PHIBSS: Unified Scaling Relations of Gas Depletion Time and Molecular Gas Fractions

This paper provides an update of our previous scaling relations between galaxy-integrated molecular gas masses, stellar masses, and star formation rates (SFRs), in the framework of the star formation main sequence (MS), with the main goal of testing for possible systematic effects. For this purpose our new study combines three independent methods of determining molecular gas masses from CO line fluxes, far-infrared dust spectral energy distributions, and ~1 mm dust photometry, in a large sample of 1444 star-forming galaxies between z = 0 and 4. The sample covers the stellar mass range log(M */M ⊙) = 9.0–11.8, and SFRs relative to that on the MS, δMS = SFR/SFR(MS), from 10−1.3 to 102.2. Our most important finding is that all data sets, despite the different techniques and analysis methods used, follow the same scaling trends, once method-to-method zero-point offsets are minimized and uncertainties are properly taken into account. The molecular gas depletion time t depl, defined as the ratio of molecular gas mass to SFR, scales as (1 + z)−0.6 × (δMS)−0.44 and is only weakly dependent on stellar mass. The ratio of molecular to stellar mass μ gas depends on ($1+z{)}^{2.5}\times {(\delta \mathrm{MS})}^{0.52}\times {({M}_{* })}^{-0.36}$, which tracks the evolution of the specific SFR. The redshift dependence of μ gas requires a curvature term, as may the mass dependences of t depl and μ gas. We find no or only weak correlations of t depl and μ gas with optical size R or surface density once one removes the above scalings, but we caution that optical sizes may not be appropriate for the high gas and dust columns at high z.