Tidal disruption rate of stars by supermassive black holes obtained by direct N-body simulations

Abstract: The disruption rate of stars by supermassive black holes (SMBHs) is calculated numerically with a modified version of Aarseth's NBODY6 code. The initial stellar distribution around the SMBH follows a S\'{e}rsic n=4 profile representing bulges and early type galaxies. In order to infer relaxation driven effects and to increase the statistical significance, a very large set of N-body integrations with different particle numbers N, ranging from 10^{3} to 0.5 \cdot 10^{6} particles, is performed. Three different black hole capture radii are taken into account, enabling us to scale these results to a broad range of astrophysical systems with relaxation times shorter than one Hubble time, i.e. for SMBHs up to M_bh \approx 10^{7} M_sun. The computed number of disrupted stars are driven by diffusion in angular momentum space into the loss cone of the black hole and the rate scales with the total number of particles as dN/dt \propto N^{b}, where b is as large as 0.83. This is significantly steeper than the expected scaling dN/dt \propto ln(N) derived from simplest energy relaxation arguments. Only a relatively modest dependence of the tidal disruption rate on the mass of the SMBH is found and we discuss our results in the context of the M_bh/sigma relation. The number of disrupted stars contribute a significant part to the mass growth of black holes in the lower mass range as long as a significant part of the stellar mass becomes swallowed by the SMBH. This also bears direct consequences for the search and existence of IMBHs in globular clusters. For SMBHs similar to the galactic center black hole SgrA*, a tidal disruption rate of 55 \pm 27 events per Myr is deduced. Finally relaxation driven stellar feeding can not account for the masses of massive black holes M_bh \geq 10^{7} M_sun. (abridged)