Using Secondary Tau Neutrinos to Probe Heavy Dark Matter Decays in Earth

Dark matter particles can be gravitationally trapped by celestial bodies, motivating searches for localized annihilation or decay. If neutrinos are among the decay products, then IceCube and other neutrino observatories could detect them. We investigate this scenario for dark matter particles above $m_{\chi} \gtrsim$ PeV producing tau neutrino signals, using updated modeling of dark matter capture and thermalization. At these energies, tau neutrino regeneration is an important effect during propagation through Earth, allowing detection at distances far longer than one interaction length. We show how large energy loss of tau leptons above $\sim$ PeV drives a wide range of initial energies to the same final energy spectrum of "secondary" tau neutrinos at the detector, and we provide an analytic approximation to the numerical results. This effect enables an experiment to constrain decays that occur at very high energies, and we examine the reach of the IceCube high-energy starting event (HESE) sample in the parameter space of trapped dark matter annihilations and decays above PeV. We find that the parameter space probed by IceCube searches would require dark matter cross sections in tension with existing direct-detection bounds.