The excess of molecular hydrogen in chemical networks without oxygen

We report the presence of a systematic excess in the molecular hydrogen fraction ($f_{\mathrm{H2}} = 2 \, n_{\mathrm{H2}}/n_{\mathrm{H}}$) in studies that use a reduced chemistry network to calculate $f_{\mathrm{H2}}$ of gas with a non-zero metal mass fraction. This is common practice in simulations of galaxy formation in which following the non-equilibrium abundances of additional elements is computationally expensive. We define the $\mathrm{H}_2$ excess as the shift in density of the \ion{H}{I}-$\mathrm{H}_2$ transition in the reduced network compared to the full chemical network (30 elements). The strength of the $\mathrm{H}_2$ excess generally increases both with temperature and metallicity, is largely independent of the radiation field strength, and persists across a large range of assumed shielding column densities. For warm gas, with $T\approx1000~\mathrm{K}$, the HI-$\mathrm{H}_2$ transition is shifted by up to 1 dex to lower densities in primordial chemistry networks already for extremely low metallicities ($Z\geq 10^{-4}\,\mathrm{Z}_{\odot}$). We confirm our earlier findings that missing reactions with oxygen are largely responsible for this $\mathrm{H}_2$ excess. A reduced chemical network of hydrogen, helium, and oxygen recovers the molecular hydrogen fractions from a full network and we therefore recommend to include destruction of molecular hydrogen by oxygen in a minimal chemical network for accurate molecular hydrogen abundances.