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Star-forming regions presenting a density gradient experience a higher starformation rate than if they were of uniform density. We refer to the ratiobetween the star formation rate of a spherical centrally-concentrated gas clumpand the star formation rate that this clump would experience if it were ofuniform density as the magnification factor $\zeta$. We map $\zeta$ as afunction of clump mass, radius, initial volume density profile and starformation time-span. For clumps with a steep density profile (i.e. power-lawslope ranging from $-3$ to $-4$, as observed in some high-density regions ofGalactic molecular clouds), we find the star formation rate to be at least anorder of magnitude higher than its top-hat equivalent. This implies that suchclumps experience faster and more efficient star formation than expected basedon their mean free-fall time. This also implies that measurements of the starformation efficiency per free-fall time of clumps based on their globalproperties, namely, mass, mean volume density and star formation rate, presentwide fluctuations. These reflect the diversity in the density profile ofstar-forming clumps, not necessarily variations in the physics of starformation. Steep density profiles inside star-cluster progenitors may beinstrumental in the formation of multiple stellar populations, such as thoseroutinely observed in old globular clusters.

The density gradient inside molecular-gas clumps as a booster of their star formation activity