Star cluster formation and disruption time-scales: l. Emperical determination of the disruption time of clusters in four galaxies

We have derived the disruption times of star clusters from cluster samples of four galaxies, M51, M33, the Small Magellanic Cloud (SMC) and the solar neighbourhood. If the disruption time of clusters in a galaxy depends only on their initial mass as tdis(yr) =t4dis(Mcl/104 M⊙)γ, and if the cluster formation rate is constant, then the mass and age distributions of the observed clusters will each be given by double power-law relations. For clusters of low mass or young age the power law depends on the fading of the clusters below the detection limit due to the evolution of the stars. For clusters of high mass and old age the power law depends on the disruption time of the clusters. The samples of clusters in M51 and M33, observed with HST-WFPC2, indeed show the predicted double power-law relations in both their mass and age distributions. The values of tdis4 and γ can be derived from these relations. For the cluster samples of the SMC and the solar neighbourhood, taken from the literature, only the age distribution is known. This also shows the characteristic double power-law behaviour, which allows the determination of t4dis and γ in these galaxies. The values of γ are the same in the four galaxies within the uncertainty, and the mean value is γ= 0.62 ± 0.06. However, the disruption time t4dis of a cluster of 104 M⊙ is very different in the different galaxies. The clusters in the SMC have the longest disruption time, t4dis≃ 8 × 109 yr, and the clusters at 1–3 kpc from the nucleus of M51 have the shortest disruption time of t4dis≃ 4 × 107 yr. The disruption time of clusters 1–5 kpc from the nucleus of M33 is t4dis≃ 1.3 × 108 yr and for clusters within 1 kpc from the Sun we find t4dis≃ 1.0 × 109 yr.