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.
