arXiv:1002.1083v2 [astro-ph.CO] 22 Apr 2010 Mon. Not. R. Astron. Soc. 000, 000–000 (0000) Printed 23 April 2010 (MN L A T E X style file v2.2) The non-evolving internal structure of early-type galaxies: the case study SDSS J0728+3835 at z = 0.206 Matteo Barnab` e 1,2⋆ , Matthew W. Auger 2 , Tommaso Treu 2,7 , L´ eon V. E. Koopmans 3 , Adam S. Bolton 4,5 , Oliver Czoske 3 and Rapha¨ el Gavazzi 6 1 Kavli Institute for Particle Astrophysics and Cosmology, Stanford University, 452 Lomita Mall, Stanford, CA 94035-4085, USA 2 Department of Physics, University of California, Santa Barbara, CA 93101, USA 3 Kapteyn Astronomical Institute, University of Groningen, PO Box 800, 9700 AV Groningen, Netherlands 4 Department of Physics and Astronomy, University of Utah, 115 South 1400 East, Salt Lake City, UT 84112, USA 5 Beatrice Watson Parrent Fellow, Institute for Astronomy, University of Hawai‘i, 2680 Woodlawn Dr., Honolulu, HI 96822 6 Institut d’Astrophysique de Paris, CNRS, UMR 7095, Universit´ e Pierre et Marie Curie, 98bis Bd Arago, 75014 Paris, France 7 Packard Research Fellow Accepted 2010 April 20. Received 2010 April 16; in original form 2010 February 03. ABSTRACT 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. Mod- elling the total density profile as a power-law of the form ρ tot ∝ 1/r γ ′ , we find that it is nearly isothermal (logarithmic slope γ ′ = 2.08 +0.04 −0.02 ), and quite flattened (axial ratio q = 0.60 +0.08 −0.03 ). The galaxy is mildly anisotropic (δ = 0.08 ± 0.02) and shows a fair amount of rotational sup- port, 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 distribu- tion 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 pro- vides 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 (σ SDSS = 214 ± 11 km s −1 ). The internal structure of SDSS J0728 is con- sistent 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. Key words: gravitational lensing — galaxies: elliptical and lenticular, cD — galaxies: kine- matics and dynamics — galaxies: structure. 1 INTRODUCTION Unveiling the mass distribution, dynamical structure and dark mat- ter content of early-type galaxies is of great interest both as a sub- ject in its own right, considering their importance in the local Uni- verse, where a large fraction of the total stellar mass is contained within E/S0 systems (Fukugita, Hogan, & Peebles 1998), and in or- der to provide stringent tests for the galaxy formation and evolution models. It is not surprising, therefore, that nearby early-type galax- ⋆ E-mail: mbarnabe@stanford.edu ies have been the object of intense study during the last decades, by taking advantage of the diverse available observational tracers. These include stellar kinematics (see e.g. Saglia, Bertin, & Stiavelli 1992, Franx et al. 1994, Rix et al. 1997, Loewenstein & White 1999, Gerhard et al. 2001, Borriello et al. 2003, Cappellari et al. 2007, Thomas et al. 2007b, Weijmans et al. 2009), globular clus- ters and planetary nebulae kinematics (e.g. Cˆ ot´ e et al. 2003; Romanowsky et al. 2003; de Lorenzi et al. 2008), the occa- sional HI disk or ring (e.g. Franx, van Gorkom, & de Zeeuw 1994; Weijmans et al. 2008) and hot X-ray emission (e.g. Matsushita et al. 1998; Fukazawa et al. 2006; Humphrey et al. 2006; Humphrey & Buote 2010). The general picture emerging