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The age distributions of stellar cluster populations have long been proposedto probe the recent formation history of the host galaxy. However, progress ishampered by the limited understanding of cluster disruption by evaporation andtidal shocks. We study the age distributions of clusters in smoothed particlehydrodynamics simulations of isolated disc galaxies, which include aself-consistent, physical model for the formation and dynamical evolution ofthe cluster population and account for the variation of cluster disruption intime and space. We show that the downward slope of the cluster age distributiondue to disruption cannot be reproduced with a single functional form, becausethe disruption rate exhibits systematic trends with cluster age (the `cruelcradle effect'). This problem is resolved by using the median cluster age totrace cluster disruption. Across 120 independent galaxy snapshots and simulatedcluster populations, we perform two-dimensional power law fits of the mediancluster age to various macroscopic physical quantities and find that it scalesas $t_{\rm med}\propto \Sigma^{-0.51\pm0.03}\sigma_{\rm1D}^{-0.85\pm0.10}M_{\rm min}^\gamma$, for the gas surface density $\Sigma$,gas velocity dispersion $\sigma_{\rm 1D}$, and minimum cluster mass $M_{\rmmin}$. This scaling accurately describes observed cluster populations andindicates disruption by impulsive tidal shocks from the interstellar medium.The term $M_{\rm min}^\gamma$ provides a model-independent way to measure themass dependence of the cluster disruption time $\gamma$. Finally, theensemble-average cluster lifetime depends on the gas density less strongly thanthe instantaneous disruption time of single clusters. These results reflect thevariation of cluster disruption in time and space. We provide quantitative waysof accounting for these physics in cluster population studies.

A tight relation between the age distributions of stellar clusters and the properties of the interstellar medium in the host galaxy