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 half-light radius and (squared) stellar velocity dispersion provides an estimate of the mass enclosed within the half-light radius of a dSph stellar component, and (2) some dSphs have chemodynamically distinct stellar 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 half-light 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 Γ ≡ Δlog M /Δlog r = 2.61 +0.43 −0.37 and Γ = 2.95 +0.51 −0.39 , 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 ⩽ 2 at all radii) with a significance ≳ 96% and ≳ 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 Γ (implying that the stated NFW exclusion levels are conservative).