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The effect of giant molecular clouds on star clusters

We study the encounters between stars clusters and giant molecular clouds (GMCs). The effect of these encounters has previously been studied analytically for two cases: 1) head-on encounters, for which the cluster moves through the centre of the GMC and 2) distant encounters, where the encounter distance p > 3*R_n, with p the encounter parameter and R_n the radius of the GMC. We introduce an expression for the energy gain of the cluster due to GMC encounters valid for all values of p and R_n. This analytical result is confronted with results from N-body simulations and excellent agreement is found. From the simulations we find that the fractional mass loss is only 25% of the fractional energy gain. This is because stars escape with velocities much higher than the escape velocity. Based on the mass loss, we derive a disruption time for star clusters due to encounters with GMCs of the form t_dis [Gyr] = 2.0*S*(M_c/10^4 M_sun)^gamma, with S=1 for the solar neighbourhood and inversely proportional with the global GMC density and gamma=1-3lambda, with lambda the index that relates the cluster half-mass radius to the cluster mass (r_h ~ M_c^lambda). The observed shallow relation between cluster radius and mass (e.g. lambda=0.1), makes the index (gamma=0.7) similar to the index found both from observations and from simulations of clusters dissolving in tidal fields (gamma=0.62). The constant of 2.0 Gyr, which is the disruption time of a 10^4 M_sun cluster in the solar neighbourhood, is close to the value of 1.3 Gyr which was empirically determined from the age distribution of open clusters. This suggests that the combined effect of GMC encounters, stellar evolution and galactic tidal field can explain the lack of old open clusters in the solar neighbourhood.