where the IMF normalization is significantly heavier than that of the Milky Way is much smaller than the scales $5\sim10$~kpc probed by the Einstein radius of the lenses in our sample, as recent spatially resolved studies of the IMF in massive galaxies suggest. The MCMC chains describing the posterior probability distribution of the model are available online, together with the code used to obtain them., Comment: Accepted for publication on A&A. 21 pages, 11 figures

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 figures

We study the faint stellar halo of isolated central galaxies, by stacking galaxy images in the HSC survey and accounting for the residual sky background sampled with random points. The surface brightness profiles in HSC $r$-band are measured for a wide range of galaxy stellar masses ($9.2<\log_{10}M_\ast/M_\odot<11.4$) and out to 120 kpc. Failing to account for the stellar halo below the noise level of individual images will lead to underestimates of the total luminosity by $\leq 15\%$. Splitting galaxies according to the concentration parameter of their light distributions, we find that the surface brightness profiles of low concentration galaxies drop faster between 20 and 100 kpc than those of high concentration galaxies. Albeit the large galaxy-to-galaxy scatter, we find a strong self-similarity of the stellar halo profiles. They show unified forms once the projected distance is scaled by the halo virial radius. The colour of galaxies is redder in the centre and bluer outside, with high concentration galaxies having redder and more flattened colour profiles. There are indications of a colour minimum, beyond which the colour of the outer stellar halo turns red again. This colour minimum, however, is very sensitive to the completeness in masking satellite galaxies. We also examine the effect of the extended PSF in the measurement of the stellar halo, which is particularly important for low mass or low concentration galaxies. The PSF-corrected surface brightness profile can be measured down to $\sim$31 $\mathrm{mag}/\mathrm{arcsec}^2$ at 3-$\sigma$ significance. PSF also slightly flattens the measured colour profiles., Comment: accepted by MNRAS - Significant changes have been made compared with the first version, including discussions on the extended PSF wings, robustness of our results to source detection and masking thresholds and more detailed investigations on the indications of positive colour gradients

We investigate the local and line-of-sight overdensities of strong gravitational lens galaxies using wide-area multiband imaging from the Hyper Suprime-Cam Subaru Strategic Program. We present 41 new definite or probable lens candidates discovered in Data Release 2 of the survey. Using a combined sample of 87 galaxy-scale lenses out to a lens redshift of $z_{\mathrm{L}} \sim 0.8$, we compare galaxy number counts in lines of sight toward known and newly-discovered lenses in the survey to those of a control sample consisting of random lines of sight. We also compare the local overdensity of lens galaxies to a sample of "twin" galaxies that have a similar redshift and velocity dispersion to test whether lenses lie in different environments from similar non-lens galaxies. We find that lens fields contain higher number counts of galaxies compared to the control fields, but this effect arises from the local environment of the lens. Once galaxies in the lens plane are removed, the lens lines of sight are consistent with the control sample. The local environments of the lenses are overdense compared to the control sample, and are slightly overdense compared to those of the twin sample, although the significance is marginal. There is no significant evidence of the evolution of the local overdensity of lens environments with redshift., Comment: Accepted for publication in the Astrophysical Journal; 22 pages, 10 figures, 9 tables

We present a catalogue of 38 spectroscopically detected strong galaxy-galaxy gravitational lens candidates identified in the Sloan Digital Sky Survey IV (SDSS-IV). We were able to simulate narrow-band images for 8 of them demonstrating evidence of multiple images. Two of our systems are compound lens candidates, each with 2 background source-planes. One of these compound systems shows clear lensing features in the narrow-band image. Our sample is based on 2812 galaxies observed by the Mapping Nearby Galaxies at APO (MaNGA) integral field unit (IFU). This Spectroscopic Identification of Lensing Objects (SILO) survey extends the methodology of the Sloan Lens ACS Survey (SLACS) and BOSS Emission-Line Survey (BELLS) to lower redshift and multiple IFU spectra. We searched ~ 1.5 million spectra, of which 3065 contained multiple high signal-to-noise background emission-lines or a resolved [OII] doublet, that are included in this catalogue. Upon manual inspection, we discovered regions with multiple spectra containing background emission-lines at the same redshift, providing evidence of a common source-plane geometry which was not possible in previous SLACS and BELLS discovery programs. We estimate more than half of our candidates have an Einstein radius > 1.7", which is significantly greater than seen in SLACS and BELLS. These larger Einstein radii produce more extended images of the background galaxy increasing the probability that a background emission-line will enter one of the IFU spectroscopic fibres, making detection more likely., Comment: Accepted for publication in MNRAS, March 8, 2018. In press. 16 pages, 5 figures, 4 tables

