  The root-mean-square of non-relativistic warm dark matter particle velocities
scales as $v_{h\textrm{rms}}(a) = v_{h\textrm{rms}}(1)/a$, where $a$ is the
expansion parameter of the universe. This velocity dispersion results in a
cut-off of the power spectrum of density fluctuations due to dark matter
free-streaming. Let $k_\textrm{fs}(t_\textrm{eq})$ be the free-streaming
comoving cut-off wavenumber at the time of equal densities of radiation and
matter. We obtain $v_{h\textrm{rms}}(1) = 0.41^{+0.14}_{-0.12} \textrm{ km/s}$,
and $k_\textrm{fs}(t_\textrm{eq}) = 2.0^{+0.8}_{-0.5} \textrm{ Mpc}^{-1}$, at
68\% confidence, from the observed distributions of galaxy stellar masses and
rest frame ultra-violet luminosities. This result is consistent with
reionization. From the velocity dispersion cut-off we obtain the limits
$v_{h\textrm{rms}}(1) < 0.54 \textrm{ km/s}$, and $k_\textrm{fs}(t_\textrm{eq})
> 1.5 \textrm{ Mpc}^{-1}$. These results are in agreement with previous
measurements based on spiral galaxy rotation curves, and on the formation of
first galaxies and reionization. These measured parameters determine the
temperature-to-mass ratio of warm dark matter. This ratio happens to be in
agreement with the no freeze-in and no freeze-out warm dark matter scenario of
spin 0 dark matter particles decoupling early on from the standard model
sector. Spin 1/2 and spin 1 dark matter are disfavored if nature has chosen the
no freeze-in and no freeze-out scenario. An extension of the standard model of
quarks and leptons, with scalar dark matter that couples to the Higgs boson,
that is in agreement with all current measurements, is briefly reviewed.
Discrepancies with limits on dark matter particle mass that can be found in the
literature, are addressed.
