THE STRUCTURE AND DARK HALO CORE PROPERTIES OF DWARF SPHEROIDAL GALAXIES

Abstract

The structure and dark matter halo core properties of dwarf spheroidal galaxies (dSphs) are investigated. A double-isothermal (DIS) model of an isothermal, non selfgravitating stellar system, in gravitational equilibrium and embedded in an isothermal dark halo core provides an excellent fit to the various observed stellar surface density distributions �∗(r). Despite its constant velocity dispersion, the stellar system can be well characterised by King profiles (King 1966) with a broad distribution of concentration parameters c = log(r∗,t/r∗,c), with r∗,t and r∗,c the stellar tidal and core radius, respectively. The DIS model confirms the suggestion of Kormendy & Freeman (2014) that the core scale length of the stellar system, defined as a∗ = −(dln�∗/dr 2 ) −1/2 , is sensitive to the central dark matter density �0. In contrast to single-component systems, r∗,t however does not trace the tidal radius of the galaxy but the core radius rc of its dark matter halo. c is therefore sensitive to the ratio �∗/�0 with �∗ and �0 the stellar and dark matter velocity dispersion, respectively. Simple empirical relationships are derived that allow to calculate the dark halo core parameters �0, rc and �0, given the observable quantities �∗, a∗ and c. The DIS model is applied to the Milky Way’s dSphs. Their halo velocity dispersions lie in a narrow range of 10 km/s ≤ �0 ≤ 18 km/s with halo core radii of 280 pc ≤ rc ≤ 1.3 kpc and rc ≈ 2a∗. All dSphs follow closely the same universal scaling relations h�0rci ≡ �0 × rc = 75 +8545 M⊙ pc −2 and � 2 0 ×r −1 c = 0.45 +0.51 −0.27 (km/s) 2 pc −1 that characterise the cores of more massive galaxies over a range of 18 magnitudes in blue magnitude MB. For given h�0rcithe core mass is a strong function of core radius, Mc ∼ r 2 . Inside a fixed radius ru, with ru the logarithmic mean of the dSph’s core radii, the total mass Mu = 2.17h�0rcir 2 u is however roughly constant. Outliers with smaller masses are expected for dSphs with core radii that are much larger or smaller than ru. For the Milky Way’s dSphs we find ru = 400 ± 100 pc and Mu = 2.6 ± 1.4 × 10 7 M⊙, in agreement with Strigari et al. (2008). Due to their small rc, the core densities of the Galaxy’s dSphs are very higher, with �0 = 0.03 - 0.3 M⊙ pc −3 . The dSphs would have to be on galactic orbits with pericenters smaller than a few kpc in order for their stellar systems to be affected by Galactic tides which is very unlikely. dSphs should therefore be tidally undisturbed. Observational evidence for tidal effects might then provide a serious challenge for the cold dark matter scenario.