The impact of free-streaming on dwarf galaxy counts in low-density regions

We study the statistics of dwarf galaxy populations as a function of environment in cold dark matter (CDM) and warm dark matter (WDM; sterile neutrino model mass M_ s=7.1~ keV; half-mode mass M_ hm = 6.3× 10⁸ M_; and thermal relic equivalent mass m_ th = 2.8~ keV) cosmogonies, using the Evolution and Assembly of GaLaxies and their Environments (EAGLE) galaxy formation model in two counterpart simulations. We measure the abundance of dwarf galaxies within 3 Mpc of DM haloes with a present-day halo mass similar to the Milky Way, finding that the number of galaxies M*> 10⁷ M_ is nearly identical for WDM and CDM. However, the cumulative mass function becomes shallower for WDM at lower masses, yielding 50 per cent fewer dwarf galaxies of M* 10⁵ M_ than CDM. The suppression of low-mass halo counts in WDM increases significantly from high- to low-density regions for haloes in the [0.5,2] × M_ hm range. The fraction of haloes hosting resolvable galaxies (M_* 10⁵ M_ ) also diverges from overdense to underdense regions for M> 2M_ hm, as the increased collapse delay at small densities pushes the collapse to after the reionization threshold. However, the stellar mass of WDM haloes at [0.5,2]× M_ hm is 30 per cent higher per unit halo mass than CDM haloes in underdense regions. We conclude that the suppression of galaxies with M* 10⁵ M_ between WDM and CDM is independent of density: the suppression of halo counts and fraction of luminous haloes is balanced by an enhancement in stellar mass–halo mass relation.