The mass of the dark matter particle: Theory and galaxy observations

Abstract In order to determine as best as possible the nature of the dark matter (DM) particle (mass and decoupling temperature) we compute analytically the DM galaxy properties as the halo density profile, halo radius and surface density and compare them to their observed values. We match the theoretically computed surface density to its observed value in order to obtain: (i) the decreasing of the phase-space density since equilibration till today (ii) the mass of the dark matter particle and the decoupling temperature T d (iii) the kind of the halo density profile (core or cusp). The dark matter particle mass turns to be between 1 and 2 keV and the decoupling temperature T d turns to be above 100 GeV. keV dark matter particles necessarily produce cored density profiles while WIMPS ( m  ∼ 100 GeV, T d  ∼ 5 GeV) inevitably produce cusped profiles at scales about 0.003 pc. We compute in addition the halo radius r 0 , the halo central density ρ 0 and the halo particle r.m.s. velocity v 2 ¯ halo 1 / 2 they all reproduce the observed values within one order of magnitude. These results are independent of the particle physics model and vary very little with the statistics of the dark matter particle. The framework presented here applies to any kind of DM particles: when applied to typical CDM GeV WIMPS, our results are in agreement with CDM simulations. keV scale DM particles reproduce all observed galaxy magnitudes within one order of magnitude while GeV DM mass particles disagree with observations in up to eleven orders of magnitude.