Disruption time scales of star clusters in different galaxies

The observed average lifetime of the population of star clusters in the Solar Neighbourhood, the Small Magellanic Cloud and in selected regions of M 51 and M 33 is compared with simple theoretical predictions and with the results of N-body simulations. The empirically derived lifetimes ( or disruption times) of star clusters depend on their initial mass as t(dis)(emp) proportional to M-cl(0.60) in all four galaxies. N-body simulations have shown that the predicted disruption time of clusters in a tidal field scales as t(dis)(pred) proportional to t(rh)(0.75)t(cr)(0.25), where t(rh) is the initial half-mass relaxation time and t(cr) is the crossing time for a cluster in equilibrium. We show that this can be approximated accurately by t(dis)(pred) proportional to M-cl(0.62) for clusters in the mass range of about 10(3) to 10(6) M-circle dot, in excellent agreement with the observations. Observations of clusters in different extragalactic environments show that t(dis) also depends on the ambient density in the galaxies where the clusters reside. Linear analysis predicts that the disruption time will depend on the ambient density of the cluster environment as t(dis) proportional to rho(amb)(-1/2). This relation is consistent with N-body simulations. The empirically derived disruption times of clusters in the Solar Neighbourhood, in the SMC and in M 33 agree with these predictions. The best fitting expression for the disruption time is t(dis) = C-env(M-cl/10(4) M-circle dot)(0.62)(rho(amb)/M-circle dot pc(-3))(-0.5) where M-cl is the initial mass of the cluster and C-env similar or equal to 300-800 Myr. The disruption times of star clusters in M 51 within 1-5 kpc from the nucleus, is shorter than predicted by about an order of magnitude. This discrepancy might be due to the strong tidal field variations in M 51, caused by the strong density contrast between the spiral arms and interarm regions, or to the disruptive forces from giant molecular clouds.