Neutrinos From Particle Decay in the Sun and Earth

Weakly interacting massive particles (WIMPs) may be indirectly detected by observation of upward muons induced by energetic neutrinos from annihilation of WIMPs that have accumulated in the Sun and/or Earth. Energetic muon neutrinos come from the decays of $\tau$ leptons, $c$, $b$, and $t$ quarks, gauge bosons, and Higgs bosons produced by WIMP annihilation. We provide analytic expressions, suitable for computing the flux of upward muons, for the neutrino energy spectra from decays of all these particles in the center of the Sun and Earth. These analytic expressions should obviate the need for Monte Carlo calculations of the upward-muon flux. We investigate the effects of polarization of the gauge bosons on the neutrino spectra and find that they are small. We also present simple expressions for the second moments of the neutrino distributions which can be used to estimate the rates for observation of neutrino-induced muons from WIMP annihilation.