A model for the possible connection between tidal disruption event and quasi-periodic eruption in GSN 069

Abstract: Quasi-periodic eruptions (QPEs) are found in the center of five galaxies, where a tidal disruption event (TDE)-like event is also reported in GSN 069 that happened a couple of years before the QPEs. We explain the connection of these phenomena based on a model of a highly eccentric white-dwarf (WD)-$10^{4-6}M_{\odot}$ massive black hole (MBH) binary formed by the Hill mechanism. In this system, the tidal induced internal oscillation of WD can heat the WD envelope thereby induces the tidal nova and inflates the WD envelope, which can be captured by the MBH and form a TDE. The tidal stripping of the surviving WD in the eccentric orbit can produce the QPEs. We also apply this model to the other four QPE sources. Based on the estimated fallback rate, we find that the remaining time after the QPE-observed time for these QPEs is only around 1-2 years based on our simple model estimation, and then the WD will be fully disrupted. We also show that the accretion rate can be much higher than Eddington accretion rate in final stage of these QPE sources. The peak frequency of spectral energy distribution of disk stays in soft X-ray band ($\sim 0.1-1$ keV), which is consistent with observational results.