A recent detection of spatially extended gamma-ray emission in the central
region of the Andromeda galaxy (M31) has led to several possible explanations
being put forth, including dark matter annihilation and millisecond pulsars.
Another possibility is that the emission in M31 can be accounted for with a
purely astrophysical cosmic-ray (CR) scenario. This scenario would lead to a
rich multi-wavelength emission that can, in turn, be used to test it.
Relativistic cosmic-ray electrons (CRe) in magnetic fields produce radio
emission through synchrotron radiation, while X-rays and gamma rays are
produced through inverse Compton scattering. Additionally, collisions of
primary cosmic-ray protons (CRp) in the interstellar medium produce charged and
neutral pions that then decay into secondary CRe (detectable through radiative
processes) and gamma-rays. Here, we explore the viability of a CR origin for
multi-wavelength emission in M31, taking into consideration three scenarios: a
CR scenario dominated by primary CRe, one dominated by CRp and the resulting
secondary CRe and gamma rays from neutral pion decay, and a final case in which
both of these components exist simultaneously. We find that the multi-component
model is the most promising, and is able to fit the multi-wavelength spectrum
for a variety of astrophysical parameters consistent with previous studies of
M31 and of cosmic-ray physics. However, the CR power injection implied by our
models exceeds the estimated CR power injection from typical astrophysical
cosmic-ray sources such as supernovae.