CII*/CII ratio in high-redshift DLAs: ISM phase separation drives the observed bimodality of [CII] cooling rates

We discuss observations of CII*/CII ratios and cooling rates due to [CII]$\,$158$\mu$m emission in high-redshift intervening damped Lyman-$\alpha$ systems towards quasars. We show that the observed bimodality in the CII cooling rates actually reflects a bimodality in the CII*/CII-metallicity plane that can be naturally explained by phase segregation of the neutral medium, without invoking differences in star-formation scenarios. Assuming realistic distributions of the physical parameters to calculate the phase diagrams, we also reproduce qualitatively the metallicity dependence of this bimodality. We emphasize that high-z DLAs mostly probe low-metallicity gas ($Z\lesssim 0.1 Z_{\odot}$), where heating is dominated by cosmic rays (and/or turbulence), and not by photoelectric heating. Therefore even if the gas of DLA is predominantly cold (where the cooling is dominated by [CII]), the excitation of CII can be used to derive the cosmic ray ionization rate (and/or turbulent heating), but not the UV field, as was previously considered. Alternatively, if the gas in DLA is predominantly warm, CII*/CII can be used to constrain its number density. Finally, we also discuss the importance of the ionized medium, which, if also present along the line of sight, can significantly increase the average CII*/CII ratio.