The initial conditions of observed star clusters - I. Method description and validation

TL;DR

This paper introduces and validates a method combining a star cluster evolution code with MCMC to estimate probable initial conditions of observed star clusters, aligning well with detailed N-body simulations.

Contribution

The paper presents a validated, efficient method to determine initial cluster conditions using coupled evolution and MCMC techniques, suitable for modeling observed star clusters' evolution.

Findings

Method accurately reproduces initial conditions for various clusters.

Distribution morphology correlates with cluster dynamical age.

Degeneracy in initial half-mass radius for core-collapsed clusters.

Abstract

We have coupled a fast, parametrized star cluster evolution code to a Markov Chain Monte Carlo code to determine the distribution of probable initial conditions of observed star clusters, which may serve as a starting point for future $N$-body calculations. In this paper we validate our method by applying it to a set of star clusters which have been studied in detail numerically with $N$-body simulations and Monte Carlo methods: the Galactic globular clusters M4, 47 Tucanae, NGC 6397, M22, $\omega$ Centauri, Palomar 14 and Palomar 4, the Galactic open cluster M67, and the M31 globular cluster G1. For each cluster we derive a distribution of initial conditions that, after evolution up to the cluster's current age, evolves to the currently observed conditions. We find that there is a connection between the morphology of the distribution of initial conditions and the dynamical age of a cluster and that a degeneracy in the initial half-mass radius towards small radii is present for clusters which have undergone a core collapse during their evolution. We find that the results of our method are in agreement with $N$-body and Monte Carlo studies for the majority of clusters. We conclude that our method is able to find reliable posteriors for the determined initial mass and half-mass radius for observed star clusters, and thus forms an suitable starting point for modeling an observed cluster\rq{}s evolution.