Constraining the Warm Dark Matter Particle Mass through Ultra-Deep UV Luminosity Functions at z=2

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 abundance 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 ~10^9 M_sun. This allowed for an efficient discrimination among predictions for different m_X which turn out to be independent of the star formation efficiency adopted to associate the observed UV luminosities of galaxies to the corresponding dark matter masses. Adopting a conservative approach to take into account the existing theoretical uncertainties in the galaxy halo mass function, we derive 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. As a baseline for comparison with forthcoming observations from the HST Frontier Field, we provide predictions for the abundance of faint galaxies with M_UV=-13 for different values of m_X and of the star formation efficiency, valid up to z~4.