The excess of molecular hydrogen in chemical networks without oxygen

Abstract

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.

Figures (9)

• Figure 1: This figure illustrates the two definitions of the $\mathrm{H}_2$ excess, $\mathcal{H}$ (top row) and $\mathcal{E}$ (bottom row) for different gas temperatures (columns). The lines in the top row indicate the molecular hydrogen fractions, $\log f_{\mathrm{H2}} \equiv \log (2 n_{\mathrm{H2}} / n_{\mathrm{H}})$, for total hydrogen densities, $n_{\mathrm{H}}$, for the reduced (H,He; dashed lines) and the full chemical network (H,He,M; solid lines). The thin horizontal line is at $\log f_{\mathrm{H2}} = - 0.5$, and serves as a marker for the transition between atomic and molecular gas. The $\mathrm{H}_2$ excess is quantified as $\mathcal{H}$, the difference in the densities at which this transition occurs between the two networks (red horizontal bar) and $\mathcal{E}$, the difference in the $\mathrm{H}_2$ fraction at the density of the HI-$\mathrm{H}_2$ transition in the reduced HHe network (indicated as blue vertical bar, also in the bottom row). The bottom panels shows $f_{\mathrm{H2}}$ from the reduced networks HHe (black dashed line) and HHeO (grey dotted line) over $f_{\mathrm{H2}}$ from the full network. The $\mathrm{H}_2$ excess is drastically reduced in the reduced network HHeO that includes oxygen.
• Figure 2: As top right panel in Fig. \ref{['fig:H2excessindividual']} but for an example in which $\mathcal{E}\ll\mathcal{H}$ ($\log I_{\mathrm{ISRF}} = -2$, $\log Z/\mathrm{Z}_{\odot} = -4$, $\log N_{\mathrm{sh}} \, [\mathrm{cm^{-2}}] = 19$ and $\log T\,[\mathrm{K}] = 3$).
• Figure 3: An overview of the densities of the HI-$\mathrm{H}_2$ transition, defined as the density at which $\log f_{\mathrm{H2}} = -0.5$. Columns (metallicity), rows (temperature), and line colors (radiation field strength) as in Fig. \ref{['fig:H2excessH']}. The solid lines show transition densities of the full chemical network, Full, and the dashed lines from the HHe network. The dashed lines therefore represent $\log n_{\mathrm{H},\mathcal{E}}$ from equation \ref{['eq:n']}.
• Figure 4: The $\mathrm{H}_2$ excess parameter, $\mathcal{H}$, as defined in equation (\ref{['eq:H']}) for the model grid described in section \ref{['sec:modelgrid']} between the full chemical network and the chemical network that only includes hydrogen and helium species, HHe. $\mathcal{H}$ is evaluated for different gas temperatures (top row: $\log T \,[\mathrm{K}]= 2$, middle row: $\log T \,[\mathrm{K}]= 2.5$, bottom row: $\log T \,[\mathrm{K}]= 3$), gas metallicities (columns from left to right: $\log Z/\mathrm{Z}_{\odot} = -4, -3, -1,0$), and shielding column densities ($\log N_{\mathrm{sh}}$, x-axis). Each panel shows $\mathcal{H} (N_{\mathrm{sh}})$ for different radiation field strengths, from $\log I_{\mathrm{ISRF}} = -2$ to $1$ (from dark to light line colors). Missing lines or line fragments indicate that the HI-$\mathrm{H}_2$ transition occurs outside the density range of our model grid (see Fig. \ref{['fig:H2excessn']}). Individual grid points are missing where Cloudy does not converge.
• Figure 5: As Fig. \ref{['fig:H2excessH']} but for the $\mathrm{H}_2$ excess parameter, $\mathcal{E}$, as defined in equation (\ref{['eq:E']}). $\mathcal{H} < \mathcal{E}$ indicates a steep increase in molecular hydrogen fraction, $f_{\mathrm{H2}}$, with density, $n_{\mathrm{H}}$, while $\mathcal{H} > \mathcal{E}$ typically represents a very shallow increase of $f_{\mathrm{H2}}$ with $n_{\mathrm{H}}$ (see Fig. \ref{['fig:H2excessindividual']}).