The Dependence of Star Formation Efficiency on Gas Surface Density

TL;DR

This paper argues that the observed relationships between gas surface density and star formation rate do not necessarily imply a specific density threshold, but can be explained by gravitational physics and observational techniques.

Contribution

It challenges the notion of a universal density threshold for star formation, proposing instead that observed correlations arise from gravitational collapse and measurement methods.

Findings

Steep increase in star formation rate per area with density is due to self-gravity and timescale effects.

Linear relation in massive cores aligns with dense gas tracing gravitational collapse.

Different correlations in low-mass and high-mass regions suggest measurement and physical differences.

Abstract

Studies by Lada (2010) and Heiderman (2010) have suggested that star formation mostly occurs above a threshold in gas surface density Sigma of Sigma_c = 120 Msun pc^{-2} (A_K = 0.8). Heiderman infer a threshold by combining low-mass star-forming regions, which show a steep increase in the star formation rate per unit area Sigma_SFR with increasing Sigma, and massive cores forming luminous stars which show a linear relation. We argue that these observations do not require a particular density threshold. The steep dependence of Sigma_SFR, approaching unity at protostellar core densities, is a natural result of the increasing importance of self-gravity at high densities along with the corresponding decrease in evolutionary timescales. The linear behavior of Sigma_SFR vs. Sigma in massive cores is consistent with probing dense gas in gravitational collapse, forming stars at a characteristic free-fall timescale given by the use of a particular molecular tracer. The low-mass and high-mass regions show different correlations between gas surface density and the area A spanned at that density, with A=Sigma^{-3} for low-mass regions and A=Sigma^{-1} for the massive cores; this difference, along with the use of differing techniques to measure gas surface density and star formation, suggests that connecting the low-mass regions with massive cores is problematic. We show that the approximately linear relationship between dense gas mass and stellar mass used by Lada similarly does not demand a particular threshold for star formation, and requires continuing formation of dense gas. Our results are consistent with molecular clouds forming by galactic hydrodynamic flows with subsequent gravitational collapse.