Dissecting the 3D structure of elliptical galaxies with gravitational lensing and stellar kinematics

The combination of strong gravitational lensing and stellar kinematics provides a powerful and robust method to investigate the mass and dynamical structure of early-type galaxies. We demonstrate this approach by analysing two massive ellipticals from the XLENS Survey for which both high-resolution HST imaging and X-Shooter spectroscopic observations are available. We adopt a flexible axisymmetric two-component mass model for the lens galaxies, consisting of a generalised NFW dark halo and a realistic self-gravitating stellar mass distribution. For both systems, we put constraints on the dark halo inner structure and flattening, and we find that they are dominated by the luminous component within one effective radius. By comparing the tight inferences on the stellar mass from the combined lensing and dynamics analysis with the values obtained from stellar population studies, we conclude that both galaxies are characterised by a Salpeter-like stellar initial mass function.Comment: Proceedings of the IAU Symposium 309, Contributed Talk, Vienna, July 2014; 4 pages, 2 figure

The SWELLS Survey. VI. hierarchical inference of the initial mass functions of bulges and discs

The long-standing assumption that the stellar initial mass function (IMF) is universal has recently been challenged by a number of observations. Several studies have shown that a "heavy" IMF (e.g., with a Salpeter-like abundance of low mass stars and thus normalisation) is preferred for massive early-type galaxies, while this IMF is inconsistent with the properties of less massive, later-type galaxies. These discoveries motivate the hypothesis that the IMF may vary (possibly very slightly) across galaxies and across components of individual galaxies (e.g. bulges vs discs). In this paper we use a sample of 19 late-type strong gravitational lenses from the SWELLS survey to investigate the IMFs of the bulges and discs in late-type galaxies. We perform a joint analysis of the galaxies' total masses (constrained by strong gravitational lensing) and stellar masses (constrained by optical and near-infrared colours in the context of a stellar population synthesis [SPS] model, up to an IMF normalisation parameter). Using minimal assumptions apart from the physical constraint that the total stellar mass within any aperture must be less than the total mass within the aperture, we find that the bulges of the galaxies cannot have IMFs heavier (i.e. implying high mass per unit luminosity) than Salpeter, while the disc IMFs are not well constrained by this data set. We also discuss the necessity for hierarchical modelling when combining incomplete information about multiple astronomical objects. This modelling approach allows us to place upper limits on the size of any departures from universality. More data, including spatially resolved kinematics (as in paper V) and stellar population diagnostics over a range of bulge and disc masses, are needed to robustly quantify how the IMF varies within galaxies.Comment: Accepted for publication in MNRAS. 15 pages, 8 figures. Code available at https://github.com/eggplantbren/SWELLS_Hierarchica

The SWELLS survey. III. Disfavouring "heavy" initial mass functions for spiral lens galaxies

We present gravitational lens models for 20 strong gravitational lens systems observed as part of the Sloan WFC Edge-on Late-type Lens Survey (SWELLS) project. Fifteen of the lenses are taken from paper I while five are newly discovered systems. The systems are galaxy-galaxy lenses where the foreground deflector has an inclined disc, with a wide range of morphological types, from late-type spiral to lenticular. For each system, we compare the total mass inside the critical curve inferred from gravitational lens modelling to the stellar mass inferred from stellar population synthesis (SPS) models, computing the stellar mass fraction f* = M(SPS)/M(lens). We find that, for the lower mass SWELLS systems, adoption of a Salpeter stellar initial mass function (IMF) leads to estimates of f* that exceed 1. This is unphysical, and provides strong evidence against the Salpeter IMF being valid for these systems. Taking the lower mass end of the SWELLS sample sigma(SIE) < 230 km/s, we find that the IMF is lighter (in terms of stellar mass-to-light ratio) than Salpeter with 98% probability, and consistent with the Chabrier IMF and IMFs between the two. This result is consistent with previous studies of spiral galaxies based on independent techniques. In combination with recent studies of massive early-type galaxies that have favoured a heavier Salpeter-like IMF, this result strengthens the evidence against a universal stellar IMF.Comment: Accepted for publication in MNRAS. Some changes (none major) to address the referee's comments. 18 pages, 8 figure

The SWELLS survey. IV. Precision measurements of the stellar and dark matter distributions in a spiral lens galaxy

