Non-Equilibirum ionisation and cooling of metal-enriched gas in the presence of a photo-ionisation background

Simulations of the formation of galaxies, as well as ionisation models used to interpret observations of quasar absorption lines, generally either assume ionisation equilibrium or ignore the presence of the extra-galactic background (EGB) radiation. We introduce a method to compute the non-equilibrium ionisation and cooling of diffuse gas exposed to the EGB. Our method iterates the ionisation states of the 11 elements that dominate the cooling and uses tabulated ion-by-ion cooling and photo-heating efficiencies to update the temperature of the gas. Our reaction network includes radiative and di-electric recombination, collisional ionisation, photo-ionisation, Auger ionisation, and charge transfer. We verify that our method reproduces published results for collisional equilibrium, collisional non-equilibrium, and photo-ionised equilibrium. Non-equilibrium effects can become very important in cooling gas, particularly below 10^6 K. Photo-ionisation and non-equilibrium effects both tend to boost the degree of ionisation and to reduce cooling efficiencies. The effect of the EGB is larger for lower densities. Hence, photo-ionisation affects cooling more under isochoric than under isobaric conditions. Non-equilibrium effects are smaller in the presence of the EGB and are thus overestimated when using collisional-only processes. The inclusion of the EGB alters the observational diagnostics of diffuse, metal-enriched gas (e.g. metal absorption lines) even more significantly than the cooling efficiencies. We argue that the cooling efficiency should be considered if ionisation models are used to infer physical conditions from observed line ratios, as the a priori probability of observing gas is lower if its cooling time is shorter. We provide on-line tables of ionisation fractions and cooling efficiencies for equilibrium and non-equilibrium scenarios. (abridged)