  By manipulating the spherical Jeans equation, Wolf et al. (2010) show that
the mass enclosed within the 3D deprojected half-light radius r_1/2 can be
determined with only mild assumptions about the spatial variation of the
stellar velocity dispersion anisotropy as long as the projected velocity
dispersion profile is fairly flat near the half-light radius, as is typically
observed. They find M_1/2 = 3 \sigma_los^2 r_1/2 / G ~ 4 \sigma_los^2 R_eff /
G, where \sigma_los^2 is the luminosity-weighted square of the line-of-sight
velocity dispersion and R_eff is the 2D projected half-light radius. This
finding can be used to show that all of the Milky Way dwarf spheroidal galaxies
(MW dSphs) are consistent with having formed within a halo of mass
approximately 3 x 10^9 M_sun assuming a LCDM cosmology. In addition, the
dynamical I-band mass-to-light ratio (M/L) vs. M_1/2 relation for
dispersion-supported galaxies follows a U-shape, with a broad minimum near M/L
~ 3 that spans dwarf elliptical galaxies to normal ellipticals, a steep rise to
M/L ~ 3,200 for ultra-faint dSphs, and a more shallow rise to M/L ~ 800 for
galaxy cluster spheroids.
