WHFAST: a fast and unbiased implementation of a symplectic Wisdom-Holman integrator for long-term gravitational simulations
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We present WHFast, a fast and accurate implementation of a Wisdom-Holman symplectic integrator for long-term orbit integrations of planetary systems. WHFast is significantly faster and conserves energy better than all other Wisdom-Holman integrators tested. We achieve this by significantly improving the Kepler-solver and ensuring numerical stability of coordinate transformations to and from Jacobi coordinates. These refinements allow us to remove the linear secular trend in the energy error that is present in other implementations. For small enough timesteps we achieve Brouwer's law, i.e. the energy error is dominated by an unbiased random walk due to floating-point round-off errors. We implement symplectic correctors up to order eleven that significantly reduce the energy error. We also implement a symplectic tangent map for the variational equations. This allows us to efficiently calculate two widely used chaos indicators the Lyapunov characteristic number (LCN) and the Mean Exponential Growth factor of Nearby Orbits (MEGNO). WHFast is freely available as a flexible C package, as a shared library, and as an easy-to-use python module.
Subfields: Numerical Analysis, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/f2e89a827a27b19641c5a8a6eeccd8b6409e39f5
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In Numerical Analysis
In Statistical and Nonlinear Physics
Citations in the corpus
- REBOUNDx: a library for adding conservative and dissipative forces to otherwise symplectic N-body integrations (2019, methodology): “In our typical example where the orbits are not too close, this is approximately the orbital period of the innermost planet; for a very eccentric orbit, T would be the much shorter timescale for pericentre passage (e.g., Rauch & Holman 1999; Rein & Tamayo 2015b), etc.”
- Characterization of the K2-18 multi-planetary system with HARPS: A habitable zone super-Earth and discovery of a second, warm super-Earth on a non-coplanar orbit (2017, methodology): “The system is then integrated forward in time from the epoch of the first K2 photometric observation (BJD = 2 456 810.26222) for 106 yr using the Wisdom-Holman symplectic integrator WHFast (Rein & Tamayo 2015) implemented in the open-source REBOUND Nbody package (Rein & Liu 2012).”
- Kepler Planet Masses and Eccentricities from TTV Analysis (2016, methodology): “Each integration is run for 106 orbits of the innermost planet using the REBOUND code’s WHFast integrator (Rein & Tamayo 2015).”