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 can not be fitted well with our model , is observed all the way to its tidal radius .
Our best fitting models have virial masses of \sim 10 ^ { 9 } M _ { \odot } , halo formation redshifts consistent with the age of oldest stars in these dwarfs , and shallow inner dark matter density profiles ( with slope \gamma \sim - 0.5 \dots 0 ) .
The inferred temperature of gas is \sim 10 ^ { 4 } 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 \Lambda CDM cosmologies .