RAYTHEIA: A high-performance ray-tracing algorithm for three-dimensional direction-dependent equations in astronomical simulations

TL;DR

RAYTHEIA is a high-performance, parallel ray-tracing algorithm for solving 3D direction-dependent equations in astronomical simulations, enabling detailed modeling of complex astrophysical phenomena.

Contribution

The paper introduces RAYTHEIA, a novel, efficient, and scalable ray-tracing algorithm with advanced data structures and parallelization for high-resolution astrophysical modeling.

Findings

Achieves near-linear speed-up in parallel performance.

Successfully models 3D PDR chemistry in turbulent star-forming clouds.

Produces high-resolution synthetic emission maps with realistic physical effects.

Abstract

We present RAYTHEIA, a high-performance reverse ray-tracing algorithm designed to efficiently solve three-dimensional direction-dependent equations in astronomical simulations. The algorithm uses a dual-grid framework in which the native simulation mesh -- serving as the source grid for ray emission -- and an adaptive mesh refinement (AMR) Cartesian contribution grid are constructed for efficient ray-walking and contribution accumulation. The core of the algorithm integrates a leaf-only linear-octree data structure to reduce memory overhead, the digital differential analyzer (DDA) traversal method to efficiently determine the ray-walking path, Morton Code indexing to fast leaf cell lookup during traversal, and the slab method to analytically compute the path length. Furthermore, RAYTHEIA employs a hybrid (MPI/OpenMP) distributed parallel framework with a chunk-to-chunk communication strategy, achieving exceptional, near-ideal linear speed-up ratio and delivering high-end performance. We integrate RAYTHEIA with the 3D-PDR code to solve the complex chemistry and radiation transfer in photodissociation regions (PDRs). This allowed the modelling of three-dimensional PDR chemistry in a turbulent, star-forming cloud at an unprecedented resolution of $512^3$ grid cells. The algorithm demonstrates accuracy and convergence even at low angular resolutions. We further showcase the capabilities of RAYTHEIA by producing high-resolution synthetic emission maps of key diagnostic lines of a star-forming region capturing physical effects such as [O I] $63\mu$m self-absorption, measuring the [C I]-bright but CO-dark molecular gas, and deriving a CO-to-H$_2$ conversion factor in agreement with observations.