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We explore the possibility that high-energy (HE) neutrinos produced at mildlyrelativistic shocks can be annihilated with low-energy (LE) neutrinos emittedfrom the accretion disk around a black hole in binary neutron star mergers andrare core-collapse supernovae. For HE neutrinos produced close to the stellarcenter ($\lesssim 10^{9}-10^{11}$ cm), we find that the emerging all-flavorspectrum for neutrinos of $E\gtrsim 0.1$ PeV could be modified by a factor$E^{-n}$ with $n\approx 0.4-0.5$. Flavor evolution of LE neutrinos does notaffect this result but can change the emerging flavor composition of HEneutrinos. As a consequence, the above annihilation effect needs to beconsidered for HE neutrinos produced at nonrelativistic or mildly relativisticshocks at small radii. In particular, we point out that models of core-collapsesupernovae with slow jets and charmed meson decay can better fit the diffuse HEneutrino flux observed by IceCube if annihilation of HE and LE neutrinos istaken into account. Moreover, the relevance of charmed meson and theannihilation effect can be tested by precise measurements of the diffuseneutrino spectrum and flavor composition.

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