A Hybrid N-Body Code Incorporating Algorithmic Regularization and Post-Newtonian Forces

TL;DR

This paper introduces a hybrid N-body simulation code that combines algorithmic regularization and post-Newtonian corrections, enabling precise and efficient modeling of star dynamics near massive black holes in galactic centers.

Contribution

The novel code integrates chain regularization with post-Newtonian terms and a fourth-order integrator, improving accuracy and performance in simulating black hole environments.

Findings

Enhanced energy conservation compared to standard schemes

Accurate reproduction of star orbits near black holes

Successful application to black hole inspiral and stellar orbit studies

Abstract

We describe a novel N-body code designed for simulations of the central regions of galaxies containing massive black holes. The code incorporates Mikkola's 'algorithmic' chain regularization scheme including post-Newtonian terms up to PN2.5 order. Stars moving beyond the chain are advanced using a fourth-order integrator with forces computed on a GRAPE board. Performance tests confirm that the hybrid code achieves better energy conservation, in less elapsed time, than the standard scheme and that it reproduces the orbits of stars tightly bound to the black hole with high precision. The hybrid code is applied to two sample problems: the effect of finite-N gravitational fluctuations on the orbits of the S-stars; and inspiral of an intermediate-mass black hole into the galactic center.