MASS ESTIMATORS FOR FLATTENED DISPERSION-SUPPORTED GALAXIES

We investigate the reliability of mass estimators based on the observable velocity dispersion and half-light radius Rh 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 give accurate values for the mass within the half-light ellipsoid, provided Rh is replaced by its "circularized" analog R-h root 1 - is an element of. 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.