# The dense-gas mass versus star formation rate relation: a misleading linearity?

## TL;DR

This study models the star formation relation in molecular clumps with an isothermal sphere density profile, revealing that a linear relation between dense gas mass and star formation rate can be misleading, as star formation also occurs in low-density outskirts.

## Contribution

It demonstrates that the linear star formation relation does not imply exclusive star formation in dense gas and highlights the importance of considering dense fragments and outskirts.

## Key findings

- Star formation rate scales linearly with dense inner region mass.
- Linearity persists even with significant star formation in low-density outskirts.
- Star formation relation is tighter when considering only dense gas.

## 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. $\rho_{clump}(r) \propto r^{-2}$. Dense gas is defined as gas whose volume density is higher than a threshold $\rho_{th}=700\,M_{\odot}.pc^{-3}$, i.e. HCN(1-0)-mapped gas. We divide the clump into two regions: a dense inner region (where $\rho_{clump}(r) \geq \rho_{th}$), and low-density outskirts (where $\rho_{clump}(r) < \rho_{th}$). 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 $\rho_{clump}(r)$ 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.