Multimass schemes for collisionless N-body simulations

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 similar to 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.