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 ( f _ { mol } ) and constrain the CO - H _ { 2 } conversion factor ( \alpha _ { CO } ) .
We compile from the literature spatially integrated low- J CO observations of six galaxy populations , including a total of 449 galaxies between 0.01 \leq z \leq 3.26 .
The CO data of each population provide an estimate of the \alpha _ { CO } -normalized mean molecular gas fraction ( f _ { mol } / \alpha _ { CO } ) .
The redshift evolution of the luminosity - line-width correlation thus indicates an evolution of f _ { mol } / \alpha _ { CO } .
We use a Bayesian-based Monte-Carlo Markov Chain sampler to derive the posterior probability distribution functions of f _ { mol } / \alpha _ { CO } 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 _ { mol } \propto ( 1 + z ) ^ { \beta } with \beta \simeq 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 require a \sim 5 \times larger \alpha _ { CO } than starburst galaxies to match their molecular gas fractions , but at z > 1 both star-forming types exhibit sub-Galactic \alpha _ { CO } values and normal star-forming galaxies 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 .