We construct a fully self-consistent mass model for the lens galaxy J2141 at z=0.14, and use it to improve on previous studies by modelling its gravitational lensing effect, gas rotation curve and stellar kinematics simultaneously. We adopt a very flexible axisymmetric mass model constituted by a generalized NFW dark matter halo and a stellar mass distribution obtained by deprojecting the MGE fit to the high-resolution K'-band LGSAO imaging data of the galaxy, with the (spatially constant) M/L ratio as a free parameter. We model the stellar kinematics by solving the anisotropic Jeans equations. We find that the inner logarithmic slope of the dark halo is weakly constrained (gamma = 0.82^{+0.65}_{-0.54}), and consistent with an unmodified NFW profile. We infer the galaxy to have (i) a dark matter fraction within 2.2 disk radii of 0.28^{+0.15}_{-0.10}, independent of the galaxy stellar population, implying a maximal disk for J2141; (ii) an apparently uncontracted dark matter halo, with concentration c_{-2} = 7.7_{-2.5}^{+4.2} and virial velocity v_{vir} = 242_{-39}^{+44} km/s, consistent with LCDM predictions; (iii) a slightly oblate halo (q_h = 0.75^{+0.27}_{-0.16}), consistent with predictions from baryon-affected models. Comparing the stellar mass inferred from the combined analysis (log_{10} Mstar/Msun = 11.12_{-0.09}^{+0.05}) with that inferred from SPS modelling of the galaxies colours, and accounting for a cold gas fraction of 20+/-10%, we determine a preference for a Chabrier IMF over Salpeter IMF by a Bayes factor of 5.7 (substantial evidence). We infer a value beta_{z} = 1 - sigma^2_{z}/sigma^2_{R} = 0.43_{-0.11}^{+0.08} for the orbital anisotropy parameter in the meridional plane, in agreement with most studies of local disk galaxies, and ruling out at 99% CL that the dynamics of this system can be described by a two-integral distribution function. [Abridged]Comment: Accepted for publication in MNRAS. 17 pages, 9 figure

The non-evolving internal structure of early-type galaxies: the case study SDSS J0728+3835 at z = 0.206

We study the internal dynamical structure of the early-type lens galaxy SDSS J0728+3835 at z = 0.206. The analysis is based on two-dimensional kinematic maps extending out to 1.7 effective radii obtained from Keck spectroscopy, on lensing geometry and on stellar mass estimates obtained from multiband Hubble Space Telescope imaging. The data are modelled under the assumptions of axial symmetry supported by a two-integral distribution function (DF), by applying the combined gravitational lensing and stellar dynamics code CAULDRON, and yielding high-quality constraints for an early-type galaxy at cosmological redshifts. Modelling the total density profile as a power-law of the form rho_tot ~ 1/r^{gamma}, we find that it is nearly isothermal (logarithmic slope gamma = 2.08^{+0.04}_{-0.02}), and quite flattened (axial ratio q = 0.60^{+0.08}_{-0.03}). The galaxy is mildly anisotropic (delta = 0.08 +/- 0.02) and shows a fair amount of rotational support, in particular towards the outer regions. We determine a dark matter fraction lower limit of 28 per cent within the effective radius. The stellar contribution to the total mass distribution is close to maximal for a Chabrier initial mass function (IMF), whereas for a Salpeter IMF the stellar mass exceeds the total mass within the galaxy inner regions. We find that the combination of a NFW dark matter halo with the maximally rescaled luminous profile provides a remarkably good fit to the total mass distribution over a broad radial range. Our results confirm and expand the findings of the SLACS survey for early-type galaxies of comparable velocity dispersion (sigma_SDSS = 214 +/- 11 km/s). The internal structure of J0728 is consistent with that of local early-type galaxies of comparable velocity dispersion as measured by the SAURON project, suggesting lack of evolution in the past two billion years.Comment: 13 pages, 10 figures. MNRAS in press. Revised to match accepted versio

