  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 novel 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 $10^{12}\text{
GeV}$.
