TTVFast: An efficient and accurate code for transit timing inversion problems

Abstract

Transit timing variations (TTVs) have proven to be a powerful technique for confirming Kepler planet candidates, for detecting non-transiting planets, and for constraining the masses and orbital elements of multi-planet systems. These TTV applications often require the numerical integration of orbits for computation of transit times (as well as impact parameters and durations); frequently tens of millions to billions of simulations are required when running statistical analyses of the planetary system properties. We have created a fast code for transit timing computation, TTVFast, which uses a symplectic integrator with a Keplerian interpolator for the calculation of transit times (Nesvorny et al. 2013). The speed comes at the expense of accuracy in the calculated times, but the accuracy lost is largely unnecessary, as transit times do not need to be calculated to accuracies significantly smaller than the measurement uncertainties on the times. The time step can be tuned to give sufficient precision for any particular system. We find a speed-up of at least an order of magnitude relative to dynamical integrations with high precision using a Bulirsch-Stoer integrator.

Submitted to ApJ. Our code is available in both C and Fortran at: http://github.com/kdeck/TTVFast . If you download this version, please check back after the referee process for a possibly updated version

References in corpus (2)

• Kepler constraints on planets near hot Jupiters
• Alignment of the stellar spin with the orbits of a three-planet system

Cited by in corpus (13)

• Seven temperate terrestrial planets around the nearby ultracool dwarf star TRAPPIST-1
• Eclipse Timing Variation Analyses of Eccentric Binaries with Close Tertiaries in the Kepler field
• 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
• Planet Hunters VII. Discovery of a New Low-Mass, Low-Density Planet (PH3 c) Orbiting Kepler-289 with Mass Measurements of Two Additional Planets (PH3 b and d)
• TRADES: A new software to derive orbital parameters from observed transit times and radial velocities. Revisiting Kepler-11 and Kepler-9
• The Effect of Conjunctions on the Transit Timing Variations of Exoplanets
• Pinning down the mass of Kepler-10c: the importance of sampling and model comparison
• Measuring the Galactic Distribution of Transiting Planets with WFIRST
• Eccentric Companions to Kepler-448b and Kepler-693b: Clues to the Formation of Warm Jupiters
• A spectral approach to transit timing variations
• Mass Constraints of the WASP-47 Planetary System from Radial Velocities
• Photo-Dynamical Analysis of Three Kepler Objects of Interest with Significant Transit Timing Variations
• The origin and 9:7 MMR dynamics of the Kepler-29 system