Formation of massive stars and black holes in self-gravitating AGN discs, and gravitational waves in LISA band

We propose a scenario in which massive stars form at the outer edges of an AGN accretion disc. We analyze the dynamics of a disc forming around a supermassive black hole, in which the angular momentum is transported by turbulence induced by the disc’s self-gravity. We find that once the surface density of the disc exceeds a critical value, the disc fragments into dense clumps. We argue that the clumps accrete material from the remaining disc and merge into larger clumps; the upper mass of a merged clump is a few tens to a few hundreds of solar mass. The biggest clumps collapse and form massive stars, which produce few-tens-solar-mass black holes at the end of their evolution. We construct a model of the AGN disc which includes extra heat sources from the embedded black holes. If the embedded black holes can accrete at the Bondi rate, then the feedback from accretion onto the embedded black holes may stabilize the AGN disc against the Toomre instability for an interesting range of the model parameters. By contrast, if the rate of accretion onto the embedded holes is below the Eddington limit, then the extra heating is insufficient to stabilize the disc. The embedded black holes will interact gravitationally with the massive accretion disc and be dragged towards the central black hole. Merger of a disc-born black hole with the central black hole will produce a burst of gravitational waves. If the central black hole is accreting at a rate comparable to the Eddington limit, the gas drag from the accretion disc will not alter significantly the dynamics of the final year of merger, and the gravitational waves should be observable by LISA. We argue that for a reasonable range of parameters such mergers will be detected monthly, and that the gravitational-wave signal from these mergers is distinct from that of other merger scenarios. Also, for some plausible black hole masses and accretion rates, the burst of gravitational waves should be accompanied by a detectable change in the optical luminosity of the central engine.