insu-03748190
https://insu.hal.science/insu-03748190
https://insu.hal.science/insu-03748190/document
https://insu.hal.science/insu-03748190/file/stab2044.pdf
arxiv:2106.02188
doi:10.1093/mnras/stab2044
[INSU] INSU - Institut National des Sciences de l'Univers
[CNRS] CNRS - Centre national de la recherche scientifique
[IAP] Institut d'Astrophysique de Paris
[SORBONNE-UNIVERSITE] Sorbonne Université
[SORBONNE-UNIV] Sorbonne Université 01/01/2018
[SU-SCIENCES] Faculté des Sciences de Sorbonne Université
[SU-TI] Sorbonne Université - Texte Intégral
[ALLIANCE-SU] Alliance Sorbonne Université
A differentiable N-body code for transit timing and dynamical modelling - I. Algorithm and derivatives
Agol, Eric
Hernandez, David M.
Langford, Zachary
[SDU] Sciences of the Universe [physics]
[SDU.ASTR] Sciences of the Universe [physics]/Astrophysics [astro-ph]
ART
planetary systems
planets and satellites: dynamical evolution and stability
Astrophysics - Earth and Planetary Astrophysics
Astrophysics - Instrumentation and Methods for Astrophysics
Astrophysics - Solar and Stellar Astrophysics
When fitting N-body models to astronomical data - such as transit times, radial velocity, and astrometric positions at observed times - the derivatives of the model outputs with respect to the initial conditions can help with model optimization and posterior sampling. Here, we describe a general purpose symplectic integrator for arbitrary orbital architectures, including those with close encounters, which we have recast to maintain numerical stability and precision for small step sizes. We compute the derivatives of the N-body coordinates and velocities as a function of time with respect to the initial conditions and masses by propagating the Jacobian along with the N-body integration. For the first time, we obtain the derivatives of the transit times with respect to the initial conditions and masses using the chain rule, which is quicker and more accurate than using finite differences or automatic differentiation. We implement this algorithm in an open source package, NbodyGradient.jl, written in the JULIA language, which has been used in the optimization and error analysis of transit-timing variations in the TRAPPIST-1 system. We present tests of the accuracy and precision of the code, and show that it compares favourably in speed to other integrators that are written in C.
2021
2022-08-09
en
Monthly Notices of the Royal Astronomical Society
Oxford University Press (OUP): Policy P - Oxford Open Option A