Prospects for detecting eV-scale sterile neutrinos from a galactic supernova

Future neutrino detectors will obtain high-statistics data from a nearby core-collapse supernova. We study the mixing with eV-mass sterile neutrinos in a supernova environment and its effects on the active neutrino fluxes as detected by Hyper-Kamiokande and IceCube. Using a Markov Chain Monte Carlo analysis, we make projections for how accurately these experiments will measure the active-sterile mixing angle $\theta_s$ given that there are substantial uncertainties on the expected luminosity and spectrum of active neutrinos from a galactic supernova burst. We find that Hyper-Kamiokande can reconstruct the sterile neutrino mixing and mass in many different situations, provided the neutrino luminosity of the supernova is known precisely. Crucially, we identify a degeneracy between the mixing angle and the overall neutrino luminosity of the supernova. This means that it will only be possible to determine the luminosity if the presence of sterile neutrinos with $\theta_s \gtrsim 0.1$ degrees can be ruled out independently. We discuss ways in which this degeneracy may be broken in the future.