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 compared to what they would
experience from a gas reservoir of uniform density. This effect should be
observed in the relation between dense-gas mass $M_{dg}$ and star formation
rate $SFR$ of molecular clouds and clumps, with steeper gas density gradients
yielding higher $SFR/M_{dg}$ ratios. The content of this paper is two-fold.
Firstly, we build on the notion of magnification factor introduced by
Parmentier (2019) to redefine the dense-gas relation (i.e. the relation between
$M_{dg}$ and $SFR$). Not only does the $SFR/M_{dg}$ ratio depend on the mean
free-fall time of the gas and on its (intrinsic) star formation efficiency per
free-fall time, it also depends on the logarithmic slope $-p$ of the gas
density profile and on the relative extent of the constant-density region at
the clump center. Secondly, 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 to nearby clouds. The
respective locii of both nearby and CMZ clouds in the $(p, SFR/M_{dg})$
parameter space is discussed.
