Coupled Disk-Star Evolution in Galactic Nuclei and the Lifetimes of QPE Sources

A modest fraction of the stars in galactic nuclei fed towards the central supermassive black hole (SMBH) approach on low-eccentricity orbits driven by gravitational-wave radiation (extreme mass ratio inspiral, EMRI). In the likely event that a gaseous accretion disk is created in the nucleus during this slow inspiral (e.g., via an independent tidal-disruption event; TDE), star-disk collisions generate regular short-lived flares consistent with the observed quasi-periodic eruption (QPE) sources. We present a model for the coupled star-disk evolution which self-consistently accounts for mass and thermal energy injected into the disk from stellar collisions and associated mass ablation. For weak collision/ablation heating, the disk is thermally-unstable and undergoes limit-cycle oscillations which modulate its properties and lead to accretion-powered outbursts on timescales of years to decades, with a time-averaged accretion rate $\sim 0.1 \dot{M}_{\rm Edd}$. Stronger collision/ablation heating acts to stabilize the disk, enabling roughly steady accretion at the EMRI-stripping rate. In either case, the stellar destruction time through ablation, and hence the maximum QPE lifetime, is $\sim 10^{2}-10^{3}$ yr, far longer than fall-back accretion after a TDE. The quiescent accretion disks in QPE sources may at the present epoch be self-sustaining and fed primarily by EMRI ablation. Indeed, the observed range of secular variability broadly match those predicted for collision-fed disks. Changes in the QPE recurrence pattern following such outbursts, similar to that observed in GSN 069, could arise from temporary misalignment between the EMRI-fed disk and the SMBH equatorial plane as the former regrows its mass after a state transition.