A Simple Model for the Relationship Between Star Formation and Surface Density

TL;DR

This paper presents a simplified model linking star formation rate per unit area to surface density, successfully reproducing observed relations and explaining the influence of spiral potential strength on star formation distribution.

Contribution

It introduces a straightforward model that explains the linear relation between star formation rate and dense gas surface density, and analyzes the effects of spiral potential on star formation distribution.

Findings

Reproduces the observed linear relation between star formation rate and dense gas surface density.

Shows that star formation rate does not significantly depend on spiral potential strength.

Finds that stronger spiral potential leads to more star formation near spiral arms.

Abstract

We investigate the relationship between the star formation rate per unit area and the surface density of the ISM (the local Kennicutt-Schmitt law) using a simplified model of the ISM and a simple estimate of the star formation rate based on the mass of gas in bound clumps, the local dynamical timescales of the clumps, and an efficiency parameter of around 5 per cent. Despite the simplicity of the approach, we are able to reproduce the observed linear relation between star formation rate and surface density of dense (molecular) gas. We use a simple model for the dependence of H_2 fraction on total surface density to argue why neither total surface density nor the HI surface density are good local indicators of star formation rate. We also investigate the dependence of the star formation rate on the depth of the spiral potential. Our model indicates that the mean star formation rate does not depend significantly on the strength of the spiral potential, but that a stronger spiral potential, for a given mean surface density, does result in more of the star formation occurring close to the spiral arms. This agrees with the observation that grand design galaxies do not appear to show a larger degree of star formation compared to their flocculent counterparts.