Stellar age spreads in clusters as imprints of cluster-parent clump densities

TL;DR

This paper models star formation in molecular clumps to explain why denser clusters have narrower stellar age distributions, showing that faster star formation in high-density regions naturally produces these observed differences.

Contribution

It introduces a model linking star formation efficiency to clump density, explaining the observed age spread variations without requiring multiple formation mechanisms.

Findings

Denser clumps have shorter star formation timescales.

Star formation efficiency influences the age distribution width.

Observed age spreads align with star formation timescales of 1-4 free-fall times.

Abstract

It has recently been suggested that high-density clusters have stellar age distributions 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 (SFE) per free-fall time, \eff, to their volume density profile. Our model predicts a steady decline of the star formation rate (SFR), which we quantify with its half-life time, namely, the time needed for the SFR to drop to half its initial value. Given the uncertainties affecting the SFE per free-fall time, we consider two distinct values: 0.1 and 0.01. For isothermal spheres, \eff=0.1 leads to a half-life time of order the clump free-fall time, \tff. Therefore, 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 \eff=0.01, the half-life time is 10 times longer. We explore what happens if the star formation duration is shorter than 10\tff, that is, if the half-life time of the SFR 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 clump density and star formation duration is expected. Therefore, regardless of whether the star formation duration is longer than the SFR half-life time, denser molecular clumps yield narrower star age distributions in clusters. Published densities and stellar age spreads of young clusters actually suggest that the time-scale for star formation is of order 1-4\tff. 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.