Formation Rate of Quasiperiodic Eruptions in Galactic Nuclei Containing Single and Dual Supermassive Black Holes

Quasiperiodic eruptions (QPEs) are a novel class of transients recently discovered in a few extragalactic nuclei. It has been suggested that a QPE can be produced by a main-sequence star undergoing repeated partial disruptions by the tidal field of a supermassive black hole (SMBH) immediately after getting captured on a tightly bound orbit through the Hills mechanism. In this Letter, we investigate the period-dependent formation rate of QPEs for this scenario, utilizing scattering experiments and the loss-cone theory. We calculate the QPE formation rates in both a single-SMBH and a dual-SMBH system, motivated by the overrepresentation of postmerger galaxies as QPE hosts. We find that for SMBHs of mass 106–107M⊙, most QPEs formed in this scenario have periods longer than ≃ 100 days. A single-SMBH system generally produces QPEs at a negligible rate of 10−10–10−8 yr−1 due to inefficient two-body relaxation. Meanwhile, in a dual-SMBH system, the QPE rate is enhanced by 3–4 orders of magnitude, mainly due to a boosted angular momentum evolution under tidal perturbation from the companion SMBH (galaxy). The QPE rate in a postmerger galactic nucleus hosting two equal-mass SMBHs separated by a few parsecs could reach 10−6–10−5 yr−1. Our results suggest that a nonnegligible fraction (≃10%–90%) of long-period QPEs should come from postmerger galaxies.