The HyLight model for hydrogen emission lines in simulated nebulae

Abstract

Hydrogen recombination lines provide key diagnostics of ionized gas in galaxies, yet most hydrodynamical simulations estimate hydrogen level populations using interpolated emissivity tables rather than computing them directly from local physical conditions. We present HyLight, a Python-based atomic model that calculates hydrogen level populations and line emissivities from the gas density, temperature, and ionization state, enabling accurate predictions in both equilibrium and non-equilibrium environments. Benchmark comparisons show that HyLight reproduces Cloudy predictions for Balmer, Paschen, and Brackett emissivities to within 1 per cent under typical photoionized nebular conditions, while discrepancies of several tens of per cent arise relative to other published calculations. As an illustrative application, we use HyLight to compute photoionization-to-line intensity ratios in an HII nebula and generate synthetic hydrogen emission maps from a radiation-hydrodynamical simulation that includes non-equilibrium thermochemistry. Combining physical consistency with flexibility, HyLight provides a robust framework for connecting hydrodynamical simulations with observational diagnostics of photoionized regions, and enhances our ability to interpret hydrogen emission in complex, non-equilibrium astrophysical environments.

Figures (24)

• Figure 1: Left panel: Profile of H$\alpha$ emissivity, $\epsilon({\rm H \alpha}) \equiv \epsilon_{3,2}$, of the idealised spherical setup for different models: the reference Cloudy model ' Ref - Sph' ( purple triangles), the Raga2015 model ( yellow crosses) and the tabulated values from Storey1995 ( black diamonds). The top panel shows the emissivity; the lower panel is the relative difference in emissivity compared to ' Ref-Sph' in per cent. In all models, the emissivity is approximately constant inside the Strömgren radius, $r\approx 1.5~\unit{pc}$, then drops rapidly. Different models differ by up to 50 per cent from the Cloudy prediction. In particular, Storey1995 values at large radii ($\gtrsim$ 2 pc) differ by over 40 per cent in terms of emissivity. Right panel: Same as left panel, but for the density of hydrogen atoms in the $3s$ state. Different models now differ by up to 100 per cent from the Cloudy prediction. In all panels, the red line is the prediction from the model described in this paper. Our model agrees with the Cloudy prediction within 1 per cent in terms of the total H$\alpha$ luminosity.
• Figure 2: Left panel: Cumulative $nl$-resolved recombination rate, $\sum_{n'=1}^n\sum_{l'=0}^{n'}\alpha_{n'l'}(T)$, up to a given $n$, for various temperatures as per the legend. Diamonds are the difference in per cent of the cumulative rate compared to the total recombination coefficient, $\alpha_\mathrm{A}$. The black dashed line at 0 is drawn to guide the eye. For $T=10^{4}$ K, the cumulative rate for $n=100$ equals the total rate to better than 0.5 per cent, quantifying the level to which recombinations to levels with $n>100$ are unimportant in setting the recombination rate. The importance of recombinations to these higher energy levels increases with decreasing $T$. Right panel: Sum of the $nl$-resolved recombination rates up to and including level $n=100$ ( diamonds) compared to the total recombination rate ( lines) for Case A ( purple) and Case B ( orange) recombinations, as tabulated by Ferland1992. The summed level-resolved recombination rate up to $n=100$ agrees to be better than a per cent with the tabulated values for $T$ in the range $10^{3.5}-10^{5.5}$ K.
• Figure 3: Convergence of the emissivity, $\epsilon$, for selected hydrogen transitions for different models in Case A. The reference setup is ' Ref - ALSh' as shown in Table \ref{['tab:cloudy_models']}. The horizontal axis is the number of resolved levels in the atomic model, while the vertical axis indicates the emissivity difference in per cent between a given model and the reference model. The dotted line shows the predictions from radiative-only HyLight predictions. The open triangles are predictions from the ' LShA - Ref - RR' Cloudy model, which only includes radiative processes, as described in Table \ref{['tab:cloudy_rr_model']}. There is excellent agreement between Cloudy and HyLight. As the number of levels increases, both models converge to the reference model. We conclude that 100 resolved levels is sufficient to produce accurate line emissivities.
• Figure 4: Profile of H$\alpha$ emissivity, $\epsilon({\rm H \alpha}) \equiv \epsilon_{3,2}$, of a gas cloud ionized by a laser beam. This Cloudy setup is labelled as ' Ref - LSph' in Table \ref{['tab:cloudy_models']}. The Strömgren radius is approximately 1.5 pc. The solid curves are HyLight predictions when including radiative and collisional contributions. Within the Strömgren radius, the H$\alpha$ emissivity gradually switches from Case A to Case B in the region $r \lesssim 0.4$ pc, a result of the finite optical depth of Lyman photons. Beyond the Strömgren radius, the radiative-only approximation does not hold any more, since collisional excitation of the ground state atoms contributes dominantly: these are not included in the radiative-only calculation. The full HyLight model agrees well with Cloudy.
• Figure 5: Convergence of the collisional contribution to H$\alpha$ emissivity as a function of the number of resolved levels, $n_{\rm max}$. The reference setup is ' Ref - LSph' where the temperature is kept at 10$^4$ K throughout the cloud. The reference emissivity, $\epsilon_{\rm ref}$, is extracted at 2 pc from the source, where the gas is neutral and collisional excitation dominates over radiative recombination. As the number of levels increases in the model, the line emissivity converges. The difference between the converged answer and the Cloudy predictions is lower for low-order series (e.g., smaller than 6% for H$\alpha$ and H$\beta$) but higher for higher series such as Paschen $\beta$ (about 8%). Given that the collisional contribution to recombination lines is only relevant in the partially neutral plasma and several orders of magnitude lower than that from radiative recombination within the Strömgren radius, the difference of a few per cent is satisfactory. The differences come from disregard of collisional excitation and de-excitation between and from levels other than the ground state, as well as the exact calculation of collisional excitation rate for $nl$-resolved levels (see Appendix \ref{['app:collisions']}).