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We present self-consistent calculations of non-equilibrium (time-dependent)cooling rates for a dust-free collisionally controlled gas in wide temperature($10 K\le T\le 10^8 K$) and metallicity ($10^{-4} Z_\odot \le Z \le 2 Z_\odot$)ranges. We confirm that molecular hydrogen dominates cooling at $10^2 \simltT\simlt 10^4$ K and $Z\simlt 10^{-3} Z_\odot$. We find that the contributionfrom H$_2$ into cooling rate around $T\sim (4-5)\times 10^3$ K stimulatesthermal instability in the metallicity range $Z\simlt 10^{-2} Z_\odot$.Isobaric cooling rates are generally lower than isochoric ones, because theassociated increase of gas density leads to both more efficient hydrogenrecombination and equilibration of the fine-structure level populations.Isochoric cooling keeps the ionization fraction remains quite high at$T\simlt10^4$ K: up to $\sim0.01$ at $T\simeq 10^3$ K and $Z\simlt 0.1Z_\odot$, and even higher at higher metallicity, contrary to isobaric coolingwhere it at least an order of magnitude lower. Despite this increase inionization fraction the gas-phase formation rate of molecular hydrogen (viaH$^-$) lowers with metallicity, because higher metallicity shorttens theevolution time. We implement our self-consistent cooling rates into themulti-dimensional parallel code ZEUS-MP in order to simulate evolution of asupernova remnant, and compare it with an analogous model with tabulatedcooling rates published in previous works. We find significant differencesbetween the two descriptions, which may appear, e.g., in mixing of the ejectedmetals in the circumstellar medium.

Non-equilibrium cooling rate for a collisionally cooled metal-enriched gas