A Method for Measuring (Slopes of) the Mass Profiles of Dwarf Spheroidal Galaxies

Abstract

We introduce a method for measuring the slopes of mass profiles within dwarf spheroidal (dSph) galaxies directly from stellar spectroscopic data and without adopting a dark matter halo model. Our method combines two recent results: 1) spherically symmetric, equilibrium Jeans models imply that the product of halflight radius and (squared) stellar velocity dispersion provides an estimate of the mass enclosed within the halflight radius of a dSph stellar component, and 2) some dSphs have chemo-dynamically distinct stellar \textit{sub}components that independently trace the same gravitational potential. We devise a statistical method that uses measurements of stellar positions, velocities and spectral indices to distinguish two dSph stellar subcomponents and to estimate their individual halflight radii and velocity dispersions. For a dSph with two detected stellar subcomponents, we obtain estimates of masses enclosed at two discrete points in the same mass profile, immediately defining a slope. Applied to published spectroscopic data, our method distinguishes stellar subcomponents in the Fornax and Sculptor dSphs, for which we measure slopes $\Gamma\equiv \Delta \log M / \Delta \log r=2.61_{-0.37}^{+0.43}$ and $\Gamma=2.95_{-0.39}^{+0.51}$, respectively. These values are consistent with 'cores' of constant density within the central few-hundred parsecs of each galaxy and rule out `cuspy' Navarro-Frenk-White (NFW) profiles ($d\log M/d\log r \leq 2$ at all radii) with significance $\ga 96%$ and $\ga 99%$, respectively. Tests with synthetic data indicate that our method tends systematically to overestimate the mass of the inner stellar subcomponent to a greater degree than that of the outer stellar subcomponent, and therefore to underestimate the slope $\Gamma$ (implying that the stated NFW exclusion levels are conservative).