tokens: et al. 2017 ; Vallini et al. 2017 ), which may affect the density field of GMCs, and ultimately increase the conversion factor. Finally, we compare our inferred conversion factor with the one resulting from the best-fitting formula, X CO /( cm 2 K km s − 1 ) = 6.3 × 10 19 α CO /(M ⊙ K km s − 1 pc 2 ), obtained by Narayanan et al. ( 2012 ). They simulate the hydrodynamic evolution of both isolated and merging disc galaxies finding that . If we substitute and Z = 0.5 Z ⊙ we obtain α CO = 2.9 M ⊙ /(K km s − 1 pc 2 ) in agreement within a factor ≈2 with our results. 4.5 ALMA observability In Section 4.3 we have shown that the peak of the Althæa CO SLED coincides with the CO(7–6) line. As CO transitions with J up ≥ 6 fall in the ALMA bands from z > 6, in what follows, we use the ALMA Sensitivity Calculator to compute the observing time required to detect the CO(7–6) line from (a galaxy similar to) Althæa. The total CO(7–6) luminosity of Althæa is L CO(7-6) = 10 7.1 L ⊙ , i.e. ≈1/16 of its [C] luminosity. If we assume the line width to be equal to that of [C] observations in LBGs at z ≈ 6 − 7 ( Maiolino et al. 2015 ; Knudsen et al. 2016 ; Pentericci et al. 2016 ; Bradač et al. 2017 ), this yields a peak flux density . 8 The ALMA full-array observing time required to detect (resolve over 1/3 × FWHM) the CO(7–6) line with a signal-to-noise ratio S/N = 5 is ≈13 h (≈38 h), i.e. it would be challenging but doable within the maximum observing time ( ≤ 50 h) allowed for ALMA regular programs. This is in line with what was found by Muñoz Furlanetto ( 2013 ), which pointed out that ALMA observations of high- J CO can be performed with reasonable integration times only in those z ≈ 6 galaxies which, like Althæa, are chemically evolved ( Z Althaea > 0.1 Z ⊙ ) and UV-bright ( M UV, Althaea ≈ −22). 5 CONCLUSIONS In this paper we have studied the CO emission properties of galaxies at the end of the Reionization Epoch. First, we have developed a semi-analytical model that, given the internal density field of a GMC and the impinging FUV flux ( G 0 ) at the cloud surface, computes the CO line emission. The density PDF of the GMC is set both by turbulence (parametrized by the Mach number ) and self-gravity (parametrized by t / t ff ). The radiative transfer is performed with cloudy and includes z = 6 CMB radiation. The model takes the mean gas density n 0 , , t / t ff , G 0 as inputs, and it returns the luminosity of the first nine CO rotational transitions. We validated the model with local observations, demonstrating its capability to reproduce: the M vir - relation; the observed CO excitation in local SB galaxies; and the CO SLED of the low-metallicity ( Z ≈ 0.5 Z ⊙ ) molecular cloud N159W in the LMC. We used our validated CO emission model to post-process a cosmological zoom-in simulation of a prototypical z ≈ 6 galaxy ( M ⋆ ∼ 10 10 M ⊙ , SFR ∼ 100 M ⊙ yr − 1 ), Althæa. We have made the following additional assumptions: (i) we adopt a constant CRIR (cfr.
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