Effects of Annihilation with Low-Energy Neutrinos on High-Energy Neutrinos from Binary Neutron Star Mergers and Rare Core-Collapse Supernovae

We explore the possibility that high-energy (HE) neutrinos produced from choked jets can be annihilated with low-energy (LE) neutrinos emitted from the accretion disk around a black hole in binary neutron star mergers and rare core-collapse supernovae. For HE neutrinos produced close to the stellar center ($\lesssim 10^{9}-10^{12}$ cm), we find that the emerging all-flavor spectrum for neutrinos of $E\gtrsim 0.1-1$ PeV could be modified by a factor $E^{-n}$ with $n\gtrsim 0.4-0.5$ under realistic conditions. Flavor evolution of LE neutrinos does not affect this result but can change the emerging flavor composition of HE neutrinos. As a consequence, the above annihilation effect may need to be considered for HE neutrinos produced from choked jets at small radii. We briefly discuss the annihilation effects for different HE neutrino production models and point out that such effects could be tested through precise measurements of the diffuse neutrino spectrum and flavor composition.