Large scale imaging surveys will increase the number of galaxy-scale strong lensing candidates by maybe three orders of magnitudes beyond the number known today. Finding these rare objects will require picking them out of at least tens of millions of images and deriving scientific results from them will require quantifying the efficiency and bias of any search method. To achieve these objectives automated methods must be developed. Because gravitational lenses are rare objects reducing false positives will be particularly important. We present a description and results of an open gravitational lens finding challenge. Participants were asked to classify 100,000 candidate objects as to whether they were gravitational lenses or not with the goal of developing better automated methods for finding lenses in large data sets. A variety of methods were used including visual inspection, arc and ring finders, support vector machines (SVM) and convolutional neural networks (CNN). We find that many of the methods will be easily fast enough to analyse the anticipated data flow. In test data, several methods are able to identify upwards of half the lenses after applying some thresholds on the lens characteristics such as lensed image brightness, size or contrast with the lens galaxy without making a single false-positive identification. This is significantly better than direct inspection by humans was able to do. (abridged), Comment: 22 pages, 16 figures, 4 tables, accepted version for A&A

The Initial Mass Function (IMF) for massive galaxies can be constrained by combining stellar dynamics with strong gravitational lensing. However, this method is limited by degeneracies between the density profile of dark matter and the stellar mass-to-light ratio. In this work we reduce this degeneracy by combining weak lensing together with strong lensing and stellar kinematics. Our analysis is based on two galaxy samples: 45 strong lenses from the SLACS survey and 1,700 massive quiescent galaxies from the SDSS main spectroscopic sample with weak lensing measurements from the Hyper Suprime-Cam survey. We use a Bayesian hierarchical approach to jointly model all three observables. We fit the data with models of varying complexity and show that a model with a radial gradient in the stellar mass-to-light ratio is required to simultaneously describe both galaxy samples. This result is driven by a subset of strong lenses with very steep total density profile, that cannot be fitted by models with no gradient. Our measurements are unable to determine whether $M_*/L$ gradients are due to variations in stellar population parameters at fixed IMF, or to gradients in the IMF itself. The inclusion of $M_*/L$ gradients decreases dramatically the inferred IMF normalisation, compared to previous lensing-based studies, with the exact value depending on the assumed dark matter profile. The main effect of strong lensing selection is to shift the stellar mass distribution towards the high mass end, while the halo mass and stellar IMF distribution at fixed stellar mass are not significantly affected., Comment: Published on MNRAS. 23 pages, 16 figures

We carry out a systematic investigation of the total mass density profile of massive (Mstar~3e11 Msun) early-type galaxies and its dependence on redshift, specifically in the range 0

Time delay lensing is a mature and competitive cosmological probe. However, it is limited in accuracy by the well-known problem of the mass-sheet degeneracy: too rigid assumptions on the density profile of the lens can potentially bias the inference on cosmological parameters. I investigate the degeneracy between the choice of the lens density profile and the inference on the Hubble constant, focusing on double image systems. By expanding lensing observables in terms of the local derivatives of the lens potential around the Einstein radius, and assuming circular symmetry, I show that three degrees of freedom in the radial direction are necessary to achieve a few percent accuracy in the time-delay distance. Additionally, while the time delay is strongly dependent on the second derivative of the potential, observables typically used to constrain lens models in time-delay studies, such as image position and radial magnification information, are mostly sensitive to the first and third derivatives, making it very challenging to accurately determine time-delay distances with lensing data alone. Tests on mock observations show that the assumption of a power-law density profile results in a 5% average bias on $H_0$, with a 6% scatter. Using a more flexible model and adding unbiased velocity dispersion constraints allows to obtain an inference with 1% accuracy. A power-law model can still provide 3% accuracy if velocity dispersion measurements are used to constrain its slope. Although this work is based on the assumption of axisymmetry, its main findings can be generalized to cases with moderate ellipticity., Comment: Accepted for publication on MNRAS. 14 pages, 9 figures

