  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 ~
r_{-3}, i.e. where the logarithmic slope of the stellar density profile is -3.
This slope ranges from ~ -1.4 for Fornax to ~ -1.1 for Sextans, both at ~ 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.
