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

Abstract

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 ($f_{\mathrm{mol}}$) and constrain the CO$-$H${}_2$ conversion factor (${\alpha }_{\mathrm{CO}}$). We compile from the literature spatially integrated low-$J$ CO observations of six galaxy populations, including a total of 449 galaxies between $0.01\le z\le 3.26$. The CO data of each population provide an estimate of the ${\alpha }_{\mathrm{CO}}$-normalized mean molecular gas fraction ($f_{\mathrm{mol}}/{\alpha }_{\mathrm{CO}}$). The redshift evolution of the luminosity$-$line-width correlation thus indicates an evolution of $f_{\mathrm{mol}}/{\alpha }_{\mathrm{CO}}$. We use a Bayesian-based Monte-Carlo Markov Chain sampler to derive the posterior probability distribution functions of $f_{\mathrm{mol}}/{\alpha }_{\mathrm{CO}}$ 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, $f_{\mathrm{mol}}\propto (1+z{)}^{\beta }$ 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 ${\alpha }_{\mathrm{CO}}$ than starburst galaxies to match their molecular gas fractions, but at $z>1$ both star-forming types exhibit sub-Galactic ${\alpha }_{\mathrm{CO}}$ 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 HI observations.

8 pages, 3 figures, 1 table. Accepted by ApJ Letters. The methodology is given in a Jupyter notebook here: https://github.com/fuhaiastro/py4astro/blob/main/emcee/IXF18.ipynb

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