  We present a model independent analysis of dark matter (DM) both decoupling
ultra relativistic (UR) and non-relativistic (NR) based in the phase-space
density D = rho_{DM}/sigma^3_{DM}. We derive explicit formulas for the DM
particle mass m and for the number of ultra relativistic degrees of freedom g_d
at decoupling. We find that for DM particles decoupling UR both at local
thermal equilibrium (LTE) and out of LTE, m turns to be at the keV scale. For
example, for DM Majorana fermions decoupling at LTE the mass results m ~ 0.85
keV. For DM particles decoupling NR, sqrt{m T_d} results in the keV scale (T_d
is the decoupling temperature) and the m value is consistent with the keV
scale. In all cases, DM turns to be cold DM (CDM). Also, lower and upper bounds
on the DM annihilation cross-section for NR decoupling are derived. We evaluate
the free-streaming (Jeans') length and Jeans' mass: they result independent of
the type of DM except for the DM self-gravity dynamics. The free-streaming
length today results in the kpc range. These results are based on our
theoretical analysis, astronomical observations of dwarf spheroidal satellite
galaxies in the Milky Way and N-body numerical simulations. We analyze and
discuss the results on D from analytic approximate formulas both for linear
fluctuations and the (non-linear) spherical model and from N-body simulations
results. We obtain in this way upper bounds for the DM particle mass which all
result below the 100 keV range.
