The Evolution of Molecular Gas Fraction Traced by the CO Tully–Fisher Relation

Carbon monoxide (CO) observations show a luminosity−line width correlation that evolves with redshift. We present a method to use CO measurements alone to infer the molecular gas fraction (fmol) and constrain the CO−H2 conversion factor (αCO). We compile from the literature spatially integrated low-J CO observations of six galaxy populations, including a total of 449 galaxies between 0.01 ≤ z ≤ 3.26. The CO data of each population provide an estimate of the ${\alpha }_{\mathrm{CO}}$-normalized mean molecular gas fraction (fmol/αCO). The redshift evolution of the luminosity−line width correlation thus indicates an evolution of fmol/αCO. We use a Bayesian-based Monte Carlo Markov Chain sampler to derive the posterior probability distribution functions of fmol/αCO for these galaxy populations, accounting for random inclination angles and measurement errors in the likelihood function. We find that the molecular gas fraction evolves rapidly with redshift, ${f}_{\mathrm{mol}}\propto {(1+z)}^{\beta }$ with β ≃ 2, for both normal star-forming and starburst galaxies. Furthermore, the evolution trend agrees well with that inferred from the Kennicutt–Schmidt relation and the star-forming main sequence. Finally, at z < 0.1 normal star-forming galaxies (SFGs) require a ∼5× larger αCO than starburst galaxies to match their molecular gas fractions, but at z > 1 both star-forming types exhibit sub-Galactic αCO values and normal SFGs appear more gas rich than starbursts. Future applications of this method include calibrating Tully–Fisher relations without inclination correction and inferring the evolution of the atomic gas fraction with H i observations.