  Recently, a diffuse emission of 1-100 GeV $\gamma$-rays has been detected
from the direction of Andromeda. The emission is centered on the galaxy, and
extends for $\sim 100-200$ kpc away from its center. Explaining the extended
$\gamma-$ray emission within the framework of standard scenarios for the escape
of cosmic rays injected in the galactic disk or in the galactic center is
problematic. In this paper, we argue that a cosmic ray origin (either leptonic
or hadronic) of the $\gamma$-ray emission is possible in the framework of non
standard cosmic ray propagation scenarios or in the case of particle
acceleration taking place in the galaxy's halo. It would imply the existence of
a giant cosmic ray halo surrounding M31, possibly powered by the galaxy nuclear
activity, or by accretion of intergalactic gas. Remarkably, if cosmic ray
halos, as the one observed around M31, are a common feature of galaxies,
including our own, the interactions between cosmic ray protons and the Milky
Way circumgalactic gas could also explain the isotropic diffuse flux of
neutrinos observed by Icecube.
