Radiance Cascades 3D

and Beyond

Chris Osborne

University of Glasgow

Prominence Modelling I

1.5D and 2D simplified slabs.
Postprocess multithread stacking (Gunar+ 2008, Peat+ 2023).
Can produce complex line profiles, but how to motivate velocity distribution?

Peat+ 2023

Prominence Modelling II

MHD prominence models have advanced dramatically in the last decade.
Radiative loss approaches have lagged behind (especially vs chromosphere).
Adopting 1.5D column-by-column approach from chromospheric modelling.

Jenkins+ 2023

But how do we gain insights on observations like this?

IRIS Mg ɪɪ k

Ray Effects

Desired Result

Radiance Cascades: Redux

Linear light source and blocker:

\begin{cases} A < B,\\ \alpha > \beta. \end{cases}

with some small angles approximations…

\begin{cases} \Delta_s < F(D) \propto D\quad&\mathrm{(spatial)}\\ \Delta_\omega < G(1/D) \propto 1/D\quad&\mathrm{(angular)} \end{cases}

We can exploit this!
Represent contributions from different shells separately.

How do we use this?

Encode radiance field as a set of cascades, each describing I_\nu in annuli around \vec{p}.
If penumbra criterion is satisfied, cascade is linearly interpolateable!
- Serves as Nyquist criterion

Interpolation leads to reuse of rays in upper cascades and the effective construction of exponentially more rays than computed directly.

Further Optimisations

GPU-first design (has achieved 40\times perf/Watt vs CPU).
Use a performance-portability library – no ifs, no buts – especially for small teams.
- We use Kokkos with some additional layers.
- Python pre/postprocessing.
First solar non-LTE code to exploit atmospheric sparsity.

Mipmaps & Ray Acceleration

Lower resolution proxies for distant rays: mipmaps (recursive spatial averaging) with directionality and adaptive error bounds (variance of log emissivity and opacity)

In practice, upper cascades (longer rays) sample upper MIPs (fewer texels) when variance is low enough.
Store data in Morton order as much as possible: design inspired by OpenVDB.
Currently under review - probably with someone here 🙈

Mipmaps & Ray Acceleration II

This approach adapts to the populations over iterations!

Science!

The Model

Donné & Keppens 2024

Ly β COCOPLOT

Mg ɪɪ k COCOPLOT

Diving into the lines I

Diving into the lines II

Radiative Losses

\begin{equation*} L = \int_0^\infty \oint_{\mathbb{S}^2} \left( \eta - \chi I \right) d\Omega d\lambda \end{equation*}

Takeaways

Simulation structures are typically axis aligned.
Significant complexity arises from looking outside this alignment.
The next step in meaningfully interpreting these structures will come from multi-line inversions.
Radiative losses and ionisation are model dependent, but what generalities can we extract?
- How does a detailed radiation treatment affect formation and evolution?
- Work in progress!
These new techniques will also feed into SAMS.

Thanks!

Christopher.Osborne@glasgow.ac.uk

Paper