Detectability of neutrino-signal fluctuations induced by the hadron-quark phase transition in failing core-collapse supernovae

We introduce a systematic and quantitative methodology for establishing the presence of neutrino oscillatory signals due to the hadron-quark phase transition (PT) in failing core-collapse supernovae from the observed neutrino event rate in water- or ice-based neutrino detectors. The methodology uses a likelihood ratio in the frequency domain as a test-statistic; it is employed for quantitative analysis of neutrino signals without assuming the frequency, amplitude, starting time, and duration of the PT-induced oscillations present in the neutrino events and thus it is suitable for analyzing neutrino signals from a wide variety of numerical simulations. We test the validity of this method by using a core-collapse simulation of a 17 solar-mass star by Zha \emph{et al.} (2021). Based on this model, we further report the presence of a PT-induced oscillations quantitatively for a core-collapse supernovae out to a distance of $\sim 10$ kpc, $\sim 5$ kpc for IceCube and to a distance of $\sim 10$ kpc, $\sim 5$ kpc and $\sim 1$ kpc for a 0.4 Mt mass water Cherenkov detector. This methodology will aid the investigation of a future galactic supernova and the study of hadron-quark phase in the core of core-collapse supernovae.