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

Abstract

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 alpha between the total hydrogen/helium gas mass and the CO(1-0) line luminosity. We also present computations of the ratio of H-2 mass to [C ii] line luminosity for optically thin conditions, for a range of gas temperatures and densities, for direct conversion of [C ii] line luminosities to 'CO-dark' H-2 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 zeta approximate to 3 x 10(-14) s(-1), plausibly consistent with the large star formation rate (similar to 10(3) M-circle dot yr(-1)) observed in this source. Enforcing the cosmological constraint posed by the abundance of dark matter haloes in the standard Lambda cold dark matter (Lambda CDM) 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 or similar to 2 Sigma 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 alpha = 1.2 M-circle dot (K km s(-1) pc(2))(-1) for the CO to H-2 mass-to-luminosity ratio (similar to the standard ultraluminous infrared galaxy value), is most consistent with the Lambda CDM cosmology.