QPEs from impacts between the secondary and a rigidly precessing accretion disc in an EMRI system

X-ray quasi-periodic eruptions (QPEs) represent a recently discovered example of extreme X-ray variability associated with supermassive black holes. Those are high amplitude bursts recurring every few hours and detected in the soft X-ray band from the nuclei of nearby galaxies whose optical spectra lack the broad emission lines typically observed in unobscured active galaxies. The physical origin of this new X-ray variability phenomenon is still unknown, and several theoretical models have been presented. However, no attempt has been made so far to account for the varying QPE recurrence time and luminosity in individual sources, nor for the diversity of the QPE phenomenology in the different known erupters. We present a semi-analytical model based on an Extreme Mass Ratio Inspiral (EMRI) system where the secondary intersects, along its orbit, a rigidly precessing accretion disc surrounding the primary. We assume QPEs to be due to emission from an adiabatically expanding, initially optically thick gas cloud expelled from the disc plane at each impact. We produce synthetic X-ray light curves that are compared with X-ray data from four QPE sources: GSN 069, eRO-QPE1, eRO-QPE2 and RX J1301.9+2747. Our model reproduces the diversity of QPE properties between the considered objects well, and is also able to account naturally for the varying QPE amplitudes and recurrence times in individual sources. Future implementations will enable us to refine the match with the data, and to estimate precisely the system parameters making also use of multi-epoch QPE data. We briefly discuss the nature of the secondary object as well as possible implications of our findings for the EMRI population at large.