Quasi-periodic eruptions from mildly eccentric unstable mass transfer in galactic nuclei

We propose that the recently observed quasi-periodic eruptions (QPEs) in galactic nuclei are produced by unstable mass transfer due to Roche lobe overflow of a low-mass main-sequence star in a mildly eccentric (e ∼0.5) orbit. We argue that the QPE emission is powered by circularization shocks, but not directly by black hole (BH) accretion. Our model predicts the presence of a time-steady accretion disc that is bolometrically brighter than the time-averaged QPE luminosity, but primarily emits in the extreme-ultraviolet. This is consistent with the quiescent soft X-ray emission detected in between the eruptions in eROSITA QPE1, QPE2, and GSN 069. Such accretion discs have an unusual νLν ∝ ν12/7 optical spectrum. The lifetime of the bright QPE phase, 102-103 yr, is set by mass-loss triggered by ram-pressure interaction between the star and the accretion disc fed by the star itself. We show that the stellar orbits needed to explain QPEs can be efficiently created by the Hills breakup of tight stellar binaries provided that (i) the stellar binary orbit is tidally hardened before the breakup due to diffusive growth of the f-mode amplitude and (ii) the captured star's orbit decays by gravitational wave emission without significant orbital angular momentum diffusion (which is the case for low-mass BHs, MBH ≲ 106 M⊙). We conclude by discussing the implications of our model for hyper-velocity stars, extreme mass ratio inspirals, repeating partial TDEs, and related stellar phenomena in galactic nuclei.