Detecting the Supernova Breakout Burst in Terrestrial Neutrino Detectors

We calculate the distance-dependent performance of a few representative terrestrial neutrino detectors in detecting and measuring the properties of the $\nu_e$ breakout burst light curve in a Galactic core-collapse supernova. The breakout burst is a signature phenomenon of core collapse and offers a probe into the stellar core through collapse and bounce. We examine cases of no neutrino oscillations and oscillations due to normal and inverted neutrino-mass hierarchies. For the normal hierarchy, other neutrino flavors emitted by the supernova overwhelm the $\nu_e$ signal, making a detection of the breakout burst difficult. For the inverted hierarchy (IH), some detectors at some distances should be able to see the $\nu_e$ breakout burst peak and measure its properties. For the IH, the maximum luminosity of the breakout burst can be measured at 10 kpc to accuracies of $\sim$30% for Hyper-Kamiokande (Hyper-K) and $\sim$60% for the Deep Underground Neutrino Experiment (DUNE). Super-Kamiokande (Super-K) and Jiangmen Underground Neutrino Observatory (JUNO) lack the mass needed to make an accurate measurement. For the IH, the time of the maximum luminosity of the breakout burst can be measured in Hyper-K to an accuracy of $\sim$3 ms at 7 kpc, in DUNE $\sim$2 ms at 4 kpc, and JUNO and Super-K can measure the time of maximum luminosity to an accuracy of $\sim$2 ms at 1 kpc. Detector backgrounds in IceCube render a measurement of the $\nu_e$ breakout burst unlikely. For the inverted hierarchy, a measurement of the maximum luminosity of the breakout burst could be used to differentiate between nuclear equations of state.