Reconstructing the Arches cluster – I. Constraining the initial conditions

We have performed a series of N-body simulations to model the Arches cluster. Our aim is to find the best-fitting model for the Arches cluster by comparing our simulations with observational data and to constrain the parameters for the initial conditions of the cluster. By neglecting the Galactic potential and stellar evolution, we are able to efficiently search through a large parameter space to determine, for example, the initial mass function (IMF), size and mass of the cluster. We find that the cluster's observed present-day mass function can be well explained with an initial Salpeter IMF. The lower mass limit of the IMF cannot be constrained well from our models. In our best models, the initial total mass down to a mass limit of 0.5 M⊙ is (4.9 ± 0.8) × 104 M⊙. The initial virial radius of the cluster is 0.77 ± 0.12 pc. A concentration parameter of the initial King model W0= 3 gives the best results.