Stellar age spreads in clusters as imprints of cluster-parent clump densities
It has recently been suggested that high-density star clusters have stellar age distributions much narrower than that of the Orion Nebula Cluster, indicating a possible trend of narrower age distributions for denser clusters. We show this effect to likely arise from star formation being faster in gas with a higher density. We model the star formation history of molecular clumps in equilibrium by associating a star formation efficiency per free-fall time, ε{sub ff}, to their volume density profile. We focus on the case of isothermal spheres and we obtain the evolution with time of their star formation rate. Our model predicts a steady decline of the star formation rate, which we quantify with its half-life time, namely, the time needed for the star formation rate to drop to half its initial value. Given the uncertainties affecting the star formation efficiency per free-fall time, we consider two distinct values: ε{sub ff} = 0.1 and ε{sub ff} = 0.01. When ε{sub ff} = 0.1, the half-life time is of the order of the clump free-fall time, τ{sub ff}. As a result, the age distributions of stars formed in high-density clumps have smaller full-widths at half-maximum than those of stars formed in low-density clumps. When the star formation efficiency per free-fall time is 0.01, the half-life time is 10 times longer, i.e., 10 clump free-fall times. We explore what happens if the duration of star formation is shorter than 10τ{sub ff}, that is, if the half-life time of the star formation rate cannot be defined. There, we build on the invariance of the shape of the young cluster mass function to show that an anti-correlation between the clump density and the duration of star formation is expected. We therefore conclude that, regardless of whether the duration of star formation is longer than the star formation rate half-life time, denser molecular clumps yield narrower star age distributions in clusters. Published densities and stellar age spreads of young clusters and star-forming regions actually suggest that the timescale for star formation is of order 1-4τ{sub ff}. We also discuss how the age bin size and uncertainties in stellar ages affect our results. We conclude that there is no need to invoke the existence of multiple cluster formation mechanisms to explain the observed range of stellar age spreads in clusters.