Star Cluster Formation and Disruption Time-Scales -- I. An empirical determination of the disruption time of star clusters in four galaxies

We present a new method to derive the cluster disruption time in selected regions of galaxies from the mass or age distribution of magnitude-limited cluster samples. If the disruption time of clusters in a region of a galaxy depends on their initial mass as t_4 x (M_cluster/10^4 M_sun)^gamma and if the cluster formation rate is constant, then the mass and age distributions of the observed clusters will each show two powerlaw relations. The values of t_4 and gamma can be derived from these relations. We used this method to derive the cluster disruption time in specific regions in four galaxies: the inner region of M51, a region of M33, the SMC and the solar neighbourhood. 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 of a cluster of 10^4 M_sun is very different in the different galaxies. The clusters in the SMC have the longest disruption time, t_4 = 8 Gyr, and the clusters at 1 to 3 kpc from the nucleus of M51 have the shortest disruption time of t_4 = 0.04 Gyr. The disruption time of clusters 1 to 5 kpc from the nucleus of M33 is t_4 = 0.13 Gyr and for clusters within 1 kpc from the Sun we find t_4 = 1.0 Gyr