Dynamical Models of Elliptical Galaxies -- I. Simple Methods
  We study dynamical models for elliptical galaxies, deriving the projected
kinematic profiles in a form that is valid for general surface-brightness
profiles and (spherical) total mass profiles, without the need for any explicit
deprojection. We then show that an almost flat rotation curve, combined with
modest velocity anisotropy, is already sufficient to recover the kinematic
profiles of nearby ellipticals. As an application, we provide two different
sets of mass estimators for elliptical galaxies, based on either the velocity
dispersion at a specific location near the effective radius, or the
aperture-averaged velocity dispersion. In the large aperture (virial) limit,
mass estimators are naturally independent of anisotropy. The spherical mass
enclosed within the effective radius $R_{\rm e}$ can be estimated as $2.4
R_{\rm e} \langle \sigma^{2}_{\rm p} \rangle/ G$, where $\langle \sigma^2_{\rm
p} \rangle$ is the average of the squared velocity dispersion over a finite
aperture. This formula does not depend on assumptions such as
mass-follows-light, and is a compromise between the cases of small and large
apertures sizes. Its general agreement with results from other methods in the
literature makes it a reliable means to infer masses in the absence of detailed
kinematic information. If on the other hand the velocity dispersion profile is
available, tight mass estimates can be found that are independent of the
mass-model and anisotropy profile (within $\approx$ 10% accuracy). Explicit
formulae are given for small anisotropy, large radii and/or power-law total
densities. Motivated by recent observational claims, we also discuss the issue
of weak homology of elliptical galaxies, emphasizing the interplay between
morphology and orbital structure.
