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 _ { \mathrm { tot } } \propto 1 / r ^ { \gamma ^ { \prime } } , we find that it is nearly isothermal ( logarithmic slope \gamma ^ { \prime } = 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 \pm 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 \pm 11 km s ^ { -1 } ) .
The internal structure of SDSS 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 .