Astronomical Radiative Transfer and Video Games:

A Match Made in the Sun

Chris Osborne

University of Glasgow

Who recognises this?

Cornell University

And how does it connect to this?

VLT (ESO)

Physics!

\begin{align*} (\hat{\omega} \cdot \nabla) L(\vec{p}, \hat{\omega}) = &-\chi(\vec{p}, \hat{\omega}) L(\vec{p}, \hat{\omega}) \\ &+ \eta(\vec{p}, \hat{\omega}) \\ &+ \sigma_s(\vec{p}, \hat{\omega}) \oint_{\mathbb{S}^2} p(\vec{p}, \hat{\omega}^\prime, \hat{\omega}) L(\vec{p}, \hat{\omega}^\prime)\, d\hat{\omega}^\prime \end{align*}
  • L radiance,
  • \eta emission coefficient,
  • \chi absorption coefficient,
  • \sigma_s scattering coefficient,
  • p phase function.

Key takeaway: this is a recursive integro-differential equation!

Radiative Transfer

  • A wealth of knowledge in spectral lines and continua between UV and IR.
  • Non-trivial to predict and interpret.

FTS, McMath-Pierce Atlas, Kitt Peak, NSO (Kurucz et al.)

The Solar Atmosphere

  • Information in these narrow wavebands samples different regions of the solar atmosphere.
  • But not uniquely determined by a single region…

Vernazza et al. 1981 (VAL3)

Non-LTE Radiative Transfer

  • Coupling between radiation field and atomic transitions.
  • Extremely computationally demanding, but necessary for many spectral lines.
  • Also determines ionisation.

HINODE BFI

Most Important Quantities

  • Radiative rates depend on intensity.
  • Intensity depends on radiative rates.


\begin{align*} J_\nu(\vec{p}) &= \frac{1}{4\pi}\oint_\mathbb{S^2} I_\nu(\vec{p},\hat{\omega}) \mathop{d \hat{\omega} } \\ &\vec{p} \in \mathbb{R}^2, \hat{\omega} \in \mathbb{S}^2\\ \end{align*}
  • Specific intensity and its first moment.
  • 3 and 5 dimensional functions! (+ wavelength…)
  • Recursive component solved by fixed-point iteration in the atomic populations.

Monte Carlo

8 spp

8192 spp (PBR Book, Pharr et al)

Ray Effects

Desired Result

Tricky Radiation

  • In the steady-state solution of radiative transfer coupling is global.
  • This hinders parallelisation.
  • Monte Carlo approaches have poor convergence rates.
  • Is there some middle ground?
  • Video games are now solving an adjacent problem at reasonable resolutions hundreds of times a second on single workstations…

Aside: Everything Old is New Again

NVIDIA H100

Radiance Cascades

Radiance Cascades: Observations

  • 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
  • The cascades sparsely encode the radiation field throughout the domain…
  • But not in a form we can use directly.
  • Solution:


Interpolation. But with minimal error.

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

Mipmaps I

  • We can employ lower resolution proxies for distant rays: mipmaps (recursive spatial averaging) with directionality and adaptive error bounds (variance of log emissivity and opacity), and also skip empty space
  • Inspired by OpenVDB and longstanding computer graphics practices.

Mipmaps II

  • Can be efficiently traversed using a hierarchical scheme.
  • This technique has provided a further order of magnitude speedup on typical models.

Mipmaps III

  • This approach adapts automatically during the iterative solution!

Ly β COCOPLOT (Donné & Keppens)

Outlook

  • This barely scratches the surface of interdisciplinary computational work, especially for radiation.
    • Need to develop common language between fields.
  • Radiance cascades provide the first meaningful change to solar non-LTE RT in 30 years and it came from outside the field.
    • This work will grow part of the recently funded STFC large award for the Solar Atmospheric Modelling Suite over the next few years.
    • More efficient cascade designs are being developed.



Thanks!

Christopher.Osborne@glasgow.ac.uk

Radiative Transfer and Video Games