Astrophysical constraints from synchrotron emission on very massive decaying dark matter

If the cosmological dark matter (DM) couples to Standard Model (SM) fields, it can decay promptly to SM states in a highly energetic hard process, which subsequently showers and hadronizes to give stable particles including $e^\pm$, $\gamma$, $p^{\pm}$ and $\nu\bar{\nu}$ at lower energy. If the DM particle is very heavy, the high-energy $e^\pm$, due to the Klein-Nishina cross section suppression, preferentially lose energy via synchrotron emission which, in turn, can be of unusually high energies. Here, we present previously unexplored bounds on heavy decaying DM up to the Planck scale, by studying the synchrotron emission from the $e^\pm$ produced in the ambient Galactic magnetic field. In particular, we explore the sensitivity of the resulting constraints on the DM decay width to (i) different SM decay channels, to (ii) the Galactic magnetic field configurations, and (iii) to various different DM density profiles proposed in the literature. We find that constraints from the synchrotron component complement and improve on constraints from very high-energy cosmic-ray and gamma-ray observatories targeting the prompt emission when the DM is sufficiently massive, most significantly for masses in excess of $10^{12}\text{ GeV}$.