Indirect dark matter searches at ultrahigh energy neutrino detectors

High to ultrahigh energy neutrino detectors can uniquely probe the properties of dark matter $\chi$ by searching for the secondary products produced through annihilation and/or decay processes. We evaluate the sensitivities to dark matter thermally averaged annihilation cross section $\langle\sigma v\rangle$ and partial decay width into neutrinos $\Gamma_{\chi\rightarrow\nu\bar{\nu}}$ (in the mass scale $10^7 \leq m_\chi/{\rm GeV} \leq 10^{15}$) for next generation observatories like POEMMA and GRAND. We show that in the range $ 10^7 \leq m_\chi/{\rm GeV} \leq 10^{11}$, space-based Cherenkov detectors like POEMMA have the advantage of full-sky coverage and rapid slewing, enabling an optimized dark matter observation strategy focusing on the Galactic center. We also show that ground-based radio detectors such as GRAND can achieve high sensitivities and high duty cycles in radio quiet areas. We compare the sensitivities of next generation neutrino experiments with existing constraints from IceCube and updated 90\% C.L. upper limits on $\langle\sigma v\rangle$ and $\Gamma_{\chi\rightarrow\nu\bar{\nu}}$ using results from the Pierre Auger Collaboration and ANITA. We show that in the range $ 10^7 \leq m_\chi/{\rm GeV} \leq 10^{11}$ POEMMA and GRAND10k will improve the neutrino sensitivity to particle dark matter by factors of 2 to 10 over existing limits, whereas GRAND200k will improve this sensitivity by two orders of magnitude. In the range $10^{11} \leq m_\chi/{\rm GeV} \leq 10^{15}$, POEMMA's fluorescence observation mode will achieve an unprecedented sensitivity to dark matter properties. Finally, we highlight the importance of the uncertainties related to the dark matter distribution in the Galactic halo, using the latest fit and estimates of the Galactic parameters.