We introduce a novel methodology for establishing the presence of Standing Accretion Shock Instabilities (SASI) in the dynamics of a core collapse supernova from the observed neutrino event rate at water- or ice-based neutrino detectors. The methodology uses a likelihood ratio in the frequency domain as a test-statistics; it is also employed to assess the potential to estimate the frequency and the amplitude of the SASI modulations of the neutrino signal. The parameter estimation errors are consistent with the minimum possible errors as evaluated from the inverse of the Fisher information matrix, and close to the theoretical minimum for the SASI amplitude. Using results from a core-collapse simulation of a 15 solar-mass star by Kuroda $it {et, al.}$ (2017) as a test bed for the method, we find that SASI can be identified with high confidence for a distance to the supernova of up to $sim 6$ kpc for IceCube and and up to $sim 3$ kpc for a 0.4 Mt mass water Cherenkov detector. This methodology will aid the investigation of a future galactic supernova.
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