Gravitational Microlensing of the Galactic Centre $γ$-Ray Excess: A New Test for Point-Like or Extended Emission?

We present a potential test of the origin of the $γ$-ray Galactic Centre Excess (GCE). We demonstrate how gravitational microlensing by stellar mass objects along the line of sight to the Galactic Bulge can distinguish between the possibility of extensive emission due to dark matter self-annihilation from more prosaic astrophysical sources, namely millisecond pulsars. Such an astrophysical origin would result in emission from a population of small, currently unresolved point-like sources - in contrast to the expected smoother emission resulting from dark matter annihilation. Given that the scale of gravitational microlensing, that is, the Einstein radius for stellar mass lenses, and hence, the degree of induced magnification, is sensitive to the size of the emitting region, such microlensing will induce time variability in the emission of astrophysical sources, whereas $γ$-ray emission from dark matter annihilation will effectively be immune to such influences. However, we find that detecting microlensing-induced variability requires significantly greater sensitivity than that of current or planned $γ$-ray detectors. For a small population of bright GCE sources, more than an order-of-magnitude increase in effective area over Fermi-LAT would be required, with events remaining extremely rare. For a large population of faint sources, events would occur multiple times a year, but would only be detectable with a four-order-of-magnitude improvement. Whilst microlensing might not be a definitive test of the origin of the GCE, in future observations, it may prove useful in determining the properties of any point-like source population.