Star cluster formation and disruption time-scales - I. An empirical determination of the disruption time of star 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 t(dis)(yr) = t(4)(dis)(M-cl/10(4) M-.)(gamma), 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 t(4)(dis) and gamma 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 t(4)(dis) and gamma in these galaxies. The values of gamma are the same in the four galaxies within the uncertainty, and the mean value is gamma = 0.62 +/- 0.06. However, the disruption time t(4)(dis) of a cluster of 10(4) M-. is very different in the different galaxies. The clusters in the SMC have the longest disruption time, t(4)(dis) similar or equal to 8 x 10(9) yr, and the clusters at 1-3 kpc from the nucleus of M51 have the shortest disruption time of t(4)(dis) similar or equal to 4 x 10(7) yr. The disruption time of clusters 1-5 kpc from the nucleus of M33 is t(4)(dis) similar or equal to 1.3 x 10(8) yr and for clusters within 1 kpc from the Sun we find t(4)(dis) similar or equal to 1.0 x 10(9) yr.