Impact of sterile neutrinos on the early time flux from a galactic supernova

We study the impact of the existence of an eV-mass scale sterile neutrino---with parameters in the ballpark of what is required to fit the laboratory anomalies---on the early time profile of the electron neutrino and antineutrino fluxes associated to a core-collapse supernova (SN). In particular, we focus on the universal feature of neutronization burst expected in the first tens of ms of the signal: provided that a detector with sufficient sensitivity is available, it is well-known that in the 3 neutrino framework the detection of the neutronization burst in neutrino channel would signal inverted mass hierarchy. This conclusion is dramatically altered in the presence of a sterile neutrino: we study here both analytically and numerically the region in parameter space where this characteristic signal disappears, mimicking normal hierarchy expectations. Conversely, the detection of a peak consistent with expectations for inverted mass hierarchy would exclude the existence of a sterile state over a much wider parameter space than what required by laboratory anomalies fits, or even probed by detectors coming on-line in the near future. Additionally, we show the peculiar alteration in the energy-time double differential flux, with a delayed peak appearing for kinematical reasons, which might offer a remarkable signature in case of favorable parameters and for a high statistics detection of a Galactic SN. We also comment on additional potentially interesting effects in the electron antineutrino channel, if more than one angle in the active-sterile sector is non-vanishing. As an ancillary result that we derived in the technical resolution of the equations, in an appendix we report the Cayley-Hamilton formalism for the evolution of a four neutrino system in matter, generalizing existing results in the literature.