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 , \epsilon _ { 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 : \epsilon _ { ff } = 0.1 and \epsilon _ { ff } = 0.01 .
When \epsilon _ { ff } = 0.1 , the half-life time is of the order of the clump free-fall time , \tau _ { 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 10 \tau _ { ff } , that is , if the half-life time of the star formation rate can not 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 time-scale for star formation is of order 1 - 4 \tau _ { 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 .