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 Atacama Large Millimeter/submillimeter Array (ALMA) public archive in the COSMOS deep field (A(3)COSMOS). Our A(3)COSMOS data set contains similar to 700 galaxies (0.3 less than or similar to z less than or similar to 6) with high-confidence ALMA detections in the (sub)millimeter continuum and multiwavelength spectral energy distributions. Multiple gas mass calibration methods are compared, and biases in band conversions (from observed ALMA wavelength to restframe Rayleigh-Jeans tail continuum) have been tested. Combining our A(3)COSMOS sample with similar to 1000 CO-observed galaxies at 0 less than or similar to z less than or similar to 4 (75% at z < 0.1), we parameterize galaxies' molecular gas depletion time (tau(depl)) and molecular gas to stellar mass ratio (mu(molgas)) each as a function of the stellar mass (M*), offset from the starforming 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 mu(molgas) 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 semianalytic modeling. These together provide a coherent picture of cold molecular gas, star formation rate, and stellar mass evolution in galaxies across cosmic time.