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.
