  We test the luminosity function of Milky Way satellites as a constraint for
the nature of Dark Matter particles. We perform dissipationless high-resolution
N-body simulations of the evolution of Galaxy-sized halo in the standard Cold
Dark Matter (CDM) model and in four Warm Dark Matter (WDM) scenarios, with a
different choice for the WDM particle mass (m_w). We then combine the results
of the numerical simulations with semi-analytic models for galaxy formation, to
infer the properties of the satellite population. Quite surprisingly we find
that even WDM models with relatively low m_w values (2-5 keV) are able to
reproduce the observed abundance of ultra faint (Mv<-9) dwarf galaxies, as well
as the observed relation between Luminosity and mass within 300 pc. Our results
suggest a lower limit of 1 keV for thermal warm dark matter, in broad agreement
with previous results from other astrophysical observations like Lyman-alpha
forest and gravitational lensing.
