We use Monte-Carlo simulations , combined with homogeneously determined age and mass distributions based on multi-wavelength 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 \alpha = -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 ” \chi ^ { 2 } sense , model mass distributions and model two-dimensional distributions in log ( mass ) vs. log ( age ) space of the detected surviving clusters to the observations .
Because of the bright detection limit ( M _ { V } ^ { lim } \simeq - 4.7 mag ) above which the observed cluster sample is complete , one can not constrain the characteristic cluster disruption time-scale for a 10 ^ { 4 } M _ { \odot } cluster , t _ { 4 } ^ { dis } ( where the disruption time-scale depends on cluster mass as t _ { dis } = t _ { 4 } ^ { dis } ( M _ { cl } / 10 ^ { 4 } { M } _ { \odot } ) ^ { \gamma } , with \gamma \simeq 0.62 ) , to better than a lower limit , t _ { 4 } ^ { dis } \geq 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 \sim 100 - 10 ^ { 7 } M _ { \odot } .
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 \sim 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 \alpha = -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 .