Non-equilibrium chemistry and cooling in the diffuse interstellar medium
  - I. Optically thin regime
  An accurate treatment of the multiphase interstellar medium (ISM) in
hydrodynamic galaxy simulations requires that we follow not only the thermal
evolution of the gas, but also the evolution of its chemical state, including
its molecular chemistry, without assuming chemical (including ionisation)
equilibrium. We present a reaction network that can be used to solve for this
thermo-chemical evolution. Our model follows the evolution of all ionisation
states of the 11 elements that dominate the cooling rate, along with important
molecules such as H2 and CO, and the intermediate molecular species that are
involved in their formation (20 molecules in total). We include chemical
reactions on dust grains, thermal processes involving dust, cosmic ray
ionisation and heating and photochemical reactions. We focus on conditions
typical for the diffuse ISM, with densities of 10^-2 cm^-3 < nH < 10^4 cm^-3
and temperatures of 10^2 K < T < 10^4 K, and we consider a range of radiation
fields, including no UV radiation. In this paper we consider only gas that is
optically thin, while paper II considers gas that becomes shielded from the
radiation field. We verify the accuracy of our model by comparing chemical
abundances and cooling functions in chemical equilibrium with the
photoionisation code Cloudy. We identify the major coolants in diffuse
interstellar gas to be CII, SiII and FeII, along with OI and H2 at densities nH
> 10^2 cm^-3. Finally, we investigate the impact of non-equilibrium chemistry
on the cooling functions of isochorically or isobarically cooling gas. We find
that, at T < 10^4 K, recombination lags increase the electron abundance above
its equilibrium value at a given temperature, which can enhance the cooling
rate by up to two orders of magnitude. The cooling gas also shows lower H2
abundances than in equilibrium, by up to an order of magnitude.
