Star cluster disruption by giant molecular clouds

We investigate encounters between giant molecular clouds (GMCs) and star clusters. We propose a single expression for the energy gain of a cluster due to an encounter with a GMC, valid for all encounter distances and GMC properties. This relation is verified with N -body simulations of cluster-GMC encounters, where the GMC is represented by a moving analytical potential. Excellent agreement is found between the simulations and the analytical work for fractional energy gains of ∆E/|E0| < 10, where |E0| is the initial total cluster energy. The fractional mass loss from the cluster scales with the fractional energy gain as (∆M/M0) = f(∆E/|E0|), where f ≃ 0.25. This is because a fraction 1 − f of the injected energy goes to the velocities of escaping stars, that are higher than the escape velocity. We therefore suggest that the disruption time of clusters, tdis, is best defined as the time needed to bring the cluster mass to zero, instead of the time needed to inject the initial cluster energy. We derive an expression for tdis based on the mass loss from the simulations, taking into account the effect of gravitational focusing by the GMC. Assuming spatially homogeneous distributions of clusters and GMCs with a relative velocity dispersion of σcn, we find that clusters loose most of their mass in relatively close encounters with high relative velocities (∼ 2 σcn). The disruption time depends on the cluster mass (Mc) and half-mass radius (rh) as tdis = 2.0S (