A self-lensing binary massive black hole interpretation of quasi-periodic eruptions

Binary supermassive black hole (SMBH) systems result from galaxy mergers, and will eventually coalesce due to gravitational wave (GW) emission if the binary separation can be reduced to $\lesssim 0.1$ pc by other mechanisms. Here, we explore a gravitational self-lensing binary SMBH model for the sharp (duration $\sim 1$ hr), quasi-regular X-ray flares -- dubbed quasi-periodic eruptions -- recently observed from two low mass active galactic nuclei: GSN 069 and RX J1301.9+2747. In our model, the binary is observed $\sim$edge-on, such that each SMBH gravitationally lenses light from the accretion disc surrounding the other SMBH twice per orbital period. The model can reproduce the flare spacings if the current eccentricity of RX J1301.9+2747 is $\epsilon_0 \gtrsim 0.16$, implying a merger within $\sim 1000$ yrs. However, we cannot reproduce the observed flare profiles with our current calculations. Model flares with the correct amplitude are $\sim 2/5$ the observed duration, and model flares with the correct duration are $\sim 2/5$ the observed amplitude. Our modelling yields three distinct behaviours of self-lensing binary systems that can be searched for in current and future X-ray and optical time-domain surveys: i) periodic lensing flares, ii) partial eclipses (caused by occultation of the background mini-disc by the foreground mini-disc), and iii) partial eclipses with a very sharp in-eclipse lensing flare. Discovery of such features would constitute very strong evidence for the presence of a supermassive binary, and monitoring of the flare spacings will provide a measurement of periastron precession.