Long-Term Illumination and Thermal Evolution of Shackleton Crater with Fast Radiosity Modeling

High-fidelity illumination and thermal modeling is crucial for understanding the stability and evolution of volatiles on airless planetary surfaces. These environments are controlled not only by direct solar illumination, but also by radiation reflected and emitted from surrounding terrain. Modeling polar craters and other rough surfaces quickly becomes computationally demanding, especially at high resolution and when repeated simulations are needed for multiple epochs, illumination geometries, or thermophysical scenarios. Potter et al., J. Comp. Phys. X (2023) addressed this challenge by compressing the radiosity view-factor matrix used to model terrain irradiance, enabling large reductions in memory use and runtime while preserving accuracy for lunar craters and small-body shape models.

Here we present ongoing work extending the Potter et al. (2023) Python-based framework, fluxpy, with a faster C/Cython backend for hierarchical matrix operations, based on the newly created butterfly library. The goal is to support high-fidelity, high-resolution thermal modeling across a broad range of planetary applications, from local polar terrains to complex three-dimensional bodies, with practical runtimes on standard computing resources. We validate the new implementation using the analytical solution for a bowl-shaped crater. We also benchmark it against the published fluxpy implementation using selected lunar crater meshes and 3D body shape models, comparing accuracy, memory use, and runtime.

We then apply the new model to Shackleton crater, one of the Moon’s most persistent polar cold-trap environments. Using high-resolution topography, we examine how illumination and radiative-equilibrium maximum temperatures change under increasing solar-declination conditions at different stages of the lunar orbital evolution. Preliminary results indicate that, within Shackleton, the area that acts as cold-trap (here taken as maximum temperature ≤110 K) decreases more rapidly with increasing solar declination than the permanently shadowed area. This suggests that terrain irradiance, multiple scattering, and self-heating significantly affect cold-trap history, particularly in steep polar terrains.

We show that the updated fast-radiosity framework enables accurate high-resolution simulations of illumination and thermal evolution without requiring high-end computing resources. This capability can support the characterization of volatile stability across planetary surfaces and help identify regions where future robotic and human missions may search for water and other resources.