Abstract
The spatial segregation between dwarf spheroidal (dSph) and dwarf irregular galaxies in the Local Group has long been regarded as evidence of an interaction with their host galaxies. In this paper, we assume that ram-pressure stripping is the dominant mechanism that removed gas from the dSphs and we use this to derive a lower bound on the density of the corona of the Milky Way at large distances (R similar to 50-90 kpc) from the Galactic Centre. At the same time, we derive an upper bound by demanding that the interstellar medium of the dSphs is in pressure equilibrium with the hot corona. We consider two dwarfs (Sextans and Carina) with well-determined orbits and star formation histories. Our approach introduces several novel features: (i) we use the measured star formation histories of the dwarfs to derive the time at which they last lost their gas and (via a modified version of the Kennicutt-Schmidt relation) their internal gas density at that time; (ii) we use a large suite of 2D hydrodynamical simulations to model the gas stripping; and (iii) we include supernova feedback tied to the gas content. Despite having very different orbits and star formation histories, we find results for the two dSphs that are in excellent agreement with one another. We derive an average particle density of the corona of the Milky Way at R = 50-90 kpc in the range n(cor) = 1.3-3.6 x 10(-4) cm(-3). Including additional constraints from X-ray emission limits and pulsar dispersion measurements (that strengthen our upper bound), we derive Galactic coronal density profiles. Extrapolating these to large radii, we estimate the fraction of baryons (missing baryons) that can exist within the virial radius of the Milky Way. For an isothermal corona (T-cor = 1.8 x 10(6) K), this is small - just 10-20 per cent of the expected missing baryon fraction, assuming a virial mass of 1-2 x 10(12) M-circle dot. Only a hot (T-cor = 3 x 10(6) K) and adiabatic corona can contain all of the Galaxy's missing baryons. Models for the Milky Way must explain why its corona is in a hot adiabatic thermal state; or why a large fraction of its baryons lie beyond the virial radius.