Neutral carbon in diffuse interstellar medium: abundance matching with H2 for damped Lyman alpha systems at high redshifts

We present a study of C i/H2 relative abundance in the diffuse cold neutral medium (CNM). Using the chemical and thermal balance model, we calculate the dependence of C i/H2 on the main parameters of the medium: hydrogen number density, metallicity, strength of the UV field, and cosmic ray ionization rate (CRIR). We show that the observed relative C i and H2 column densities in damped Lyman alpha systems (DLAs) at high redshifts can be reproduced within our model assuming the typically expected conditions in the diffuse CNM. Using additional observed information on metallicity, H i column density, and excitation of C i fine-structure levels, as well as temperature, we estimated for a wide range metallicities in the CNM at high redshifts that CRIRs are in the range from ∼10−16 to a $\rm few \times 10^{-15}\, \rm s^{-1}$, hydrogen number densities are in the range ∼10−103 cm−3, and the UV field is in the range from 10−2 to a $\rm few \times 10^2$ of the Mathis field. We argue that because the observed quantities used in this work are quite homogeneous and much less affected by radiative transfer effects (in comparison with, for example, the dissociation of HD and UV pumping of H2 rotational levels), our estimates are quite robust against the assumption of the exact geometrical model of the cloud and local sources of the UV field.