Mass estimators for flattened dispersion-supported galaxies

Abstract

We investigate the reliability of mass estimators based on the observable velocity dispersion and half-light radius $R_\mathrm{h}$ for dispersion-supported galaxies. We show how to extend them to flattened systems and provide simple formulae for the mass within an ellipsoid under the assumption the dark matter density and the stellar density are stratified on the same self-similar ellipsoids. We demonstrate explicitly that the spherical mass estimators (Walker et al. 2009, Wolf et al. 2010) give accurate values for the mass within the half-light ellipsoid, provided $R_\mathrm{h}$ is replaced by its `circularized' analogue $R_\mathrm{h}\sqrt{1-\epsilon}$. We provide a mathematical justification for this surprisingly simple and effective workaround. It means, for example, that the mass-to-light ratios are valid not just when the light and dark matter are spherically distributed, but also when they are flattened on ellipsoids of the same constant shape.