2015ApJ...808..158B

The structure and dark matter halo core properties of dwarf spheroidal galaxies (dSphs) are investigated. A double-isothermal (DIS) model of an isothermal, non-self-gravitating stellar system embedded in an isothermal dark halo core provides an excellent fit to the various observed stellar surface density distributions. The stellar core scale length a_* is sensitive to the central dark matter density ρ_0,d. The maximum stellar radius traces the dark halo core radius r_c,d. The concentration c_*of the stellar system, determined by a King profile fit, depends on the ratio of the stellar-to-dark-matter velocity dispersion σ_*/σ_d. Simple empirical relationships are derived that allow us to calculate the dark halo core parameters ρ_0,d, r_c,d, and σ_dgiven the observable stellar quantities σ_*, a_*, and c_*. The DIS model is applied to the Milky Way's dSphs. All dSphs closely follow the same universal dark halo scaling relations ρ_0,d x r_c,d = 75 _–45⁺⁸⁵ M_☉/pc2 that characterize the cores of more massive galaxies over a large range in masses. The dark halo core mass is a strong function of core radius, M_c,d ∼ r_c,d². Inside a fixed radius of ∼400 pc the total dark matter mass is, however, roughly constant with M_c,d = 2.6 ± 1.4 x 10⁷ M_☉, although outliers are expected. The dark halo core densities of the Galaxy's dSphs are very high, with ρ_0,d ≈ 0.2 M_☉/pc3. dSphs should therefore be tidally undisturbed. Evidence for tidal effects might then provide a serious challenge for the CDM scenario.