Understanding elliptical galaxies with warm dark matter

We fit the solution of hydrostatic equations to the observed total and baryonic mass densities ${\rho }_{\text{tot}}\left(r\right)$ and ${\rho }_b\left(r\right)$ of 23 massive elliptical galaxies. Our purpose is to investigate how well these measurements constrain the cusp or core of elliptical galaxies, and the dark matter comoving temperature-to-mass ratio, or equivalently, the adiabatic invariant $v_{h\text{rms}}\left(1\right)$, of dark matter. These studies reinforce the view that the lower bound of the measured distribution of the comoving thermal velocity $v_{h\text{rms}}\left(1\right)$ is of cosmological origin, in agreement with studies of spiral and dwarf galaxies.