Addressing the too big to fail problem with baryon physics and sterile neutrino dark matter

N-body dark matter simulations of structure formation in the Lambda cold dark matter (Lambda CDM) model predict a population of subhaloes within Galactic haloes that have higher central densities than inferred for the Milky Way satellites, a tension known as the 'too big to fail' problem. Proposed solutions include baryonic effects, a smaller mass for the Milky Way halo and warm dark matter (WDM). We test these possibilities using a semi-analytic model of galaxy formation to generate luminosity functions for Milky Way halo-analogue satellite populations, the results of which are then coupled to the Jiang & van den Bosch model of subhalo stripping to predict the subhalo V-max functions for the 10 brightest satellites. We find that selecting the brightest satellites (as opposed to the most massive) and modelling the expulsion of gas by supernovae at early times increases the likelihood of generating the observed Milky Way satellite V-max function. The preferred halo mass is 6 x 10(11) M-circle dot, which has a 14 per cent probability to host a V-max function like that of the Milky Way satellites. We conclude that the Milky Way satellite V-max function is compatible with a CDM cosmology, as previously found by Sawala et al. using hydrodynamic simulations. Sterile neutrino-WDM models achieve a higher degree of agreement with the observations, with a maximum 50 per cent chance of generating the observed Milky Way satellite V-max function. However, more work is required to check that the semi-analytic stripping model is calibrated correctly for each sterile neutrino cosmology.