Possibility of multi-messenger observations of quasi-periodic eruptions with X-rays and gravitational waves

Abstract Recent X-ray observations have discovered a class of periodic X-ray flares in galactic nuclei known as quasi-periodic eruptions (QPEs) whose recurrence time ranges from hours to days. A promising explanation of QPEs is an emission produced when a stellar-mass object orbiting a central supermassive black hole crosses an accretion disk formed by a tidal disruption event (TDE). If the companion is a compact object and the recurrence time is shorter than 10 min, such systems would be prospective multi-messenger targets for the space-based observatory LISA and its successors. Here we quantify the prospects for joint X-ray and gravitational wave (GW) detection of QPEs with recurrence times of about 10 min, corresponding to orbital frequencies in the mHz band, using a minimal flare-emission model in which a stellar-mass black hole companion collides with a TDE-formed accretion disk. Our analysis shows that X-ray observations are most effective at orbital frequencies up to roughly 1 mHz, whereas LISA is sensitive chiefly above about 1 mHz. Because the optimal sensitivity windows overlap only marginally, we predict at most one joint detection during LISA’s nominal mission lifetime. Extending GW sensitivity into the sub-millihertz regime (0.1 mHz) would raise the possibility of the joint detection by an order of magnitude, enabling QPEs to be interesting multi-messenger targets.