Modeling mass independent of anisotropy

الأصل · EN

By manipulating the spherical Jeans equation, Wolf et al. (2010) show that the mass enclosed within the 3D deprojected half-light radius r₁/2 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 M₁/2 = 3 σₗos² r₁/2 / G 4 σₗos² Rₑff / G, where σₗos² is the luminosity-weighted square of the line-of-sight velocity dispersion and Rₑff 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 10⁹ Mₛun assuming a LCDM cosmology. In addition, the dynamical I-band mass-to-light ratio (M/L) vs. M₁/2 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.