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

The disruption rate of stars by supermassive black holes (SMBHs) is calculated numerically with a modified version of Aarseth’s nbody6 code. Equal-mass systems without primordial binaries are treated. The initial stellar distribution around the SMBH follows a Sérsic n= 4 profile representing bulges of late-type galaxies as well of early-type galaxies without central light deficits, i.e. without cores. 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 103 to 0.5 × 106 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•≈ 107 M⊙. The computed number of disrupted stars is 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) ∝Nb, where b is as large as 0.83. This is significantly steeper than the expected scaling (d N/dt) ∝ 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•–σ relation. The number of disrupted stars contributes 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 intermediate-mass black holes in globular clusters. For SMBHs similar to the galactic centre black hole Sgr A★, a tidal disruption rate of 55 ± 27 events Myr−1 is deduced. Finally relaxation-driven stellar feeding cannot account for the masses of massive black holes M•≥ 107 M⊙ in complete agreement with conventional gas accretion and feedback models.