Dynamics of a superdense cluster of black holes and the formation of the Galactic supermassive black hole

The centre of our Galaxy is known to host a massive compact object, Sgr A∗, which is commonly considered as a supermassive black hole of ${sim} 4 imes 106 , ext{${ m M}{odot } , $}$. It is surrounded by a dense and massive nuclear star cluster, with a half-mass radius of about 5 pc and a mass larger than $10{7} , ext{${ m M}{odot } , $}$. In this paper, we studied the evolutionary fate of a very dense cluster of intermediate-mass black holes, possible remnants of the dissipative orbital evolution of massive globular cluster hosts. We performed a set of high-precision N-body simulations taking into account deviations from pure Newtonian gravitational interaction via a post-Newtonian development up to 2.5 order, which is the one accounting for energy released by gravitational wave emission. The violent dynamics of the system leads to various successive merger events to grow a single object containing ∼25 per cent of the total cluster mass before partial dispersal of the cluster, and to generate, in different bursts, a significant quantity of gravitational wave emission. If generalized, the present results suggest a mechanism of mass growth up to the scale of a supermassive black hole.