A New Parameterization of the Star Formation Rate Dense Gas Mass Relation: Embracing Gas Density Gradients

It is well established that a gas density gradient inside molecular clouds and clumps raises their star formation rate (SFR) compared with what they would experience from a gas reservoir of uniform density. This effect should be observed in the relation between dense-gas mass Mdg and SFR of molecular clouds and clumps, with steeper gas density gradients yielding higher SFR/Mdg ratios. The content of this paper is twofold. First, we build on the notion of a magnification factor introduced by Parmentier to redefine the dense-gas relation (i.e., the relation between Mdg and SFR). Not only does the SFR/M-dg ratio depend on the mean freefall time of the gas and on its (intrinsic) star formation efficiency per freefall time, but it also depends on the clump density profile (e.g., the logarithmic slope -p of the gas density profile and on the relative extent of the constant-density region at the clump center). Second, we show that nearby molecular clouds follow the newly defined dense-gas relation, provided that their dense-gas mass is defined based on a volume density criterion. We also find the same trend for the dense molecular clouds of the Central Molecular Zone (CMZ) of the Galaxy, although this one is scaled down by a factor of 10 compared with nearby clouds, even when including the Sgr C and Sgr B2 clouds. The respective locii of both nearby and CMZ clouds in the (p, SFR M-dg) parameter space is discussed.