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 ${10}^6$–${10}^7{M}_{\odot }$, most QPEs formed in this scenario have periods longer than $\simeq 100$ days. A single-SMBH system generally produces QPEs at a negligible rate of ${10}^{-10}$–${10}^{-8}{\mathrm{y}\mathrm{r}}^{-1}$ 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 ${10}^{-6}$–${10}^{-5}{\mathrm{y}\mathrm{r}}^{-1}$. Our results suggest that a nonnegligible fraction ($\simeq 10$–$90\mathrm{\%}$) of long-period QPEs should come from postmerger galaxies.