# The Relationship Between Molecular Gas Tracers and Kennicutt-Schmidt Laws

## TL;DR

This paper models how the Kennicutt-Schmidt laws depend on molecular line tracers, explaining observed correlations and predicting slope changes based on median gas densities in galaxies.

## Contribution

It introduces a simple isothermal cloud model to explain variations in star formation laws based on molecular line critical densities, aligning with observed data.

## Key findings

- High critical density lines show linear luminosity-SFR correlation.
- Low critical density lines exhibit superlinear correlation.
- Predicted slope changes in IR-line luminosity relations for dense, high-redshift galaxies.

## Abstract

We provide a model for how Kennicutt-Schmidt (KS) laws, which describe the correlation between star formation rate and gas surface or volume density, depend on the molecular line chosen to trace the gas. We show that, for lines that can be excited at low temperatures, the KS law depends on how the line critical density compares to the median density in a galaxy's star-forming molecular clouds. High critical density lines trace regions with similar physical properties across galaxy types, and this produces a linear correlation between line luminosity and star formation rate. Low critical density lines probe regions whose properties vary across galaxies, leading to a star formation rate that varies superlinearly with line luminosity. We show that a simple model in which molecular clouds are treated as isothermal and homogenous can quantitatively reproduce the observed correlations between galactic luminosities in far infrared and in the CO(1->0) and HCN(1->0) lines, and naturally explains why these correlations have different slopes. We predict that IR-line luminosity correlations should change slope for galaxies in which the median density is close to the line critical density. This prediction may be tested by observations of lines such as HCO^+(1->0) with intermediate critical densities, or by HCN(1->0) observations of intensely star-forming high redshift galaxies with very high densities. Recent observations by Gao et al. hint at just such a change in slope. We argue that deviations from linearity in the HCN(1->0)-IR correlation at high luminosity are consistent with the assumption of a constant star formation efficiency.