A prescription and fast code for the long-term evolution of star clusters

TL;DR

This paper presents EMACSS, a simple, physically motivated computational model for simulating the long-term evolution of star clusters, accurately reproducing N-body simulation results with minimal computational effort.

Contribution

The paper introduces EMACSS, a new fast code for star cluster evolution based on energy flow principles, offering accurate results without complex many-body simulations.

Findings

Reproduces N-body simulation results within ~10% accuracy.

Efficiently models cluster mass and radius evolution over time.

Applicable to various initial conditions and tidal field strengths.

Abstract

We introduce the star cluster evolution code Evolve Me A Cluster of StarS (EMACSS), a simple yet physically motivated computational model that describes the evolution of some fundamental properties of star clusters in static tidal fields. We base our prescription upon the flow of energy within the cluster, which is a constant fraction of the total energy per half-mass relaxation time. According to Henon's predictions, this flow is independent of the precise mechanisms for energy production within the core, and therefore does not require a complete description of the many-body interactions therein. For a cluster of equal-mass stars, we thence use dynamical theory and analytic descriptions of escape mechanisms to construct a series of coupled differential equations expressing the time evolution of cluster mass and radius. These equations are numerically solved using a fourth-order Runge-Kutta integration kernel, and the results benchmarked against a data base of direct N-body simulations. We use simulations containing a modest initial number of stars (1024 <= N <= 65 536) and point-mass tidal fields of various strengths. Our prescription is publicly available and reproduces the N-body results to within ~10 per cent accuracy for the entire post-collapse evolution of star clusters.