Million-Body Star Cluster Simulations: Comparisons between Monte Carlo and Direct $N$-body

TL;DR

This study compares million-body globular cluster simulations using Monte Carlo and direct N-body methods, finding excellent agreement and confirming black hole retention in old clusters, validating the faster Monte Carlo approach.

Contribution

First detailed comparison showing Monte Carlo and direct N-body simulations produce consistent results for million-body globular clusters with realistic physics.

Findings

Both models retain large numbers of stellar-mass black holes for 12 Gyr.

Monte Carlo simulations are capable of accurately modeling long-term cluster evolution.

Minor differences are due to small-N dynamics, but overall agreement is very high.

Abstract

We present the first detailed comparison between million-body globular cluster simulations computed with a H\'enon-type Monte Carlo code, CMC, and a direct $N$-body code, NBODY6++GPU. Both simulations start from an identical cluster model with $10^6$ particles, and include all of the relevant physics needed to treat the system in a highly realistic way. With the two codes "frozen" (no fine-tuning of any free parameters or internal algorithms of the codes) we find excellent agreement in the overall evolution of the two models. Furthermore, we find that in both models, large numbers of stellar-mass black holes (> 1000) are retained for 12 Gyr. Thus, the very accurate direct $N$-body approach confirms recent predictions that black holes can be retained in present-day, old globular clusters. We find only minor disagreements between the two models and attribute these to the small-$N$ dynamics driving the evolution of the cluster core for which the Monte Carlo assumptions are less ideal. Based on the overwhelming general agreement between the two models computed using these vastly different techniques, we conclude that our Monte Carlo approach, which is more approximate, but dramatically faster compared to the direct $N$-body, is capable of producing a very accurate description of the long-term evolution of massive globular clusters even when the clusters contain large populations of stellar-mass black holes.