Supermassive black holes with higher Eddington ratios preferentially form in gas-rich galaxies

The Eddington ratio ($\lambda_{\rm Edd}$) of supermassive black holes (SMBHs) is a fundamental parameter that governs the cosmic growth of SMBHs. Although gas mass accretion onto SMBHs is sustained when they are surrounded by large amounts of gas, little is known about the molecular content of galaxies, particularly those hosting super-Eddington SMBHs ($\lambda_{\rm Edd} > 1$: the key phase of SMBH growth). Here, we compiled reported optical and $^{12}$CO(1--0) data of local quasars to characterize their hosts. We found that higher $\lambda_{\rm Edd}$ SMBHs tend to reside in gas rich (i.e., high gas mass to stellar mass fraction = $f_{\rm gas}$) galaxies. We used two methods to make this conclusion: one uses black hole mass as a surrogate for stellar mass by assuming a local co-evolutionary relationship, and the other directly uses stellar masses estimated from near-infrared observations. The $f_{\rm gas}$--$\lambda_{\rm Edd}$ correlation we found concurs with the cosmic decreasing trend in $\lambda_{\rm Edd}$, as cold molecular gas is primarily consumed by star formation. This correlation qualitatively matches predictions of recent semi-analytic models about the cosmic downsizing of SMBHs as well. As the gas mass surface density would eventually be a key parameter controlling mass accretion, we need high-resolution observations to identify further differences in the molecular properties around super-Eddington and sub-Eddington SMBHs.