2016ApJ...818...90M

We compute the mass function of galactic dark matter halos for different values of the warm dark matter (WDM) particle mass m_X 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 M_UV= -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 m_Xwhich 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 m_X≥ 1.8 keV for the mass of thermal relic WDM particles when comparing with the measured abundance of the faintest galaxies, while m_X≥ 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 m_sterile≳ 4 keV holds for the Shi-Fuller mechanism. We discuss the impact of observational uncertainties on the above bound on m_X. In the cold dark matter (CDM) limit m_x ≫ 1 keV 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 M_UV= -13 for different values of the WDM particle mass and of the star formation efficiency η, which are valid up to z ≈ 4.