Multi-mass 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 multi-mass 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 ~100 reduction in the variance in 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.

8 pages, 8 figures. Added discussion on Nbody codes updated to match published version

References in corpus (17)

• Evolution of massive binary black holes
• Rates of tidal disruption of stars by massive central black holes
• Revised Rates of Stellar Disruption in Galactic Nuclei
• A Family of Models for Spherical Stellar Systems
• Long Term Evolution of Massive Black Hole Binaries
• Efficient Merger of Binary Supermassive Black Holes in Non-Axisymmetric Galaxies
• Generating Equilibrium Dark Matter Halos: Inadequacies of the Local Maxwellian Approximation
• A Very Fast and Momentum-Conserving Tree Code
• Towards optimal softening in 3D N-body codes: I. Minimizing the force error
• Tidal disruption rates of stars in observed galaxies
• The Bar-Halo Interaction - II. Secular evolution and the religion of N-body simulations
• The Evolution of Cuspy Triaxial Galaxies Harboring Central Black Holes
• Bar-Halo Friction in Galaxies III: Halo Density Changes
• Multimass spherical structure models for N-body simulations
• Halo evolution in the presence of a disc bar
• Models of Galaxies with Central Black Holes: Simulation Methods
• Grommet: an N-body code for high-resolution simulations of individual galaxies

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