Model-independent analysis of dark matter points to a particle mass at the keV scale

We present a model-independent analysis of darkmatter (DM) decoupling both ultrarelativistically (UR) and non-relativistically (NR) based on the DM phase-space density D = rho(DM)/sigma(3)(DM). We derive explicit formulae for the DM particle mass m and for the number of ultrarelativistic 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 out to be in the keV scale. For example, for DM Majorana fermions decoupling at LTE the resulting mass is m similar or equal to 0.85 keV. For DM particles decoupling NR, root mT(d) results in the keV scale (T-d is the decoupling temperature) and the value of m is consistent with the keV scale. In all cases, DM turns out to be cold DM (CDM). In addition, lower and upper bounds on the DM annihilation cross-section for NR decoupling are derived. We evaluate the free-streaming (Jeans) wavelength and Jeans mass: they are independent of the type of DM except for the DM self-gravity dynamics. The free-streaming wavelength today turns to be in the kpc range. These results are based on our theoretical analysis, on astronomical observations of dwarf spheroidal satellite galaxies in the Milky Way and on N-body numerical simulations. We analyse and discuss the results for D from analytic approximate formulae for both linear fluctuations and the (non-linear) spherical model and from N-body simulations results. In this way we obtain upper bounds for the DM particle mass, which are all below the 100-keV range.