The dust-to-gas mass ratio of luminous galaxies as a function of their
  metallicity at cosmic noon
  We aim to quantify the relation between the dust-to-gas (DTG) mass ratio and
gas-phase metallicity of $z=$2.1-2.5 luminous galaxies and contrast this
high-redshift relation against analogous constraints at $z=$0. We present a
sample of 10 star-forming main-sequence galaxies in the redshift range
$2.1<z<2.5$ with rest-optical emission-line information available from the
MOSDEF survey and with ALMA 1.2 millimeter and CO J$=$3--2 follow-up
observations. The galaxies have stellar masses ranging from $10^{10.3}$ to
$10^{10.6}\,\rm{M}_\odot$ and cover a range in star-formation rate from 35 to
145 $\rm{M}_\odot\,\rm{yr}^{-1}$. We calculate the gas-phase oxygen abundance
of these galaxies from rest-optical nebular emission lines (8.4 < $12 +
\log{(\rm{O/H})} < 8.8$, corresponding to 0.5-1.25 Z$_\odot$). We estimate the
dust and H2 masses (using a metallicity dependent CO-to-H2 conversion factor)
of the galaxies from the 1.2 mm and CO J$=$3-2 observations, respectively, from
which we estimate a DTG. We find that the galaxies in this sample follow the
earlier observed trends between CO line luminosity and dust-continuum
luminosity from $z=0$ to $z=3$, extending such trends to fainter galaxies at
$2.1<z<2.5$ than observed to date. We find no second-order metallicity
dependence in the CO - dust-continuum luminosity relation for the galaxies
presented in this work. The DTG of main-sequence galaxies at $2.1<z<2.5$ are
consistent with an increase in DTG with gas-phase metallicity. Galaxies at
$z=$2.1-2.5 are furthermore consistent with the DTG-metallicity relation found
at $z=$0, providing relevant constraints for galaxy formation models. These
results furthermore imply that the metallicity of galaxies should be taken into
account when estimating cold-gas masses from dust-continuum emission,
especially relevant when studying metal-poor low-mass or high-redshift
galaxies. [abridged]
