The Molecular Gas Reservoirs of $z\sim 2$ Galaxies: A comparison of CO(1-0) and dust-based molecular gas masses

Abstract: We test the use of long-wavelength dust continuum emission as a molecular gas tracer at high redshift, via a unique sample of 12, z~2 galaxies with observations of both the dust continuum and CO(1-0) line emission (obtained with the Atacama Large Millimeter Array and Karl G. Jansky Very Large Array, respectively). Our work is motivated by recent, high redshift studies that measure molecular gas masses (\ensuremath{\rm{M}{\rm{mol}}}) via a calibration of the rest-frame $850\mu$m luminosity ($L\mathrm{850\mu m,rest}$) against the CO(1-0)-derived \ensuremath{\rm{M}{\rm{mol}}}\ of star-forming galaxies. We hereby test whether this method is valid for the types of high-redshift, star-forming galaxies to which it has been applied. We recover a clear correlation between the rest-frame $850\mu$m luminosity, inferred from the single-band, long-wavelength flux, and the CO(1-0) line luminosity, consistent with the samples used to perform the $850\mu$m calibration. The molecular gas masses, derived from $L\mathrm{850\mu m,rest}$, agree to within a factor of two with those derived from CO(1-0). We show that this factor of two uncertainty can arise from the values of the dust emissivity index and temperature that need to be assumed in order to extrapolate from the observed frequency to the rest-frame at 850$\mathrm{\mu m}$. The extrapolation to 850$\mathrm{\mu m}$ therefore has a smaller effect on the accuracy of \Mmol\ derived via single-band dust-continuum observations than the assumed CO(1-0)-to-\ensuremath{\rm{M}_{\rm{mol}}}\ conversion factor. We therefore conclude that single-band observations of long-wavelength dust emission can be used to reliably constrain the molecular gas masses of massive, star-forming galaxies at $z\gtrsim2$.