Which phase of the interstellar medium correlates with the star formation rate?

Nearby spiral galaxies show an extremely tight correlation between tracers of molecular hydrogen (H₂) in the interstellar medium and tracers of recent star formation, but it is unclear whether this correlation is fundamental or accidental. In the galaxies that have been surveyed to date, H₂ resides predominantly in gravitationally bound clouds cooled by carbon monoxide (CO) molecules, but in galaxies of low metal content the correlations between bound clouds, CO, and H₂ break down, and it is unclear if the star formation rate (SFR) will then correlate with H₂ or with some other quantity. Here, we show that star formation will continue to follow H ₂ independent of metallicity. This is not because H₂ is directly important for cooling, but instead because the transition from predominantly atomic hydrogen (H I) to H₂ occurs under the same conditions as a dramatic drop in gas temperature and Bonnor-Ebert mass that destabilizes clouds and initiates collapse. We use this model to compute how SFR will correlate with total gas mass, with mass of gas where the hydrogen is H₂, and with mass of gas where the carbon is CO in galaxies of varying metallicity, and show that preliminary observations match the trend we predict.