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.
