THE EINSTEIN CROSS: CONSTRAINT ON DARK MATTER FROM STELLAR DYNAMICS AND GRAVITATIONAL LENSING

We present two-dimensional line-of-sight stellar kinematics of the lens galaxy in the Einstein Cross, obtained with the GEMINI 8 m telescope, using the GMOS integral-field spectrograph. The stellar kinematics extend to a radius of 4 '' (with 0 ''.2 spaxels), covering about two-thirds of the effective (or half-light) radius R-e similar or equal to 6 '' of this early-type spiral galaxy at redshift z(l) similar or equal to 0.04, of which the bulge is lensing a background quasar at redshift z(s) similar or equal to 1.7. The velocity map shows regular rotation up to similar to 100 km s(-1) around the minor axis of the bulge, consistent with axisymmetry. The velocity dispersion map shows a weak gradient increasing toward a central (R < 1 '') value of sigma(0) = 170 +/- 9 km s(-1). We deproject the observed surface brightness from Hubble Space Telescope imaging to obtain a realistic luminosity density of the lens galaxy, which in turn is used to build axisymmetric dynamical models that fit the observed kinematic maps. We also construct a gravitational lens model that accurately fits the positions and relative fluxes of the four quasar images. We combine these independent constraints from stellar dynamics and gravitational lensing to study the total mass distribution in the inner parts of the lens galaxy. We find that the resulting luminous and total mass distribution are nearly identical around the Einstein radius R-E = 0 ''.89, with a slope that is close to isothermal, but which becomes shallower toward the center if indeed mass follows light. The dynamical model fits to the observed kinematic maps result in a total mass-to-light ratio gamma(dyn) = 3.7 +/- 0.5 gamma(circle dot, I) (in the I band). This is consistent with the Einstein mass M-E = 1.54 x 10(10) M-circle dot divided by the (projected) luminosity within R-E, which yields a total mass-to-light ratio of gamma(E) = 3.4 gamma(circle dot, I), with an error of at most a few percent. We estimate from stellar population model fits to colors of the lens galaxy a stellar mass-to-light ratio gamma(star) from 2.8 to 4.1 gamma(circle dot, I). Although a constant dark matter fraction of 20% is not excluded, dark matter may play no significant role in the bulge of this similar to L-star early-type spiral galaxy.