  Nearby spiral galaxies show an extremely tight correlation between tracers of
molecular hydrogen (H_2) in the interstellar medium (ISM) 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, H_2 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 H_2 break down, and it is unclear if the star formation rate
will then correlate with H_2 or with some other quantity. Here we show that
star formation will continue to follow H_2 independent of metallicity. This is
not because H_2 is directly important for cooling, but instead because the
transition from predominantly atomic hydrogen (HI) to H_2 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
star formation rate will correlate with total gas mass, with mass of gas where
the hydrogen is H_2, 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.
