How Bright in Gravitational Waves are Millisecond Pulsars for the Galactic Center GeV Gamma-Ray Excess? A Systematic Study

Abstract: The existence of dark matter (DM) is supported by various macroscopic observations, but its microscopic nature remains elusive. The Galactic Center GeV gamma-ray excess (GCE) has been a leading candidate signal for particle dark matter annihilation. However, an unresolved population of millisecond pulsars (MSPs) in the bulge provides the alternative explanation for the excess. Identifying these MSPs in electromagnetic bands is difficult due to source confusion, pulse broadening, and extinction. Gravitational waves (GWs) provide a complementary probe: a steadily rotating, non-axisymmetric MSP emits a nearly monochromatic GW signal in the sensitive band of ground-based detectors, with amplitude set by its ellipticity. In this work, we systematically investigate the GW emission from the MSP population proposed to explain the GCE and its detectability with current and future detectors. We consider three major scenarios for the origin of ellipticity and model the population properties of these MSPs. We also consider both isolated MSPs and MSPs in binary systems, as well as Doppler effects in the detection. We find that while the signal is below the reach of current interferometers, next-generation detectors such as the Einstein Telescope (ET) and Cosmic Explorer (CE) can detect a fraction of those MSPs, offering a novel test of the MSP interpretation of the GCE. Future directed searches toward the Galactic Center with continued improvements in sensitivities will either uncover this long-sought MSP population or place stringent limits on their ellipticities and abundance, with important implications for both the astrophysical and dark-matter interpretations of the GCE.