Multimass schemes for collisionless N-body simulations

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.