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

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, that 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, ω 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 halfmass radius towards small radii is present for clusters that 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 modelling an observed cluster's evolution.