On Atomic Line Opacities for Modeling Astrophysical Radiative Transfer

TL;DR

This paper investigates how atomic line opacities are treated in radiative-transfer modeling of expanding astrophysical plasmas, showing that the common Eastman & Pinto (1993) expansion-opacity formalism can substantially underestimate photon emissivity and reprocessing compared with high-resolution, frequency-dependent opacities. It demonstrates that bound-free opacities are highly sensitive to the equation of state, particularly hydrogen, due to Hummer-Mihalas-type cutoffs, and that bound-bound opacities derived from coarse-frequency averaging differ from high-resolution results depending on the expansion treatment used. To address these issues, the authors propose a physically grounded modification to line emissivity that caps line-strength by the expansion rate $(\rho c t_{exp})^{-1}$, bridging the gap between simple averaging and full expansion formalisms. They also implement this approach in a revised high-resolution opacity table (morag_frequency_2023) with features tailored for multi-group simulations, offering practical paths to more accurate radiative-transfer predictions in optically thick, expanding flows such as supernova ejecta.

Abstract

In astrophysics, atomic transition line opacity is a primary source of uncertainty in theoretical calculations of radiative transfer. Much of this uncertainty is dominated by the inability to resolve the lines in frequency, leading to the use of approximate frequency-averaged treatments, often employing the `line-expansion formalism'. In this short paper we assess the usage of this formalism in simulations, specifically the prominent Eastman \& Pinto 1993 formula (hereafter EP93). As a case study, we reproduce EP93 opacities from the commonly-used STELLA simulations. The latter previously yielded orders of magnitude discrepancy in observed emission relative to similar simulations from our group. The discrepancy is due to differences in line opacity treatment. We show that the widely used EP93 expansion opacity substantially underestimates photon emissivity and reprocessing rates, even when it correctly captures photon mean-free-paths. We also highlight the importance of introducing micro-plasma electron excitation level cutoffs in the equation of state (EOS) for calculating opacity. We propose a new method for calculating emissivity, based on a modification of the simple frequency-bin averaged opacity method, in a way that incorporates the effect of expansion on effective line strength. This formulation should reduce the overestimation of the opacity that may occur with the simple averaging method. To our knowledge, no fully-consistent coarse-frequency solution currently exists for line modeling in these systems. Finally, we describe new features in our updated publicly available high-resolution frequency-dependent opacity table.

Figures (4)

• Figure 1: Our imitation of the bound-free opacity in blinnikov_comparative_1998 (black line) for the example case of $\rho=10^{-13} ~ \rm ~cm^{-3}$, $T=15,000$ K for a solar mixture. In red dashed-line, we show the result when the hummer_equation_1988 factor is not included, and we limit the Hydrogen partition function to $n_{\rm max}=400$, finding reasonable agreement with blinnikov_comparative_1998. In blue solid lines we show the result of a converged H partition function, representative of what we insert into the simulations in morag_shock_2024. The difference in the opacities can be orders of magnitude in the H photoinization opacity (He photoionization is less affected).
• Figure 2: Bound-bound opacity example from blinnikov_comparative_1998 fig. 1, compared with our reproduction using morag_frequency_2023 modified to employ the eastman_spectrum_1993 prescription. We finding good agreement to a factor of a few or better. The plasma parameters are $\rho=10^{-13} ~ \rm ~cm^{-3}$, $T=15,000$ K, $t_{\rm exp}=15$ days. Similarly to blinnikov_comparative_1998, we use a coarse frequency grid with $\Delta\nu/\nu\sim0.01$. The lines that are in excellent agreement in the range 200 Å $< \lambda <$ 400 Å are dominated by a Helium line ($\lambda=227$Å) and a set of Oxygen lines.
• Figure 3: Same as fig. \ref{['fig: bb opacity Blin vs ours']}, at lower frequency resolution ($\Delta\nu/\nu\sim0.1$). For ease of comparison, the $\kappa_{\rm es}$ baseline has been added to the average and eastman_spectrum_1993 opacities, despite not normally being added to the emission / absorption terms. The Ross mean opacity also includes bound-free opacities (unlike other opacities in the figure), as these cannot be separated in a harmonic average.
• Figure 4: Example high resolution opacity for a solar mixture at density and temperature $\rho=10^{-13} \, \rm g \, cm^{-3}$, $T=1 \, \rm eV$, showing the effect of the proposed expansion limit. As $t_{exp}$ increases, the maximum line strength decreases, as the net photon production rate depends on the rate at which photons are swept in frequency out of the line resonance region. This high-resolution opacity can be averaged for use in coarse multi-group expansion methods. It was created using the publicly available morag_frequency_2023, which now includes the expansion limit.