Binary black holes and tori in AGN - I. Ejection of stars and merging of the binary

Observations of HST and groundbased data strongly suggest that most galaxies harbour central supermassive black holes and that most galaxies merge with others. Consequently a black hole binary emerges as the two black holes are spiraling into the center towards each other. In our work we are investigating two basic questions of our understanding of the central activity of galaxies and find that both can be answered with "yes": (1) Do the black holes actually merge? (2) And does the effect of the torque of the black hole binary on the surrounding stellar distribution help to explain the presence of the ubiquitous torus of molecular material surrounding apparently all active galactic nuclei? The first question is the topic of the present article, while the second question will be subject of a subsequent paper. Simulating the evolution of a stellar cluster in the potential of such a binary by solving the equations of the restricted three body problem we obtained the following results: provided that the cluster is about as massive as the black hole binary the two black holes coalesce after similar to 10(7) yr due to ejection of stars and finally via emission of gravitational radiation. Whether a star is ejected or not crucially depends on its angular momentum. Almost all stars whose angular momentum is twice as large as that of a star circulating around the binary in a distance corresponding to that between the black holes, stay bound to the binary. In a sequence of models where the mass of the secondary black hole increases while M-1 is fixed, a bigger fraction of stars is ejected. For a more massive binary also the cluster has to be more massive in order to allow the two black holes to coalesce. The merger then proceeds on smaller time scales. The cluster is depleted in the central region and the final distribution of stars assumes a torus-like structure, peaking at three times the initial distance of the two black holes. The relationship of the bound stars to the obscuring torus in active galactic nuclei will be investigated in a subsequent paper.