Probing the millisecond pulsar origin of the <i>γ</i> -ray excess in the Galactic centre with LISA

The gigaelectronvolt γ -ray excess observed towards the Galactic centre remains unexplained. While dark matter annihilation has long been considered a leading explanation, an alternative scenario involving a large population of millisecond pulsars remains viable. Testing this hypothesis with electromagnetic observations is difficult, as pulsar searches in the bulge are strongly affected by interstellar scattering, high sky temperature, and source confusion. We investigate whether gravitational-wave observations with the Laser Interferometer Space Antenna (LISA) could provide an independent probe of the millisecond pulsar binary population in the Galactic bulge in the future. We constructed synthetic populations of detached millisecond pulsar–white dwarf binaries under two illustrative formation scenarios: an accreted scenario, in which systems are deposited by disrupted globular clusters, and an in situ scenario, in which binaries form through isolated binary evolution. In both cases, only 10 −5 –10 −4 of the underlying bulge population is detectable by LISA. Still, even a few detections would imply tens to hundreds of thousands of unseen systems. Accreted binaries are expected to have lower chirp masses (∼0.4 M ⊙ ), while in situ binaries produce more massive companions (∼0.9 M ⊙ ), though part of this contrast reflects our modelling assumptions. LISA will measure binary frequencies with high precision, but chirp masses can only be determined for the most massive or highest-frequency systems. Thus, identifying millisecond-pulsar binaries among the far more numerous double white dwarfs will be challenging, as their gravitational-wave signals alone are indistinguishable. However, coordinated follow-up with the Square Kilometre Array of LISA-selected targets could directly test the millisecond-pulsar explanation of the γ -ray excess.