Atomic Data for Non-Equilibrium Modeling of Kilonovae: The Ionization Properties of Te I - III

Abstract

Kilonovae, the electromagnetic transients produced from two merging neutron stars, exhibit evolving spectral signatures in ultraviolet, visible, and infrared radiation. Starting around one week post-merger, equilibrium assumptions describing the local ionization balance and atomic level populations in the ejecta come into question, and non-equilibrium modeling is required. In this non-equilibrium regime, interactions with non-thermal electrons are critical inputs to ionization balance models. With most databases storing rate coefficients, the necessary cross sections describing these interactions are generally unavailable. We report new level-resolved calculations of the ionization cross sections of a species tentatively identified in kilonovae, Te I - III, using the Flexible Atomic Code. Good agreement is found between the calculated cross sections and a limited number of available measurements. Particular attention is paid to diagnosing the accuracy of the above-threshold channels that contribute through excitation autoionization. Calculations in the configuration average approximation yield ionization cross sections close to both experimental and level-resolved theoretical values. The computed cross sections are combined with a Spencer-Fano non-thermal electron energy solver and subsequent ionization balance models to probe the impact of improved cross section datasets on ion fractions of Te I - IV at kilonova-like plasma conditions.

Figures (7)

• Figure 1: Comparison of the present single ionization calculations (level-resolved and configuration average) for the Te$\;$ ground state and the measurements of Freund1990. Calculations built on a central potential optimized on the ground state of Te$\;$ ($5p^4$) are shown in the left column, with calculations optimized on the Te$\;$ ground state ($5p^3$) shown in the right column. The calculations allowed for configuration interaction between all states within each non-relativistic configuration. Excitation autoionization contributions are computed with the Distorted Wave approximation. Direct ionization of the $5s$, $5p$, and $4d$ sub-shells are shown for the Binary Encounter Dipole approximation (top row), and the Distorted Wave approximation (bottom row). Total cross sections are produced by summing the direct $5s$ and $5p$ channels, and the excitation autoionization multiplied by a scale factor of 0.15 (see text). Lotz ionization cross sections are shown for comparison.
• Figure 2: Comparison of the present single ionization calculations for the Te$\;$ ground state and the measurements of Djuric1994. Calculations built on a central potential optimized on the ground state of Te$\;$ ($5p^3$) are shown in the left column, with calculations optimized on the Te$\;$ ground state ($5p^2$) shown in the right column. The calculations allowed for configuration interaction between all states within each non-relativistic electron configuration. Excitation autoionization contributions are computed with the Distorted Wave approximation. Direct ionization of the $5s$, $5p$, and $4d$ sub-shells are shown for the Binary Encounter Dipole approximation (top row), and the Distorted Wave approximation (bottom row). Total cross sections are produced by summing the direct $5s$ and $5p$ channels, and the excitation autoionization multiplied by a scale factor of 0.17. Lotz cross sections for the $5s$ and $5p$ channels are summed and shown for comparison.
• Figure 3: Comparison of the present single ionization calculations for Te$\;$. Calculations built on a central potential optimized on the ground state of Te$\;$ ($5p^2$) are shown in the left column, with calculations optimized on the Te$\;$ ground state ($5p^1$) shown in the right column. The calculations allowed for configuration interaction between all states within each given non-relativistic electron configuration. Excitation autoionization contributions are computed with the Distorted Wave approximation. Direct ionization of the $5s$, $5p$, and $4d$ sub-shells are shown for the Binary Encounter Dipole approximation (top row), and the Distorted Wave approximation (bottom row). Total cross sections are produced by summing the direct ($5s$ and $5p$) channels and excitation autoionization.
• Figure 4: Non-thermal electron energy distribution functions computed for electrons initially injected at $E = 5$ keV into a plasma with ion fractions described by Saha equilibrium at 2200 K (top panel) and 4500 K (bottom panel). Level-resolved (LR) and configuration average (CA) data were taken from the FAC calculations described in Sec. \ref{['sec:results']}. Empirical (EMP) curves were generated using ionization and excitation cross sections predicted by the Lotz1967 and vanRegemorter1962 approximations. Empirical models utilizing Lotz cross sections with $a_i = 4\times10^{-4}$ and $a_i = 1.33\times10^{-4}$ are labeled as EMP $\#1$ and EMP $\#2$, respectively.
• Figure 5: Ion fractions of Te$\;$ -$\;$ in Saha Equilibrium (solid lines) and non-LTE (dashed lines) for $n_\textrm{e} = 10^6$ cm$^{-3}$. Contributions from non-thermal electrons are excluded.