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 ∝ 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 ∝ 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 ∝ M_cl^0.62 for clusters in the mass range of about 10³ to 10⁶ M_⊙, 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 ∝ r_{hmo_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/10⁴ M_⊙)^0.62 (r_hmoamb / M_⊙ pc^-3)^-0.5 where M_cl is the initial mass of the cluster and C_env ≃ 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.