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 .
Our goal is to compare dark matter profile models of these four systems using Bayesian evidence .
We consider NFW , Einasto and several cored profiles for their dark halos and present the probability distribution functions of the model parameters .
When considering each system separately , we find there is no preference for one of these specific parametric density profiles .
However , the combined evidence shows that it is unlikely that all galaxies are embedded in the same type of cored profiles of the form \rho _ { DM } \propto 1 / ( 1 + r ^ { 2 } ) ^ { \beta / 2 } , where \beta = 3 , 4 .
For each galaxy , we also obtain an almost model independent , and therefore accurate , measurement of the logarithmic slope of the dark matter density distribution at a radius \sim r _ { -3 } , i.e .
where the logarithmic slope of the stellar density profile is -3 .
This slope ranges from \sim - 1.4 for Fornax to \sim - 1.1 for Sextans , both at \sim 1 kpc .
All our 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 .