Radiance Cascades: A Novel High-Resolution Formal Solution for Multidimensional Non-LTE Radiative Transfer

TL;DR

This work addresses the computational challenge of multidimensional non-LTE radiative transfer by introducing radiance cascades, a interval-based formalism that adaptively allocates angular resolution to local penumbra structure. The DexRT implementation on GPUs demonstrates a scalable, ray-interval approach that suppresses ray effects while delivering high angular and spatial detail at a fraction of traditional costs. Applied to a high-resolution solar prominence snapshot, the method yields self-consistent hydrogen and Ca II non-LTE populations and synthesizes Lyβ, Hα, Ca II K spectra, revealing both agreement with less-detailed models and important two-dimensional transfer effects. The framework offers a practical path toward routine, high-fidelity multidimensional non-LTE radiative transfer on HPC systems and outlines future enhancements such as including PRD and multigrid accelerations for full 3D scalability.

Abstract

Non-LTE radiative transfer is a key tool for modern astrophysics: it is the means by which many key synthetic observables are produced, thus connecting simulations and observations. Radiative transfer models also inform our understanding of the primary formation layers and parameters of different spectral lines, and serve as the basis of inversion tools used to infer the structure of the solar atmosphere from observations. The default approach for computing the radiation field in multidimensional solar radiative transfer models has long remained the same: a short characteristics, discrete ordinates method, formal solver. In situations with complex atmospheric structure and multiple transitions between optically-thick and -thin regimes these solvers require prohibitively high angular resolution to correctly resolve the radiation field. Here, we present the theory of radiance cascades, a technique designed to exploit structure inherent to the radiation field, allowing for efficient reuse of calculated samples, thus providing a very high-resolution result at a fraction of the computational cost of existing methods. We additionally describe our implementation of this method in the DexRT code, and present initial results of the synthesis of a snapshot of a magnetohydrodynamic model of a solar prominence formed via levitation-condensation. The approach presented here provides a credible route for routinely performing multidimensional radiative transfer calculations free from so-called ray effects, and scaling high-quality non-LTE models to next-generation high-performance computing systems with GPU accelerators.

Figures (14)

• Figure 1: Comparison of the state-of-the-art short characteristics method (using a 10th order quadrature) with two different variants of the radiance cascades solution. For this scene, the "Radiance Cascades (Bilinear Fix)" panel may be taken as the ground truth. The scene is composed of opaque emissive circles of different intensities (at three different, independent wavelengths, represented by the red, green, blue triad), along with several absorbing features. For readability, the images are tonemapped from high-dynamic range into a visual proxy, enhancing the visibility of dim regions over a simple linear scaling. The large dark red box in the centre of the frame is weakly absorptive in red, and $100\times$ more absorptive in blue and green. The two small black circles near the blue and red circles at the top and bottom of the frame are strongly to all of the colour channels. The short characteristics solution presents very strong ray effects, demonstrating its unsuitability for problems that transition between finely-structured optically thick and optically thin regions. The basic radiance cascades method provides a very high-quality solution with minor ringing artefacts discussed in Section \ref{['Sec:RadianceCascadeArtefacts']}, whilst the radiance cascades with bilinear fix solution effectively provides the expected ground truth solution.
• Figure 2: Illustration of the penumbra criterion motivating the radiance cascades method. Considering a linear light source illuminating a two-dimensional plane with a blocker casting a shadow we observe that points close to the blocker (on the segment $\mathrm{A}$) require high spatial- but low angular-resolution to resolve the illumination of the penumbra, whereas those far from the blocker (on the segment $\mathrm{B}$) require lower spatial- but higher angular-resolution.
• Figure 3: Comparison of long characteristics style ray-casting from a point against two different radiance intervals over the same field. The three coloured primitives can be considered opaque emissive sources. In a) we show the a conventional ray-casting approach, whilst b) and c) show the radiance found inside annuli described by closer and further radiance intervals (shown in grey). Note that in b) only the blue circle is found by these samples, whilst in c) obscured components of the orange rectangle and green triangle are sampled.
• Figure 4: A set of five radiance cascades with following the scaling laws of \ref{['Eq:RcScalingLaw']} with branching factor $\alpha=1$. These cascades (ordered blue, orange, green, red, purple) capture progressively higher angular-resolution representations of increasingly distant radiation field components at decreasing spatial resolution, thus exploiting the properties of the penumbra criterion.
• Figure 5: Five radiance cascades, interpolated on one probe of cascade 0. The colour of each cascade is the same as Figure. \ref{['Fig:RcGrid']}. In quadrant 0 a single ray constructed by cascade interpolation and merging is highlighted in dashed black. The constructed rays that make up quadrant 2 are highlighted in pink.