A general study of decaying scalar dark matter: existing limits and projected radio signals at the SKA

Abstract: We consider a decaying scalar dark matter (DM) with mass $m_\chi$ in the range 10 GeV - 10 TeV and vary the branching ratios of all possible two-body SM final states (excluding and including $\nu\bar{\nu}$) in the range $0\%-100\%$ to derive constraints on the total decay width $\Gamma$ using the data collected by several astrophysical and cosmological observations. We find that, $\Gamma \lesssim 10^{-26} - 10^{-27}\,{\rm s}^{-1}$ (excluding $\nu\bar{\nu}$) and $\Gamma \lesssim 10^{-24} - 10^{-26}\,{\rm s}^{-1}$ (including $\nu\bar{\nu}$) are allowed, depending on the values of $m_\chi$, which are most robust upper limits on $\Gamma$ for a generic decaying scalar DM. We then investigate the prospect of the upcoming Square Kilometre Array (SKA) radio telescope in detecting the DM decay induced radio signals originating inside the dwarf spheroidal (dSph) galaxies. We have classified the DM parameter space, allowed by the existing observations, independently of the branching ratio of each individual two-body SM final state, based on the detectability at the SKA. Excluding the $\nu\bar{\nu}$ decay mode, we find that, throughout the DM mass range considered, $\Gamma \gtrsim 10^{-30}\,{\rm s}^{-1} - 10^{-29}\,{\rm s}^{-1}$ is detectable for all possible branching ratio combinations at the SKA (assuming 100 hours of observation time), with conservative choices for the relevant astrophysical parameters. On the other hand, when arbitrary branching ratios are allowed also for the $\nu\bar{\nu}$ decay mode, DM decays can be probed independently of the branching ratio of each SM final state for $\Gamma \gtrsim 2 \times 10^{-29}\,{\rm s}^{-1}$, provided DM masses are greater than a few hundreds of GeV.