Accurate masses for dispersion-supported galaxies

Abstract

We derive an accurate mass estimator for dispersion-supported stellar systems and demonstrate its validity by analyzing resolved line-of-sight velocity data for globular clusters, dwarf galaxies, and elliptical galaxies. Specifically, by manipulating the spherical Jeans equation we show that the dynamical 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. We 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. While deceptively familiar in form, this formula is not the virial theorem, which cannot be used to determine accurate masses unless the radial profile of the total mass is known a priori. We utilize this finding 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 in Lambda CDM cosmology. The faintest MW dSphs seem to have formed in dark matter halos that are at least as massive as those of the brightest MW dSphs, despite the almost five orders of magnitude spread in luminosity. We expand our analysis to the full range of observed dispersion-supported stellar systems and examine their I-band mass-to-light ratios (M/L). The 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.Comment: 20 pages, 13 figures. Accepted to MNRAS on March 27th, 201

The orbital PDF: general inference of the gravitational potential from steady-state tracers

“…The existence of a best-constrained mass despite the parameter degeneracy is broadly in line with empirical results on the robustness of the mass constraint inside the half-light radius from Jeans equation modelling of dwarf galaxies (Walker et al 2009;Wolf et al 2010). The existence of such a characteristic point in the Jeans analysis is further proved by Wolf et al (2010).…”

Comparison of simple mass estimators for slowly rotating elliptical galaxies

“…for a wide range of stellar distributions (global estimator; Wolf et al 2010). We test the accuracy and robustness of these simple mass estimators on analytical models, on a sample of cosmological zoom-simulations of individual elliptical galaxies and on real elliptical galaxies that have already been analyzed by means of a Schwarzschild approach.…”

“…This idea is the basis of the simple dynamical mass scaling relations discussed in detail by Churazov et al (2010) and Wolf et al (2010). In the remainder of the paper we concentrate on these two mass estimators and test their performance.…”

“…Recently two simple mass estimation methods have been suggested (Churazov et al 2010 andWolf et al 2010) which evaluate masses at a special radius from the surface brightness and projected velocity dispersion profiles without detailed modeling. Although these approaches recover the mass at some particular radius only and not the mass distribution within that radius, these estimates could be used (i) to determine the non-thermal contribution to the total gas pressure when compared with the X-ray mass estimate at the same radius; (ii) to derive a slope of the mass profile when combined with the mass estimate from strong lensing; (iii) as a virial mass proxy.…”

“…These methods recover the mass at a specific radius where the mass estimate is expected to be least sensitive to the anisotropy of stellar orbits. One method (Wolf et al 2010) uses the total luminosityweighted velocity dispersion and evaluates the mass at a 3D half-light radius r 1/2 , i.e., it depends on the global galaxy properties. Another approach (Churazov et al 2010) estimates the mass from the velocity dispersion at a radius R 2 where the surface brightness declines as R −2 , i.e., it depends on the local properties.…”