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 an
d 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.
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-resolut
ion 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 (<gamma> = 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)
We apply the joint lensing and dynamics code for the analysis of early-type galaxies, CAULDRON, to a rotating N-body stellar system with dark matter halo which significantly violates the two major assumptions of the method, i.e. axial symmetry suppor
ted by a two-integral distribution function. The goal is to study how CAULDRON performs in an extreme case, and to determine which galaxy properties can still be robustly recovered. Three data sets, corresponding to orthogonal lines of sight, are generated from the N-body system and analysed with the identical procedure followed in the study of real lens galaxies, adopting an axisymmetric power-law total density distribution. We find that several global properties of the N-body system are recovered with remarkable accuracy, despite the fact that the adopted power-law model is too simple to account for the lack of symmetry of the true density distribution. In particular, the logarithmic slope of the total density distribution is robustly recovered to within less than 10 per cent (with the exception of the ill-constrained very inner regions), the inferred angle-averaged radial profile of the total mass closely follows the true distribution, and the dark matter fraction of the system (inside the effective radius) is correctly determined within ~ 10 per cent of the total mass. Unless the line of sight direction is almost parallel to the total angular momentum vector of the system, reliably recovered quantities also include the angular momentum, the V/sigma ratio, and the anisotropy parameter delta. We conclude that the CAULDRON code can be safely and effectively applied to real early-type lens galaxies, providing reliable information also for systems that depart significantly from the methods assumptions.
