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arXiv · 2510.15049

Gradus.jl: spacetime-agnostic general relativistic ray-tracing for X-ray spectral modelling

Fergus J. E. Baker·Andrew J. Young
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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.

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Fergus J. E. Baker, Andrew J. Young. 2025-10-16. Gradus.jl: spacetime-agnostic general relativistic ray-tracing for X-ray spectral modelling. https://doi.org/10.1093/mnras%2Fstaf1770

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