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

TL;DR

This paper provides a model-independent analysis indicating dark matter particles are likely in the keV mass range, based on phase-space density, observational data, and simulations, suggesting they are cold dark matter.

Contribution

It derives explicit formulas for dark matter particle mass and decoupling degrees of freedom, establishing the keV scale as consistent with various decoupling scenarios.

Findings

Dark matter particles decouple at the keV mass scale.

Free-streaming length is in the kpc range, consistent with observations.

Upper bounds on dark matter particle mass are below 100 keV.

Abstract

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.