Can one observe Earth matter effects with supernova neutrinos?

Neutrino oscillations in Earth matter may introduce peculiar modulations in supernova (SN) neutrino spectra. The detection of this effect has been proposed as a diagnostic tool for the neutrino mass hierarchy at a large 1-3 leptonic mixing angle, θ ₁₃. We perform an updated study on the observability of this effect at large next-generation underground detectors (i.e., 0.4 Mton water Cherenkov, 50 kton scintillation, and 100 kton liquid argon detectors) based on neutrino fluxes from state-of-the-art SN simulations and accounting for statistical fluctuations via Monte Carlo simulations. Since the average energies predicted by recent simulations are lower than previously expected, and a tendency towards the equalization of the neutrino fluxes appears during the SN cooling phase, the detection of the Earth matter effect will be more challenging than expected from previous studies. We find that none of the proposed detectors shall be able to detect the Earth modulation for the neutrino signal of a typical galactic SN at 10 kpc. It should be observable in a 100 kton liquid argon detector for a SN at a few kpc, and all three detectors would clearly see the Earth signature for very close-by stars only (d∼0.2kpc). Finally, we show that adopting IceCube as a codetector together with a Mton water Cherenkov detector is not a viable option either.