The disruption time of clusters in selected regions of four galaxies

If the cluster formation rate is constant and the disruption time of clusters depends on their initial mass as t_dis= t_4 x (M_i/10^4 Msun)^gamma, where M_i is the initial mass of a cluster, t_4 is the disruption time of a cluster of M_i=10^4 Msun and gamma is an exponent, then the values of t_4 and gamma can be derived in a very simple way from the age and mass histograms of large homogeneous samples of clusters with reliable age and/or mass determinations. We demonstrate the method and derive the values of t_4 and gamma from cluster samples in selected fields of four galaxies: M51, M33, SMC and the solar neighbourhood. The values of the exponent gamma are the same within their uncertainties in the four galaxies with gamma = 0.62 +- 0.06. However, the disruption time t_4 of clusters of 10^4 Msun is very different in the different locations. It is shortest in the inner region of M51 (t_4 = 40 Myr) and highest in the SMC (t_4=8 Gyr).