The Molecular Gas Reservoirs of $z\sim 2$ Galaxies: A comparison of
  CO(1-0) and dust-based molecular gas masses
  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 $z\gtrsim2$.
