Molecular gas in AzTEC/C159: a star-forming disk galaxy 1.3Gyr after the
  Big Bang
  We studied the molecular gas properties of AzTEC/C159, a star-forming disk
galaxy at $z=4.567$. We secured $^{12}$CO molecular line detections for the
$J=2\to1$ and $J=5\to4$ transitions using the Karl G. Jansky VLA and the NOEMA
interferometer. The broad (FWHM$\sim750\,{\rm km\,s}^{-1}$) and tentative
double-peaked profiles of both $^{12}$CO lines are consistent with an extended
molecular gas reservoir, which is distributed in a rotating disk as previously
revealed from [CII] 158$\mu$m line observations. Based on the
$^{12}$CO(2$\to$1) emission line we derived
$L'_{\rm{CO}}=(3.4\pm0.6)\times10^{10}{\rm \,K\,km\,s}^{-1}{\rm \,pc}^{2}$,
that yields a molecular gas mass of $M_{\rm H_2 }(\alpha_{\rm
CO}/4.3)=(1.5\pm0.3)\times 10^{11}{\rm M}_\odot$ and unveils a gas-rich system
with $\mu_{\rm gas}(\alpha_{\rm CO}/4.3)\equiv M_{\rm H_2}/M_\star=3.3\pm0.7$.
The extreme star formation efficiency (SFE) of AzTEC/C159, parametrized by the
ratio $L_{\rm{IR}}/L'_{\rm{CO}}=(216\pm80)\, {\rm L}_{\odot}{\rm
\,(K\,km\,s}^{-1}{\rm \,pc}^{2})^{-1}$, is comparable to merger-driven
starbursts such as local ultra-luminous infrared galaxies (ULIRGs) and SMGs.
Likewise, the $^{12}$CO(5$\to$4)/CO(2$\to$1) line brightness temperature ratio
of $r_{52}= 0.55\pm 0.15$ is consistent with high excitation conditions,
similar to that observed in SMGs. We constrained the value for the
$L'_{\text{CO}}-{\rm H}_2$ mass conversion factor in AzTEC/C159, i.e.
$\alpha_{\text{CO}}=3.9^{+2.7}_{-1.3}{\rm \,M}_{\odot}{\rm \,K}^{-1}{\rm
\,km}^{-1}{\rm \,s\,pc}^{-2}$, that is consistent with a self-gravitating
molecular gas distribution as observed in local star-forming disk galaxies.
Cold gas streams from cosmological filaments might be fueling a gravitationally
unstable gas-rich disk in AzTEC/C159, which breaks into giant clumps forming
stars as efficiently as in merger-driven systems and generate high gas
excitation.
