John Magorrian

Abstract:

We present a general scheme for constructing Monte Carlo realizations of equilibrium, collisionless galaxy models with known distribution function (DF) f 0. Our method uses importance sampling to find the sampling DF f s that minimizes the mean-square formal errors in a given set of projections of the DF f 0. The result is a multimass N-body realization of the galaxy model in which 'interesting' regions of phase space are densely populated by lots of low-mass particles, increasing the effective N there, and less interesting regions by fewer, higher mass particles. As a simple application, we consider the case of minimizing the shot noise in estimates of the acceleration field for an N-body model of a spherical Hernquist model. Models constructed using our scheme easily yield a factor of ~100 reduction in the variance at the central acceleration field when compared to a traditional equal-mass model with the same number of particles. When evolving both models with a real N-body code, the diffusion coefficients in our model are reduced by a similar factor. Therefore, for certain types of problems, our scheme is a practical method for reducing the two-body relaxation effects, thereby bringing the N-body simulations closer to the collisionless ideal. © 2008 The Author. Journal compilation © 2008 RAS.

Abstract:

Supermassive black hole binaries (SMBHBs) are expected by the hierarchical galaxy formation model in ACDM cosmology. There is some evidence in the literature for SMBHBs in active galactic nuclei, but there are few observational constraints on the evolution of SMBHBs in inactive galaxies and gas-poor mergers. On the theoretical front, it is unclear how long is needed for a SMBHB in a typical galaxy to coalesce. In this paper we investigate the tidal interaction between stars and binary black holes (BHs) and calculate the tidal disruption rates of stellar objects by the BH components of the binary. We derive the interaction cross sections between SMBHBs and stars from intensive numerical scattering experiments with particle number ∼ 107 and calculate the tidal disruption rates by both single and binary BHs for a sample of realistic galaxy models, taking into account the general relativistic effects and the loss-cone refilling because of two-body interaction. We estimate the frequency of tidal flares for different types of galaxies using the BH mass function in the literature. We find that because of the three-body slingshot effect, the tidal disruption rate in the SMBHB system is more than 1 order of magnitude smaller than that in a single super-massive black hole (SMBH) system. The difference is more significant in less massive galaxies and does not depend on detailed stellar dynamical processes. Our calculations suggest that comparisons of the calculated tidal disruption rates for both single and binary BHs and the surveys of X-ray or UV flares at galactic centers could tell us whether most SMBHs in nearby galaxies are single and whether the SMBHBs formed in gas-poor galaxy mergers coalesce rapidly. © 2008. The American Astronomical Society. All rights reserved.