The ratio of CO to total gas mass in high-Redshift galaxies

Walter et al. have recently identified the J = 6 - 5, 5 - 4, and 2 - 1 CO rotational emission lines, and [C II] fine-structure emission line from the star-forming interstellar medium (ISM) in the high-redshift submillimetre source HDF 850.1, at z = 5.183. We employ large velocity gradient (LVG) modelling to analyse the spectra of this source assuming the [C_II] and CO emissions originate from (i) separate virialized regions, (ii) separate unvirialized regions, (iii) uniformly mixed virialized regions and (iv) uniformly mixed unvirialized regions. We present the best-fitting set of parameters, including for each case the ratio a between the total hydrogen/helium gas mass and the CO(1-0) line luminosity. We also present computations of the ratio of H2 mass to [C _II] line luminosity for opticallythin conditions, for a range of gas temperatures and densities, for direct conversion of [C _II] line luminosities to 'CO-dark' H₂ masses. For HDF 850.1 we find that a model in which the CO and C⁺ are uniformly mixed in gas that is shielded from ultraviolet radiation requires a cosmic ray or X-ray ionization rate of Ζ ~ 3 × 10^-14 s^-1, plausibly consistent with the large star formation rate (~10³M_⊙ yr^-1) observed in this source. Enforcing the cosmological constraint posed by the abundance of dark matter haloes in the standard λ cold dark matter (λCDM) cosmology and taking into account other possible contributions to the total gas mass, we find that the two models in which the virialization condition is enforced can be ruled out at the {greater than but not similar to}2Σ level, while the model assuming mixed unvirialized regions is less likely. We conclude that modelling HDF 850.1's ISM as a collection of unvirialized molecular clouds with distinct CO and C⁺ layers, for which α = 1.2M_⊙(K km s^-1 pc²)^-1 for the CO to H₂ mass-to-luminosity ratio (similar to the standard ultraluminous infrared galaxy value), is most consistentwith the λCDM cosmology.