Estimation of the Mass of Dark Matter Using the Observed Mass Profiles of Late-Type Galaxies

Abstract

The system of stability equations for galactic halos is under-determined in most of the models of dark matter (DM). Conventionally, the issue is resolved by taking the temperature as a constant, and the chemical potential and the mass density as position-dependent variables. In this paper, to close the under-determined set of equations, we remove the mass density using observations and leave the temperature and the chemical potential as position-dependent variables. We analyze observations of the mass profiles of 175 late-type galaxies in the Spitzer Photometry \& Accurate Rotation Curves (SPARC) database as well as 26 late-type dwarfs in the Little Things database, to construct the temperature profile of their DM halos by assuming that (1) DM in the halos obeys either the Fermi-Dirac or the Maxwell-Boltzmann distribution, and (2) the halos are in the virial state. We derive the dispersion velocity of DM at the center of the halos and show that its correlation with the halo's total mass is consistent with the direct observations of visible matter. Taking the latter agreement as a validation of our analysis, we derive the mass to the temperature of DM at the edge of the halos and show that it is galaxy independent and is equal to $m/T_{R_{200}}\simeq 10^{10}$ in natural units. In the thermal models of DM, such universal temperature is inherently assumed. In this paper, we derive the universal temperature from observations without imposing it by assumptions. Therefore, $T_{R_{200}}$ in the above ratio can be expressed in terms of the temperature of the cosmic microwave background (CMB) at the time of DM decoupling. This result is used to study possible cosmological scenarios. We show that observations are at odds with (1) non-thermal DM, (2) hot DM, and (3) collision-less cold DM. If DM is warm, we estimate its mass to be in the range of keV--MeV.