Modeling Star Formation in Dwarf Spheroidal Galaxies: A Case for Extended Dark Matter Halos

We propose a simple model for the formation of dwarf spheroidal galaxies, in which stars are assumed to have formed from isothermal gas in hydrostatic equilibrium inside extended dark matter halos. After expelling the leftover gas, the stellar system undergoes a dynamical relaxation inside the dark matter halo. These models can adequately describe the observed properties of three (Draco, Sculptor, and Carina) out of four Galactic dwarf spheroidal satellites studied in this paper. We suggest that the fourth galaxy (Fornax), which cannot be fitted well with our model, is observed all the way to its tidal radius. Our best-fitting models have virial masses of ~109 M☉, halo formation redshifts consistent with the age of oldest stars in these dwarfs, and shallow inner dark matter density profiles (with slope γ ~ -0.5, … ,0). The inferred temperature of gas is ~104 K. In our model, the "extratidal" stars observed in the vicinity of some dwarf spheroidal galaxies are gravitationally bound to the galaxies and are a part of the extended stellar halos. The inferred virial masses make Galactic dwarf spheroidals massive enough to alleviate the "missing satellites" problem of Λ cold dark matter cosmologies.