A Simple and Accurate Network for Hydrogen and Carbon Chemistry in the
  ISM
  Chemistry plays an important role in the interstellar medium (ISM),
regulating heating and cooling of the gas, and determining abundances of
molecular species that trace gas properties in observations. Although solving
the time-dependent equations is necessary for accurate abundances and
temperature in the dynamic ISM, a full chemical network is too computationally
expensive to incorporate in numerical simulations. In this paper, we propose a
new simplified chemical network for hydrogen and carbon chemistry in the atomic
and molecular ISM. We compare results from our chemical network in detail with
results from a full photo-dissociation region (PDR) code, and also with the
Nelson & Langer (1999) (NL99) network previously adopted in the simulation
literature. We show that our chemical network gives similar results to the PDR
code in the equilibrium abundances of all species over a wide range of
densities, temperature, and metallicities, whereas the NL99 network shows
significant disagreement. Applying our network in 1D models, we find that the
$\mathrm{CO}$-dominated regime delimits the coldest gas and that the
corresponding temperature tracks the cosmic ray ionization rate in molecular
clouds. We provide a simple fit for the locus of $\mathrm{CO}$ dominated
regions as a function of gas density and column. We also compare with
observations of diffuse and translucent clouds. We find that the $\mathrm{CO}$,
$\mathrm{CHx}$ and $\mathrm{OHx}$ abundances are consistent with equilibrium
predictions for densities $n=100-1000~\mathrm{cm^{-3}}$, but the predicted
equilibrium $\mathrm{C}$ abundance is higher than observations, signaling the
potential importance of non-equilibrium/dynamical effects.