We present a Bayesian hierarchical inference formalism to study the relation between the properties of dark matter halos and those of their central galaxies using weak gravitational lensing. Unlike traditional methods, this technique does not resort to stacking the weak lensing signal in bins, and thus allows for a more efficient use of the information content in the data. Our method is particularly useful for constraining scaling relations between two or more galaxy properties and dark matter halo mass, and can also be used to constrain the intrinsic scatter in these scaling relations. We show that, if observational scatter is not properly accounted for, the traditional stacking method can produce biased results when exploring correlations between multiple galaxy properties and halo mass. For example, this bias can affect studies of the joint correlation between galaxy mass, halo mass, and galaxy size, or galaxy color. In contrast, our method easily and efficiently handles the intrinsic and observational scatter in multiple galaxy properties and halo mass. We test our method on mocks with varying degrees of complexity. We find that we can recover the mean halo mass and concentration, each with a $0.1$ dex accuracy, and the intrinsic scatter in halo mass with a $0.05$ dex accuracy. In its current version, our method will be most useful for studying the weak lensing signal around central galaxies in groups and clusters, as well as massive galaxies samples with $\log{M_*} > 11$, which have low satellite fractions., Comment: Published on MNRAS. 19 pages, 13 figures

The Hyper Suprime-Cam Subaru Strategic Program (HSC SSP) is an excellent survey for the search for strong lenses, thanks to its area, image quality and depth. We use three different methods to look for lenses among 43,000 luminous red galaxies from the Baryon Oscillation Spectroscopic Survey (BOSS) sample with photometry from the S16A internal data release of the HSC SSP. The first method is a newly developed algorithm, named YATTALENS, which looks for arc-like features around massive galaxies and then estimates the likelihood of an object being a lens by performing a lens model fit. The second method, CHITAH, is a modeling-based algorithm originally developed to look for lensed quasars. The third method makes use of spectroscopic data to look for emission lines from objects at a different redshift from that of the main galaxy. We find 15 definite lenses, 36 highly probable lenses and 282 possible lenses. Among the three methods, YATTALENS, which was developed specifically for this problem, performs best in terms of both completeness and purity. Nevertheless five highly probable lenses were missed by YATTALENS but found by the other two methods, indicating that the three methods are highly complementary. Based on these numbers we expect to find $\sim$300 definite or probable lenses by the end of the HSC SSP., Comment: Published on PASJ. 17 pages, 8 figures. Image quality of Figures 6 and 7 has been degraded due to arXiv file size limit. Full quality versions can be found at http://member.ipmu.jp/alessandro.sonnenfeld/sugohi1_candidates.html

We carry out a systematic investigation of the total mass density profile of massive (Mstar>2e11 Msun) early-type galaxies and its dependence on galactic properties and host halo mass with the aid of a variety of lensing/dynamical data and large mock galaxy catalogs. The latter are produced via semi-empirical models that, by design, are based on just a few basic input assumptions. Galaxies, with measured stellar masses, effective radii and S\'{e}rsic indices, are assigned, via abundance matching relations, host dark matter halos characterized by a typical LCDM profile. Our main results are as follows: (i) In line with observational evidence, our semi-empirical models naturally predict that the total, mass-weighted density slope at the effective radius gamma' is not universal, steepening for more compact and/or massive galaxies, but flattening with increasing host halo mass. (ii) Models characterized by a Salpeter or variable initial mass function and uncontracted dark matter profiles are in good agreement with the data, while a Chabrier initial mass function and/or adiabatic contractions/expansions of the dark matter halos are highly disfavored. (iii) Currently available data on the mass density profiles of very massive galaxies (Mstar>1e12 Msun), with Mhalo>3e14 Msun, favor instead models with a stellar profile flatter than a S\'{e}rsic one in the very inner regions (r<3-5 kpc), and a cored NFW or Einasto dark matter profile with median halo concentration a factor of ~2 or <1.3, respectively, higher than those typically predicted by N-body numerical simulations., Comment: 23 pages, 10 figures, 3 Appendices (with an extra 7 figures). ApJ, accepted. Main results in Figures 3, 5, 6, 8

The empirical correlation between the mass of a super-massive black hole (MBH) and its host galaxy properties is widely considered to be evidence of their co-evolution. A powerful way to test the co-evolution scenario and learn about the feedback processes linking galaxies and nuclear activity is to measure these correlations as a function of redshift. Unfortunately, currently MBH can only be estimated in active galaxies at cosmological distances. At these distances, bright active galactic nuclei (AGN) can outshine the host galaxy, making it extremely difficult to measure the host's luminosity. Strongly lensed AGNs provide in principle a great opportunity to improve the sensitivity and accuracy of the host galaxy luminosity measurements as the host galaxy is magnified and more easily separated from the point source, provided the lens model is sufficiently accurate. In order to measure the MBH-L correlation with strong lensing, it is necessary to ensure that the lens modelling is accurate, and that the host galaxy luminosity can be recovered to at least a precision and accuracy better than that of the typical MBH measurement. We carry out extensive and realistic simulations of deep Hubble Space Telescope observations of lensed AGNs obtained by our collaboration. We show that the host galaxy luminosity can be recovered with better accuracy and precision than the typical uncertainty on MBH(~ 0.5 dex) for hosts as faint as 2-4 magnitudes dimmer than the AGN itself. Our simulations will be used to estimate bias and uncertainties on the actual measurements to be presented in a future paper., Comment: 18 pages, 13 figures. Revised version after submitted to MNRAS

