We compute the mass function of galactic dark matter halos for different values of the warm dark matter (WDM) particle mass mX and compare it with the number density of ultra-faint galaxies derived from the deepest UV luminosity function available so far at redshift z?≈?2. The magnitude limit MUV?=??13 reached by such observations allows us to probe the WDM mass functions down to scales close to or smaller than the half-mass mode mass scale ~109 M⊙. This allowed for an efficient discrimination among predictions for different mX which turn out to be in practice independent of the star formation efficiency η adopted to associate the observed UV luminosities of galaxies to the corresponding dark matter halo masses. Adopting a conservative approach to take into account the existing theoretical uncertainties in the galaxy halo mass function, we obtain a robust limit mX?≥?1.8 keV for the mass of thermal relic WDM particles when comparing with the measured abundance of the faintest galaxies, while mX?≥?1.5 keV is obtained when we compare with the Schechter fit to the observed luminosity function. The corresponding lower limit for sterile neutrinos depends on the modeling of the production mechanism; for instance msterile 4 keV holds for the Shi–Fuller mechanism. We discuss the impact of observational uncertainties on the above bound on mX. In the cold dark matter (CDM) limit we recover the generic CDM result that very inefficient star formation efficiency is required to match the observed galaxy abundances. As a baseline for comparison with forthcoming observational results from the Hubble Space Telescope Frontier Field project, we provide predictions for the number density of faint galaxies with MUV?=??13 for different values of the WDM particle mass and of the star formation efficiency η, which are valid up to z?≈?4.
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