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. The biggest clumps collapse and form massive stars, which produce few-tens-solar-mass black holes at the end of their evolution. 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.