Two-dimensional kinematics of SLACS lenses - IV. The complete VLT-VIMOS data set

This paper presents the full VLT/VIMOS-IFU data set and related data products from an ESO Large Programme with the observational goal of obtaining two-dimensional kinematic data of early-type lens galaxies, out to one effective radius. The sample consists of 17 early-type galaxies (ETG) selected from the SLACS gravitational-lens survey. The galaxies cover the redshift range from 0.08 to 0.35 and have stellar velocity dispersions between 200 and 350 km/s. This programme is complemented by a similar observational programme on Keck, using long-slit spectroscopy. In combination with multi-band imaging data, the kinematic data provide stringent constraints on the inner mass profiles of ETGs beyond the local universe. Our Large Programme thus extends studies of nearby early-type galaxies (e.g. SAURON/ATLAS3D) by an order of magnitude in distance and toward higher masses. We provide an overview of our observational strategy, the data products (luminosity-weighted spectra and Hubble Space Telescope images) and derived products (i.e. two-dimensional fields of velocity dispersions and streaming motions) that have been used in a number of published and forthcoming lensing, kinematic and stellar-population studies.These studies also pave the way for future studies of early-type galaxies at z=1 with the upcoming extremely large telescopes.Comment: 13 pages, 7 figures, 2 tables; typos corrected; accepted for publication in MNRA

Two-dimensional kinematics of SLACS lenses: III. Mass structure and dynamics of early-type lens galaxies beyond z ~ 0.1

We combine in a self-consistent way the constraints from both gravitational lensing and stellar kinematics to perform a detailed investigation of the internal mass distribution, amount of dark matter, and dynamical structure of the 16 early-type lens galaxies from the SLACS Survey, at z = 0.08 - 0.33, for which both HST/ACS and NICMOS high-resolution imaging and VLT VIMOS IFU spectroscopy are available. Based on this data set, we analyze the inner regions of the galaxies, i.e. typically within one (3D) effective radius r_e, under the assumption of axial symmetry and by constructing dynamical models supported by two-integral stellar DFs. For all systems, the total mass density distribution is found to be well approximated by a simple power-law: this profile is on average slightly super-isothermal, with a logarithmic slope = 2.074^{+0.043}_{-0.041} (68% CL) and an intrinsic scatter 0.144^{+0.055}_{-0.014}, and is fairly round, with an average axial ratio = 0.77+/-0.04. The lower limit for the dark matter fraction (fDM) inside r_e ranges, in individual systems, from nearly zero to almost a half, with a median value of 12%. By including stellar masses derived from SPS models with a Salpeter IMF, we obtain an average fDM = 31%. The fDM rises to 61% if, instead, a Chabrier IMF is assumed. For both IMFs, the dark matter fraction increases with the total mass of the galaxy (3-sigma correlation). Based on the intrinsic angular momentum parameter calculated from our models, we find that the galaxies can be divided into two dynamically distinct groups, which are shown to correspond to the usual classes of the slow and fast rotators. Overall, the SLACS systems are structurally and dynamically very similar to their nearby counterparts, indicating that the inner regions of early-type galaxies have undergone little, if any, evolution since redshift z ~ 0.35. (Abridged)Comment: 27 pages, 34 figures. MNRAS, in pres

Two-dimensional kinematics of SLACS lenses: II. Combined lensing and dynamics analysis of early-type galaxies at z = 0.08 - 0.33

We present the first detailed analysis of the mass and dynamical structure of a sample of six early-type lens galaxies, selected from the Sloan Lens ACS Survey, in the redshift range 0.08 < z < 0.33. Both Hubble Space Telescope (HST)/ACS high-resolution imaging and VLT VIMOS integral field spectroscopy are available for these systems. The galaxies are modelled - under the assumptions of axial symmetry and two-integral stellar distribution function - by making use of the CAULDRON code, which self-consistently combines gravitational lensing and stellar dynamics, and is fully embedded within the framework of Bayesian statistics. The principal results of this study are: (i) all galaxies in the sample are well described by a simple axisymmetric power-law profile for the total density, with a logarithmic slope gamma very close to isothermal ( = 1.98 +/- 0.05 and an intrinsic spread close to 5 per cent) showing no evidence of evolution over the probed range of redshift; (ii) the axial ratio of the total density distribution is rounder than 0.65 and in all cases, except for a fast rotator, does not deviate significantly from the flattening of the intrinsic stellar distribution; (iii) the dark matter fraction within the effective radius has a lower limit of about 15 to 30 per cent; (iv) the sample galaxies are only mildly anisotropic, with delta <= 0.16; (v) the physical distinction among slow and fast rotators, quantified by the v/sigma ratio and the intrinsic angular momentum, is already present at z > 0.1. Altogether, early-type galaxies at z = 0.08 - 0.33 are found to be markedly smooth and almost isothermal systems, structurally and dynamically very similar to their nearby counterparts. (Abridged)Comment: MNRAS, in press. 17 pages, 18 figure