Neutrino Echos following Black Hole Formation in Core-Collapse Supernovae

During a failed core-collapse supernova, the protoneutron star eventually collapses under its own gravitational field and forms a black hole. This collapse happens quickly, on the dynamical time of the protoneutron star, $\lesssim$0.5 ms. During this collapse, barring any excessive rotation, the entire protoneutron star is accreted into the newly formed black hole. The main source of neutrinos is now removed and the signal abruptly shuts off over this formation timescale. However, while the source of neutrinos is turned off, the arrival times at an Earth-based detector will depend on the neutrino path. We show here that a modest amount of neutrinos, emitted just prior to the black hole forming, scatter on the infalling material into our line of sight and arrive after the formation of the black hole, up to 15 ms in our model. This neutrino echo, which we characterize with Monte Carlo simulations and analytic models, has a significantly higher average energy (upwards of $\sim$ 50 MeV) compared to the main neutrino signal, and for the canonical failed supernova explored here, is likely detectable in $\mathcal{O}$(10 kT) supernova neutrino detectors for Galactic failed supernovae. The presence of this signal is important to consider if using black hole formation as a time post for triangulation or the post black hole timing profile for neutrino mass measurements. On its own, it can also be used to characterize or constrain the structure and nature of the accretion flow.