On the Gravitational Wave Counterpart to a Gamma-ray Galactic Center Signal from Millisecond Pulsars

The new tools of gravitational wave and multi-messenger astronomy allow for the study of astrophysical phenomenon in new ways and enables light to be shed on some of the longest-enduring mysteries of high-energy astrophysics. Among the latter stands the Galactic center gamma-ray excess, associated with a source whose nature could be annihilating dark matter or a yet-unresolved population of millisecond pulsars (MSPs). MSPs are most likely asymmetric about their axis of rotation, and are thus thought to also source quasi-monochromatic gravitational waves, that dark matter processes would not emit. Using statistical methods, we simulate realistic MSP population samples with differing morphology and moment of inertia, that could give rise to the gamma-ray excess, and we compute the corresponding gravitational wave signal amplitude and frequency. We find that the gravitational wave signal frequency likely ranges between $\sim$200 and 1400 Hz, and that the collective dimensionless strain from the center of the Galaxy has an amplitude between $10^{-26}$ and $10^{-24}$, thus most likely beyond current and near-term detectors, unless the unresolved MSPs are extraordinarily gamma-ray dim.