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| Main Authors: | , |
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| Format: | Preprint |
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2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.15049 |
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| _version_ | 1866918162391367680 |
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| author | Baker, Fergus J. E. Young, Andrew J. |
| author_facet | Baker, Fergus J. E. Young, Andrew J. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_15049 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gradus.jl: spacetime-agnostic general relativistic ray-tracing for X-ray spectral modelling Baker, Fergus J. E. Young, Andrew J. High Energy Astrophysical Phenomena 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. |
| title | Gradus.jl: spacetime-agnostic general relativistic ray-tracing for X-ray spectral modelling |
| topic | High Energy Astrophysical Phenomena |
| url | https://arxiv.org/abs/2510.15049 |