Model comparison of the dark matter profiles of Fornax, Sculptor, Carina and Sextans

Aims. We compare dark matter profile models of four dwarf spheroidal galaxies satellites of the MilkyWay using Bayesian evidence. Methods. We use orbit based dynamical models to fit the 2nd and 4th moments of the line of sight velocity distributions of the Fornax, Sculptor, Carina and Sextans dwarf spheroidal galaxies. We compare NFW, Einasto and several cored profiles for their dark halos and present the probability distribution functions of the model parameters. Results. For each galaxy separately we compare the evidence for the various dark matter profiles, and find that it is not possible to distinguish between these specific parametric dark matter density profiles using the current data. Nonetheless, from the combined evidence, we find that is unlikely that all galaxies are embedded in the same type of cored profiles of the form PDM 1/(1 + r(2))(beta/2), where beta = 3, 4. For each galaxy, we also obtain an almost model independent, and therefore accurate, constraint on the logarithmic slope of the dark matter density distribution at a radius similar to r-3, i. e. where the logarithmic slope of the stellar density profile is -3. Conclusions. For each galaxy, we find that all best fit models essentially have the same mass distribution over a large range in radius (from just below r-3 to the last measured data point). This remarkable finding likely implies much stronger constraints on the characteristics that subhalos extracted from cosmological simulations should have in order to host the dSph galaxies around the Milky Way.