Lighting the dark molecular gas: H$_{2}$ as a direct tracer
Robust knowledge of molecular gas mass is critical for understanding star formation in galaxies. The H$_{2}$ molecule does not emit efficiently in the cold interstellar medium, hence the molecular gas content of galaxies is typically inferred using indirect tracers. At low metallicity and in other extreme environments, these tracers can be subject to substantial biases. We present a new method of estimating total molecular gas mass in galaxies directly from pure mid-infrared rotational H$_{2}$ emission. By assuming a power-law distribution of H$_{2}$ rotational temperatures, we can accurately model H$_{2}$ excitation and reliably obtain warm ($T\!\gtrsim\!100$ K) H$_{2}$ gas masses by varying only the power law's slope. With sensitivities typical of Spitzer/IRS, we are able to directly probe the H$_{2}$ content via rotational emission down to ~80 K, accounting for ~15% of the total molecular gas mass in a galaxy. By extrapolating the fitted power law temperature distributions to a calibrated \emph{single} lower cutoff temperature, the model also recovers the total molecular content within a factor of ~2.2 in a diverse sample of galaxies, and a subset of broken power law models performs similarly well. In ULIRGs, the fraction of warm H$_{2}$ gas rises with dust temperature, with some dependency on $\alpha_\mathrm{CO}$. In a sample of five low metallicity galaxies ranging down to 12+log[O/H]=7.8, the model yields molecular masses up to ~100 times larger than implied by CO, in good agreement with other methods based on dust mass and star formation depletion timescale. This technique offers real promise for assessing molecular content in the early universe where CO and dust-based methods may fail.