Refining lower bounds on sterile neutrino dark matter mass from estimates of phase space densities in dwarf galaxies

Dwarf spheroidal galaxies (dSphs) are recognized as being highly dominated by Dark Matter (DM), making them excellent targets for testing DM models through astrophysical observations. One effective method involves estimating the coarse-grained phase-space density (PSD) of the galactic DM component. By comparing this PSD with that of DM particles produced in the early Universe, it is possible to establish lower bounds on the DM particle mass. These constraints are particularly relevant for models of warm DM, such as those involving sterile neutrinos. By utilizing the GravSphere code, we obtain a fit of the DM PSD based on the latest reliable stellar dynamics data for twenty of the darkest dSphs, refining earlier lower bounds on sterile neutrino masses in nonresonant production scenarios. Additionally, we introduce an alternative approach involving the Excess Mass Function (EMF), which yields even tighter constraints. Specifically, using the maximum PSD, we derive a lower bound of [Formula: see text] [Formula: see text]keV at 95% confidence level, while the EMF method provides a stronger limit of [Formula: see text] [Formula: see text]keV at 95% CL. For the general thermal relic fermion dark matter mass, the limits translate into [Formula: see text] [Formula: see text]keV and [Formula: see text] [Formula: see text]keV, respectively. Both methods are versatile and can be extended to more complex DM production mechanisms in the early Universe. For the first time, we also constrain parameters of models involving nonstandard cosmologies during the epoch of neutrino production. Our analysis yields [Formula: see text] [Formula: see text]keV for models with kination domination and [Formula: see text] [Formula: see text]keV for scenarios with extremely low reheating temperature.