Big Three Dragons. III: A Study of Molecular Gas in a Bright Lyman-Break
  Galaxy at $z=7.15$ with ALMA
  We report ALMA Band 3 observations of CO(6-5), CO(7-6) and [CI](2-1) in
B14-65666 ("Big Three Dragons"), one of the brightest Lyman-Break Galaxies at
$z>7$ in the rest-frame ultraviolet continuum, far-infrared continuum, and
emission lines of [OIII] 88 $\mu$m and [CII] 158 $\mu$m. None of CO(6-5),
CO(7-6) and [CI](2-1) are detected, whose $3\sigma$ upper limits on the
luminosities are about 50 times fainter than the [CII] luminosity. Based on
three methods of i) [CII] luminosity and a [CII]-to-H$_{2}$ conversion factor
reported in local metal-poor dwarf galaxies, ii) a dust mass and
metallicity-dependent dust-to-gas mass ratio, and iii) a dynamical mass
estimate, we obtain the molecular gas mass ($M_{\rm mol}$) to be
$(0.05-11)\times10^{10} M_{\rm \odot}$, which is consistent with its upper
limit inferred from the non-detection of mid-$J$ CO and [CI](2-1). Albeit with
large uncertainty in $M_{\rm mol}$, we estimate a high molecular gas-to-stellar
mass ratio ($\mu_{\rm gas}$) of $0.65-140$ and a short gas depletion time
($t_{\rm dep}$) of $2.5-550$ Myr, which are broadly consistent with
extrapolations of $\mu_{\rm gas}$ and $t_{\rm dep}$ as functions of redshift,
specific-star formation rate, and stellar mass as reported in previous studies.
The short $t_{\rm dep}$ partly reflects the starburst nature of the target,
likely to be induced by a major-merger event. B14-65666 can be an ancestor of a
passive galaxy at $z\gtrsim4$ if no gas is fueled from outside the galaxy.
Overall, our observations highlight difficulty in obtaining robust conclusion
from mid-$J$ CO alone particularly in the epoch of reionization, and motivate
studies that use other tracers as an alternative gas mass tracer.
