The observation of Earth matter effects in the spectrum of neutrinos coming from a next galactic core-collapse supernova (CCSN) could, in principle, reveal if neutrino mass ordering is normal or inverted. One of the possible ways to identify the mass ordering is through the observation of the modulations that appear in the spectrum when neutrinos travel through the Earth before they arrive at the detector. These features in the neutrino spectrum depend on two factors, the average neutrino energies, and the difference between the primary neutrino fluxes of electron and other flavors produced inside the supernova. However, recent studies indicate that the Earth matter effect for CCSN neutrinos is expected to be rather small and difficult to be observed by currently operating or planned neutrino detectors mainly because of the similarity of average energies and fluxes between electron and other flavors of neutrinos, unless the distance to CCSN is significantly smaller than the typically expected one, $sim 10$ kpc. Here, we are looking towards the possibility if the non-standard neutrino properties such as decay of neutrinos can enhance the Earth matter effect. In this work we show that invisible neutrino decay can potentially enhance significantly the Earth matter effect for both $ u_e$ and $bar{ u}_e$ channels at the same time for both mass orderings, even if the neutrino spectra between electron and other flavors of neutrinos are very similar, which is a different feature not expected for CCSN neutrinos with standard oscillation without the decay effect.
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