Comparison of simple mass estimators for slowly rotating elliptical galaxies

We compare the performance of mass estimators for elliptical galaxies that rely on the directly observable surface brightness and velocity dispersion profiles, without invoking computationally expensive detailed modeling. These methods recover the mass at a specific radius where the mass estimate is expected to be least sensitive to the anisotropy of stellar orbits. One method (Wolf et al. 2010) uses the total luminosity-weighted velocity dispersion and evaluates the mass at a 3D half-light radius $r_{1/2}$, i.e., it depends on the GLOBAL galaxy properties. Another approach (Churazov et al. 2010) estimates the mass from the velocity dispersion at a radius $R_2$ where the surface brightness declines as $R^{-2}$, i.e., it depends on the LOCAL properties. We evaluate the accuracy of the two methods for analytical models, simulated galaxies and real elliptical galaxies that have already been modeled by the Schwarzschild's orbit-superposition technique. Both estimators recover an almost unbiased circular speed estimate with a modest RMS scatter ($\lesssim 10 \%$). Tests on analytical models and simulated galaxies indicate that the local estimator has a smaller RMS scatter than the global one. We show by examination of simulated galaxies that the projected velocity dispersion at $R_2$ could serve as a good proxy for the virial galaxy mass. For simulated galaxies the total halo mass scales with $\sigma_p(R_2)$ as $M_{vir} \left[M_{\odot}h^{-1}\right] \approx 6\cdot 10^{12} \left( \frac{\sigma_p(R_2)}{200\, \rm km\, s^{-1}} \right)^{4}$ with RMS scatter $\approx 40 \%$.