The Dense-gas Mass versus Star Formation Rate Relation: A Misleading Linearity?

Abstract

We model the star formation relation of molecular clumps in dependence of their dense-gas mass when their volume density profile is that of an isothermal sphere, i.e. ρ clump (r) ∝ r −2 . Dense gas is defined as gas whose volume density is higher than a threshold ρ th = 700 M ⊙ · pc −3 , i.e. HCN(1-0)-mapped gas. We divide the clump into two regions: a dense inner region (where ρ clump (r) ≥ ρ th ), and low-density outskirts (where ρ clump (r) < ρ th ). We find that the total star formation rate of clumps scales linearly with the mass of their dense inner region, even when more than half of the clump star formation activity takes place in the low-density outskirts. We therefore emphasize that a linear star formation relation does not necessarily imply that star formation takes place exclusively in the gas whose mass is given by the star formation relation. The linearity of the star formation relation is strengthened when we account for the mass of dense fragments (e.g. cores, fibers) seeding star formation in the low-density outskirts, and which our adopted clump density profile ρ clump (r) does not resolve. We also find that the star formation relation is significantly tighter when considering the dense gas than when considering all the clump gas, as observed for molecular clouds of the Galactic plane. When the clumps have no low-density outskirts (i.e. they consist of dense gas only), the star formation relation becomes superlinear and progressively wider.

The Density Gradient Inside Molecular-gas Clumps as a Booster of Their Star Formation Activity

“…(ii) it is unclear which fraction of their YSOs clouds actually form in their dense gas as the existence of a gas density threshold for star formation remains debated (Parmentier 2016(Parmentier , 2017Elmegreen 2018); (iii) p is unknown in the number density regime beyond the resolution limit of the observations, i.e. > 5 · 10 4 cm −3 (Kainulainen et al 2014); (iv) the observed YSO census measures the past star formation history and, therefore, results from the cloud and clump structures prevailing before the time t of the observations; presentlyobserved structures, as quantified by the observed steepness p, drive the present and forthcoming star formation rate.…”

On the Appearance of Thresholds in the Dynamical Model of Star Formation

“…Molecular clouds appear to be composed of numerous filaments (André et al 2010;Molinari et al 2010) and it might be that collisions between these filaments trigger local star formation (Myers 2009;Schneider et al 2012). Parmentier (2017) considered the cloud KS law with filamentary extensions to large radius. The density PDF for filamentary structure has been considered by Myers (2015).…”

“…2.5), and a cloud area that varies inversely with surface density. Parmentier (2017) explained the apparently constant star formation rate per unit dense gas mass inside molecular clouds by showing that the total rate integrated over a cloud with an isothermal density profile is proportional to the dense mass in the core of the cloud, even though a significant fraction of the stars form outside the core without an actual density threshold. She also found, for a fixed cloud radius, that the SFR transitions from a linear dense mass proportionality when the density at the edge of the cloud is less than the threshold for molecule detection, to a 1.5 power of dense gas mass at a higher mass because of the extra square root dependence on density for the collapse rate.…”