Early-type galaxies provide unique tests for the predictions of the cold dark matter cosmology and the baryonic physics assumptions entering models for galaxy formation. In this work, we use the Illustris simulation to study correlations of three main properties of early-type galaxies, namely, the stellar orbital anisotropies, the central dark matter fractions and the central radial density slopes, as well as their redshift evolution since $z=1.0$. We find that lower-mass galaxies or galaxies at higher redshift tend to be bluer in rest-frame colour, have higher central gas fractions, and feature more tangentially anisotropic orbits and steeper central density slopes than their higher-mass or lower-redshift counterparts, respectively. The projected central dark matter fraction within the effective radius shows a very mild mass dependence but positively correlates with galaxy effective radii due to the aperture effect. The central density slopes obtained by combining strong lensing measurements with single aperture kinematics are found to differ from the true density slopes. We identify systematic biases in this measurement to be due to two common modelling assumptions, isotropic stellar orbital distributions and power-law density profiles. We also compare the properties of early-type galaxies in Illustris to those from existing galaxy and strong lensing surveys, we find in general broad agreement but also some tension, which poses a potential challenge to the stellar formation and feedback models adopted by the simulation., Comment: 27 pages, 19 figures, 7 tables, accepted for publication in MNRAS. Reported galaxy properties (regardless of galaxy types) are cataloged as the "Photometry, Morphology, Strong-lensing and Dynamics (PMSD)" supplementary catalog, publicly available from the Illustris website (http://www.illustris-project.org)

The stellar initial mass function (IMF) of early-type galaxies is the combination of the IMF of the stellar population formed in-situ and that of accreted stellar populations. Using as an observable the effective IMF $\alpha_{IMF}$, defined as the ratio between the true stellar mass of a galaxy and the stellar mass inferred assuming a Salpeter IMF, we present a theoretical model for its evolution as a result of dry mergers. We use a simple dry merger evolution model, based on cosmological $N$-body simulations, together with empirically motivated prescriptions for the IMF to make predictions for how the effective IMF of massive early-type galaxies changes from $z=2$ to $z=0$. We find that the IMF normalization of individual galaxies becomes lighter with time. At fixed velocity dispersion, $\alpha_{IMF}$ is predicted to be constant with redshift. Current constraints on the evolution of the IMF are in slight tension with this prediction, even though systematic uncertainties prevent a conclusive statement. The correlation of $\alpha_{IMF}$ with stellar mass becomes shallower with time, while the correlation between $\alpha_{IMF}$ and velocity dispersion is mostly preserved by dry mergers. We also find that dry mergers can mix the dependence of the IMF on stellar mass and velocity dispersion, making it challenging to infer, from $z=0$ observations of global galactic properties, what is the quantity that is originally coupled with the IMF., Comment: Submitted to MNRAS. 14 pages, 7 figures

Strong gravitational lenses with measured time delays between the multiple images allow a direct measurement of the time-delay distance to the lens, and thus a measure of cosmological parameters, particularly the Hubble constant, $H_{0}$. We present a blind lens model analysis of the quadruply-imaged quasar lens HE 0435-1223 using deep Hubble Space Telescope imaging, updated time-delay measurements from the COSmological MOnitoring of GRAvItational Lenses (COSMOGRAIL), a measurement of the velocity dispersion of the lens galaxy based on Keck data, and a characterization of the mass distribution along the line of sight. HE 0435-1223 is the third lens analyzed as a part of the $H_{0}$ Lenses in COSMOGRAIL's Wellspring (H0LiCOW) project. We account for various sources of systematic uncertainty, including the detailed treatment of nearby perturbers, the parameterization of the galaxy light and mass profile, and the regions used for lens modeling. We constrain the effective time-delay distance to be $D_{\Delta t} = 2612_{-191}^{+208}~\mathrm{Mpc}$, a precision of 7.6%. From HE 0435-1223 alone, we infer a Hubble constant of $H_{0} = 73.1_{-6.0}^{+5.7}~\mathrm{km~s^{-1}~Mpc^{-1}}$ assuming a flat $\Lambda$CDM cosmology. The cosmographic inference based on the three lenses analyzed by H0LiCOW to date is presented in a companion paper (H0LiCOW Paper V)., Comment: Accepted for publication in MNRAS; 22 pages, 9 figures, 6 tables