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We introduce a systematic and quantitative methodology for establishing thepresence of neutrino oscillatory signals due to the hadron-quark phasetransition (PT) in failing core-collapse supernovae from the observed neutrinoevent rate in water- or ice-based neutrino detectors. The methodology uses alikelihood ratio in the frequency domain as a test-statistic; it is employedfor quantitative analysis of neutrino signals without assuming the frequency,amplitude, starting time, and duration of the PT-induced oscillations presentin the neutrino events and thus it is suitable for analyzing neutrino signalsfrom a wide variety of numerical simulations. We test the validity of thismethod 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 aPT-induced oscillations quantitatively for a core-collapse supernovae out to adistance of $\sim 10$ kpc, $\sim 5$ kpc for IceCube and to a distance of $\sim10$ kpc, $\sim 5$ kpc and $\sim 1$ kpc for a 0.4 Mt mass water Cherenkovdetector. This methodology will aid the investigation of a future galacticsupernova and the study of hadron-quark phase in the core of core-collapsesupernovae.

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