Measurement of the Dark Matter Velocity Dispersion with Dwarf Galaxy Rotation Curves

Abstract

Warm dark matter has, by definition, a velocity dispersion. Let v hms ( a )= v hms (1)/ a be the root-mean-square velocity of non-relativistic warm dark matter particles in the early universe at expansion parameter a . v hms (1) is an adiabatic invariant. We obtain v hms (1) in the core of 11 dwarf galaxies dominated by dark matter, from their observed rotation curves, up to a rotation and relaxation correction. We obtain a mean 0.490 km/s and standard deviation 0.160 km/s, with a distribution peaked at the lower end. We apply a mild, data driven, rotation and relaxation correction that obtains the adiabatic invariant in the core of the galaxies: v hms (1) =0.406 ± 0.069 km/s. These two small relative standard deviations justify the prediction that the adiabatic invariant v hms (1) in the core of the galaxies is of cosmological origin if dark matter is warm. This result is in agreement with measurements of v hms (1) based on spiral galaxy rotation curves, galaxy ultra-violet luminosity distributions, galaxy stellar mass distributions, the formation of first galaxies, reionization, and the velocity dispersion cut-off mass.