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We present fluxes in both neutral carbon [CI] lines at the centers of 76galaxies with FIR luminosities between 10^{9} and 10^{12} L(o) obtained withHerschel-SPIRE and with ground-based facilities, along with the J=7-6, J=4-3,J=2-1 12CO and J=2-1 13CO line fluxes. We investigate whether these lines canbe used to characterize the molecular ISM of the parent galaxies in simple waysand how the molecular gas properties define the model results. In moststarburst galaxies, the [CI]/13CO flux ratio is much higher than in Galacticstar-forming regions, and it is correlated to the total FIR luminosity. The[CI](1-0)/CO(4-3), the [CI](2-1) (2-1)/CO(7-6), and the [CI] (2-1)/(1-0) fluxratios are also correlated, and trace the excitation of the molecular gas. Inthe most luminous infrared galaxies (LIRGs), the ISM is fully dominated bydense and moderately warm gas clouds that appear to have low [C]/[CO] and[13CO]/[12CO] abundances. In less luminous galaxies, emission from gas cloudsat lower densities becomes progressively more important, and a multiple-phaseanalysis is required to determine consistent physical characteristics. Neitherthe CO nor the [CI] velocity-integrated line fluxes are good predictors of H2column densities in individual galaxies, and X(CI) conversion factors are notsuperior to X(CO) factors. The methods and diagnostic diagrams outlined in thispaper also provide a new and relatively straightforward means of deriving thephysical characteristics of molecular gas in high-redshift galaxies up to z=5,which are otherwise hard to determine.

Neutral carbon and CO in 76 (U)LIRGs and starburst galaxy centers A method to determine molecular gas properties in luminous galaxies