The density gradient inside molecular-gas clumps as a booster of their
  star formation activity
  Star-forming regions presenting a density gradient experience a higher star
formation rate than if they were of uniform density. We refer to the ratio
between the star formation rate of a spherical centrally-concentrated gas clump
and the star formation rate that this clump would experience if it were of
uniform density as the magnification factor $\zeta$. We map $\zeta$ as a
function of clump mass, radius, initial volume density profile and star
formation time-span. For clumps with a steep density profile (i.e. power-law
slope ranging from $-3$ to $-4$, as observed in some high-density regions of
Galactic molecular clouds), we find the star formation rate to be at least an
order of magnitude higher than its top-hat equivalent. This implies that such
clumps experience faster and more efficient star formation than expected based
on their mean free-fall time. This also implies that measurements of the star
formation efficiency per free-fall time of clumps based on their global
properties, namely, mass, mean volume density and star formation rate, present
wide fluctuations. These reflect the diversity in the density profile of
star-forming clumps, not necessarily variations in the physics of star
formation. Steep density profiles inside star-cluster progenitors may be
instrumental in the formation of multiple stellar populations, such as those
routinely observed in old globular clusters.
