  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.
