Gradus.jl: spacetime-agnostic general relativistic ray-tracing for X-ray spectral modelling
Abstract
We introduce Gradus.jl, an open-source and publicly available general relativistic ray-tracing toolkit for spectral modelling in arbitrary spacetimes. Our software is written in the Julia programming language, making use of forward-mode automatic differentiation for computing the Christoffel symbols during geodesic integration, and for propagating derivatives through the entire ray-tracer. Relevant numerical methods are detailed, and our models are validated using a number of tests and comparisons to other codes. The differentiability is used to optimally calculate Cunningham transfer functions -- used to efficiently pre-compute relativistic effects in spectral models. A method is described for calculating such transfer functions for disc with non-zero vertical height, including the treatment of self-obscuration. An extension of the transfer function formalism that includes timing information is described, and used to calculate high-resolution reverberation lag spectra for a lamppost corona. The lag-frequency and lag-energy spectra for a Shakura-Sunyaev accretion disc with various lamppost heights and Eddington ratios are calculated, and the general impact of disc thickness in reflection models is discussed.
Keywords
Cite
@article{arxiv.2510.15049,
title = {Gradus.jl: spacetime-agnostic general relativistic ray-tracing for X-ray spectral modelling},
author = {Fergus J. E. Baker and Andrew J. Young},
journal= {arXiv preprint arXiv:2510.15049},
year = {2025}
}
Comments
17 pages, 19 figures; accepted MNRAS