Phase space mass bound for fermionic dark matter from dwarf spheroidal galaxies

We reconsider the lower bound on the mass of a fermionic dark matter (DM) candidate resulting from the existence of known small Dwarf Spheroidal galaxies, in the hypothesis that their DM halo is constituted by degenerate fermions, with phase-space density limited by the Pauli exclusion principle. By relaxing the common assumption that the DM halo scale radius is tied to that of the luminous stellar component and by marginalizing on the unknown stellar velocity dispersion anisotropy, we prove that observations lead to rather weak constraints on the DM mass, that could be as low as tens of eV. In this scenario, however, the DM halos would be quite large and massive, so that a bound stems from the requirement that the time of orbital decay due to dynamical friction in the hosting Milky Way DM halo is longer than their lifetime. The smallest and nearest satellites Segue I and Willman I lead to a final lower bound of $m\gtrsim100$ eV, still weaker than previous estimates but robust and independent on the model of DM formation and decoupling. We thus show that phase space constraints do not rule out the possibility of sub-keV fermionic DM.