  [Abridged] Indirect detection of dark matter (DM) by multi-wavelength
astronomical observations provides a promising avenue for probing the particle
nature of DM. In the case of DM consisting of Weakly-Interacting Massive
Particles (WIMPs), self-annihilation ultimately produces observable products
including $e^{\pm}$ pairs and gamma rays. The gamma rays can be detected
directly, while the $e^{\pm}$ pairs can be detected by radio emission from
synchrotron radiation or X-rays and soft gamma rays from inverse Compton
scattering. An intriguing region to search for astrophysical signs of DM is the
Galactic center (GC) of the Milky Way, due in part to an observed excess of
gamma-rays that could be DM. A recent observation by the Fermi-LAT
collaboration of a similar excess in the central region of the Andromeda galaxy
(M31) leads us to explore the possibility of a DM-induced signal there as well.
We use the RX-DMFIT tool to perform a multi-frequency analysis of potential DM
annihilation emissions in M31. We consider WIMP models consistent with the GC
excess and calculate the expected emission across the electromagnetic spectrum
in comparison with available observational data from M31. We find that the
particle models that best fit the M31 excess favor lower masses than the GC
excess. The best fitting models are for a $b\bar{b}$ final state with
$M_{\chi}=11$ GeV and $\left<\sigma v\right>=2.6\times 10^{-26}$
cm$^3$s$^{-1}$, as well as an evenly mixed $b\bar{b}/\tau^+\tau^-$ final state
with $M_{\chi}=5.8$ GeV and $\left<\sigma v\right>=2.03\times 10^{-26}$
cm$^3$s$^{-1}$. For conservative estimates of the diffusion and magnetic field
models the expected radio emissions appear to be in tension with currently
available data in the central region of M31, although this constraint has a
fairly strong dependence on the values chosen for parameters describing the
magnetic field strength and geometry.
