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

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, 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 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.