  The ANITA experiment, which is designed to detect ultra-high energy
neutrinos, has reported the observation of two anomalous events, directed at
angles of $27^{\circ}$ and $35^{\circ}$ with respect to the horizontal. At
these angles, the Earth is expected to efficiently absorb ultra-high energy
neutrinos, making the origin of these events unclear and motivating
explanations involving physics beyond the Standard Model. In this study, we
consider the possibility that ANITA's anomalous events are the result of
Askaryan emission produced by exotic weakly interacting particles scattering
elastically with nuclei in the Antarctic ice sheet. Such particles could be
produced by superheavy ($\sim 10^{10}-10^{13}$ GeV) dark matter particles
decaying in the halo of the Milky Way. Such scenarios can be constrained by
existing measurements of the high-latitude gamma-ray background and the
ultra-high energy cosmic ray spectrum, along with searches for ultra-high
energy neutrinos by IceCube and other neutrino telescopes.
