Full non-LTE multi-level radiative transfer I. An atom with three bound infinitely sharp levels

TL;DR

The paper tackles the full non-LTE (FNLTE) radiative-transfer problem for a multi-level atom while allowing deviations of the velocity distribution of massive particles from Maxwellian. It develops a numerical scheme that iterates the radiative-transfer equation, kinetic-equilibrium equations, and Boltzmann equations for the velocity distributions, starting from a MALI-CRD initialization and using a three-level, infinitely sharp- level atom. It validates the method against standard two-level PRD, multi-level CRD, and cross-redistribution XRD benchmarks, and then presents new FNLTE results showing non-Maxwellian features in the excited-level velocity distributions and the impact on emergent line profiles. The work highlights the conceptual and practical importance of fully coupled FNLTE treatment and discusses limitations and directions for future improvements, including extending broadening, additional levels, and computational efficiency.

Abstract

The standard nonlocal thermodynamic equilibrium (non-LTE) multi-level radiative transfer problem only takes into account the deviation of the radiation field and atomic populations from their equilibrium distribution. We aim to show how to solve for the full non-LTE (FNLTE) multi-level radiative transfer problem, also accounting for deviation of the velocity distribution of the massive particles from Maxwellian. We considered, as a first step, a three-level atom with zero natural broadening. In this work, we present a new numerical scheme. Its initialisation relies on the classic, multi-level approximate Lambda-iteration (MALI) method for the standard non-LTE problem. The radiative transfer equations, the kinetic equilibrium equations for atomic populations, and the Boltzmann equations for the velocity distribution functions were simultaneously iterated in order to obtain self-consistent particle distributions. During the process, the observer's frame absorption and emission profiles were re-computed at every iterative step by convolving the atomic frame quantities with the relevant velocity distribution function. We validate our numerical strategy by comparing our results with the standard non-LTE solutions in the limit of a two-level atom with Hummer's partial redistribution in frequency, and with a three-level atom with complete redistribution. In this work, we considered the so-called cross-redistribution problem. We then show new FNLTE results for a simple three-level atom while evaluating the assumptions made for the emission and absorption profiles of the standard non-LTE problem with partial and cross-redistribution.

Figures (10)

• Figure 1: Frequency variation of normalised source function $S_{12}$ of $1\leftrightarrow 2$ line at different optical depths $\tau$ for a two-level atom. Horizontal dashed black lines show CRD solutions for $\tau=0, 1, 10, 100, 10^3, 10^4$. We compare FNLTE results (coloured lines) with Hummer's PRD results (black open circle). CRD and PRD solutions were computed using the ALI and FBF methods, respectively. Clearly, we accurately recover the results presented by hummer69_solutions and PSP23.
• Figure 2: Optical depth variations of normalised source functions for each line of a three-level hydrogen atom in CRD. Our three-level FNLTE code (coloured lines) accurately reproduces reference solutions (open black circle) computed with MALI-CRD.
• Figure 3: Optical depth variations of normalised source functions for the $1 \leftrightarrow 3$ line of a three-level hydrogen atom in the frame of XRD approximation. We compare FNLTE results (coloured lines) for various frequencies $x=0,1,2,3,4$ with XRD reference solutions (open black circle) computed using the MALI-XRD method of MALI_XRD. The dashed black line shows the CRD solution computed using the MALI-CRD method.
• Figure 4: Same as Fig. \ref{['fig:Fig03_aa55008-25']}, but for $2 \leftrightarrow 3$ line.
• Figure 5: Optical depth variations of normalised source functions for $1 \leftrightarrow 3$ line of a three-bound-level hydrogen atom. It shows FNLTE results (coloured lines) obtained for various frequencies: $x=0,1,2,3,4$. The dashed black line represents the MALI-CRD solution.