The poorly constrained cluster disruption time-scale in the Large Magellanic Cloud

We use Monte Carlo simulations, combined with homogeneously determined age and mass distributions, based on multiwavelength photometry, to constrain the cluster formation history and the rate of bound cluster disruption in the Large Magellanic Cloud (LMC) star cluster system. We evolve synthetic star cluster systems formed with a power-law initial cluster mass function (ICMF) of spectral index α = -2 assuming different cluster disruption time-scales. For each of these cluster disruption time-scales, we derive the corresponding cluster formation rate (CFR) required to reproduce the observed cluster age distribution. We then compare, in a 'Poissonian' χ² sense, model mass distributions and model two-dimensional distributions in log(mass) versus log(age) space of the detected surviving clusters to the observations. Because of the bright detection limit (M^lim_V ≃ -4.7 mag) above which the observed cluster sample is complete, one cannot constrain the characteristic cluster disruption time-scale for a 10⁴ M_⊙ cluster, t^dis₄ [where the disruption time-scale depends on cluster mass as t_dis = t^dis₄(M_cl/10⁴ M_⊙)^γ, with γ ≃ 0.62], to better than a lower limit, t^dis₄ ≥ 1 Gyr. We conclude that the CFR has been increasing steadily from 0.3 clusters Myr^-1 5 Gyr ago to a present rate of (20-30) clusters Myr^-1 for clusters spanning a mass range of ∼100-10⁷ M_⊙. For older ages, the derived CFR depends sensitively on our assumption of the underlying CMF shape. If we assume a universal Gaussian ICMF, then the CFR has increased steadily over a Hubble time from ∼1 cluster Gyr^-1 15 Gyr ago to its present value. On the other hand, if the ICMF has always been a power law with a slope close to α = -2, the CFR exhibits a minimum some 5 Gyr ago, which we tentatively identify with the well-known age gap in the LMC's cluster age distribution.