Millisecond pulsar origin of the Galactic center excess and extended gamma-ray emission from Andromeda - a closer look

A new measurement of a spatially extended gamma-ray signal from the center of the Andromeda galaxy (M31) has been recently published by the Fermi-LAT collaboration, reporting that the emission broadly resembles the so-called Galactic center excess (GCE) of the Milky Way (MW). At the same time, evidence is accumulating on a millisecond pulsar (MSPs) origin for the GCE. These elements prompt us to compare the mentioned observations with what is, perhaps, the simplest model for an MSP population, solely obtained by rescaling of the MSP luminosity function determined in the local MW disk via the respective stellar mass of the systems. It is remarkable that without free fitting parameters, this model can account for both the energetics and the morphology of the GCE within uncertainties. For M31, the estimated luminosity due to primordial MSPs is expected to contribute only about a quarter of the detected emission, although a dominant contribution cannot be excluded given the large uncertainties. If correct, the model predicts that the M31 disk emission due to MSP is not far below the present upper bound. We also discuss a few refinements of this simple model. In particular, we use the correlation between globular cluster gamma-ray luminosity and stellar encounter rate to gauge the dynamical MSP formation in the bulge. This component is expected to contribute to the GCE only at a level $\lesssim 5\%$, but it may be of some importance in explaining the signal's morphology in the inner region of the Galaxy. We also comment on some effects which may lead to violations of the simple scaling used, on alternative models, and on future perspectives for improved diagnostics.