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, 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.
