Automated mining of the ALMA archive in the COSMOS field (A3COSMOS): II. Cold molecular gas evolution out to Redshift 6

We present new measurements of the cosmic cold molecular gas evolution out to redshift 6 based on systematic mining of the ALMA public archive in the COSMOS deep field (A3COSMOS). Our A3COSMOS dataset contains ~700 galaxies (0.3 < z < 6) with high-confidence ALMA detections in the (sub-)millimeter continuum and multi-wavelength spectral energy distributions (SEDs). Multiple gas mass calibration methods are compared and biases in band conversions (from observed ALMA wavelength to rest-frame Rayleigh-Jeans(RJ)-tail continuum) have been tested. Combining our A3COSMOS sample with ~1,000 CO-observed galaxies at 0 < z < 4 (75% at z < 0.1), we parameterize galaxies' molecular gas depletion time and molecular gas to stellar mass ratio (gas fraction) each as a function of the stellar mass, offset from the star-forming main sequence (Delta MS) and cosmic age (or redshift). Our proposed functional form provides a statistically better fit to current data (than functional forms in the literature), and implies a "downsizing" effect (i.e., more-massive galaxies evolve earlier than less-massive ones) and "mass-quenching" (gas consumption slows down with cosmic time for massive galaxies but speeds up for low-mass ones). Adopting galaxy stellar mass functions and applying our function for gas mass calculation, we for the first time infer the cosmic cold molecular gas density evolution out to redshift 6 and find agreement with CO blind surveys as well as semi-analytic modeling. These together provide a coherent picture of cold molecular gas, SFR and stellar mass evolution in galaxies across cosmic time.