Thermal Phases of the Neutral Atomic Interstellar Medium -- from Solar Metallicity to Primordial Gas

We study the thermal structure of the neutral atomic (H {\small I}) interstellar medium across a wide range of metallicities, from supersolar down to vanishing metallicity, and for varying UV intensities and cosmic-ray ionization rates. We calculate self-consistently the gas temperature and species abundances (with a special focus on the residual H$_2$), assuming thermal and chemical steady-state. For solar metallicity, $Z' \equiv 1$, we recover the known result that there exists a pressure range over which the gas is multiphased, with the warm ($\sim 10^4$ K, WNM) and cold ($\sim 100$ K, CNM) phases coexisting at the same pressure. At a metallicity $Z' \approx 0.1$, the CNM is colder (compared to $Z'=1$) due to the reduced efficiency of photoelectric heating. For $Z' \lesssim 0.1$, cosmic-ray ionization becomes the dominant heating mechanism and the WNM-to-CNM transition shifts to ever increasing pressure/density as the metallicity is reduced. For metallicities $Z' \lesssim 0.01$, H$_2$ cooling becomes important, lowering the temperature of the WNM (down to $\approx 600$ K), and smoothing out the multiphase phenomenon. At vanishing metallicities, H$_2$ heating becomes effective and the multiphase phenomenon disappears entirely. We derive analytic expressions for the critical densities for the warm-to-cold phase transition in the different regimes, and the critical metallicities for H$_2$ cooling and heating. We discuss potential implications on the star-formation rates of galaxies and self-regulation theories.