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

TL;DR

This paper presents a unified dynamical model explaining the different observed power laws in the Kennicutt-Schmidt star formation relation, linking gas density, galaxy structure, and star formation efficiency without requiring thresholds.

Contribution

It introduces a model that accounts for multiple KS relations through gas collapse dynamics and density probability distribution, eliminating the need for star formation thresholds.

Findings

Different KS slopes arise from gas collapse at fixed dynamical fractions.

Observed star formation efficiencies relate to dense gas fractions via the model.

Predictions include specific behaviors for failed galaxies and young molecular-rich systems.

Abstract

The Kennicutt-Schmidt (KS) relationship between the surface density of the star formation rate (SFR) and the gas surface density has three distinct power laws that may result from one model in which gas collapses at a fixed fraction of the dynamical rate. The power law slope is 1 when the observed gas has a characteristic density for detection, 1.5 for total gas when the thickness is about constant as in the main disks of galaxies, and 2 for total gas when the thickness is regulated by self-gravity and the velocity dispersion is about constant, as in the outer parts of spirals, dwarf irregulars, and giant molecular clouds. The observed scaling of the star formation efficiency (SFR per unit CO) with the dense gas fraction (HCN/CO) is derived from the KS relationship when one tracer (HCN) is on the linear part and the other (CO) is on the 1.5 part. Observations of a threshold density or column density with a constant SFR per unit gas mass above the threshold are proposed to be selection effects, as are observations of star formation in only the dense parts of clouds. The model allows a derivation of all three KS relations using the probability distribution function of density with no thresholds for star formation. Failed galaxies and systems with sub-KS SFRs are predicted to have gas that is dominated by an equilibrium warm phase where the thermal Jeans length exceeds the Toomre length. A squared relation is predicted for molecular gas-dominated young galaxies.