Molecular gas in AzTEC/C159: a star-forming disk galaxy 1.3 Gyr after the Big Bang

We studied the molecular gas properties of AzTEC/C159, a star-forming disk galaxy at z = 4 : 567, in order to better constrain the nature of the high-redshift end of the submillimeter-selected galaxy (SMG) population. We secured (CO)-C-12 molecular line detections for the J = 2 -> 1 and J = 5 -> 4 transitions using the Karl G. Jansky Very Large Array (VLA) and the NOrthern Extended Millimeter Array (NOEMA) interferometer. The broad (FWHM similar to 750 km s(-1)) and tentative double-peaked profiles of the two (CO)-C-12 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 (CO)-C-12(2 -> 1) emission line, we derived L'(CO) = (3.4 +/- 0.6) x 10(10) Kkm s(-1) pc(2), which yields a molecular gas mass of M-H2 (alpha(CO) = 4.3) = (1. 5 +/- 0.3) x 10(11) M-circle dot and unveils a gas-rich system with mu(gas)(alpha(CO) = 4.3) equivalent to M-H2 = M-* = 3.3 +/- 0.7. The extreme star formation efficiency of AzTEC/C159, parametrized by the ratio L-IR = L'(CO) = (216 +/- 80) L-circle dot(K km s(-1) pc(2))(-1), is comparable to merger-driven starbursts such as local ultra-luminous infrared galaxies and SMGs. Likewise, the (CO)-C-12(5 -> 4)/CO(2 -> 1) line brightness temperature ratio of r(52) = 0.55 +/- 0.15 is consistent with high-excitation conditions as observed in SMGs. Based on mass budget considerations, we constrained the value for the L 0 CO -H2 mass conversion factor in AzTEC/C159, that is, alpha(CO) = 3.9(-1.3)(+2.7) M-circle dot K-1 km(-1) s pc(-2), which 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 and forms stars as efficiently as in merger-driven systems and generates high gas excitation. These results support the evolutionary connection between AzTEC/C159-like systems and massive quiescent disk galaxies at z similar to 2.