Combined CO & Dust Scaling Relations of Depletion Time and Molecular Gas
  Fractions with Cosmic Time, Specific Star Formation Rate and Stellar Mass
  We combine molecular gas masses inferred from CO emission in 500 star forming
galaxies (SFGs) between z=0 and 3, from the IRAM-COLDGASS, PHIBSS1/2 and other
surveys, with gas masses derived from Herschel far-IR dust measurements in 512
galaxy stacks over the same stellar mass/redshift range. We constrain the
scaling relations of molecular gas depletion time scale (tdepl) and gas to
stellar mass ratio (Mmolgas/M*) of SFGs near the star formation main-sequence
with redshift, specific star formation rate (sSFR) and stellar mass (M*). The
CO- and dust-based scaling relations agree remarkably well. This suggests that
the CO-H2 mass conversion factor varies little within 0.6dex of the main
sequence (sSFR(ms,z,M*)), and less than 0.3dex throughout this redshift range.
This study builds on and strengthens the results of earlier work. We find that
tdepl scales as (1+z)^-0.3 *(sSFR/sSFR(ms,z,M*))^-0.5, with little dependence
on M*. The resulting steep redshift dependence of Mmolgas/M* ~(1+z)^3 mirrors
that of the sSFR and probably reflects the gas supply rate. The decreasing gas
fractions at high M* are driven by the flattening of the SFR-M* relation.
Throughout the redshift range probed a larger sSFR at constant M* is due to a
combination of an increasing gas fraction and a decreasing depletion time
scale. As a result galaxy integrated samples of the Mmolgas-SFR rate relation
exhibit a super-linear slope, which increases with the range of sSFR. With
these new relations it is now possible to determine Mmolgas with an accuracy of
0.1dex in relative terms, and 0.2dex including systematic uncertainties.
