Transit timing to first order in eccentricity

TL;DR

This paper derives simple analytic formulas for transit timing variations in multi-planet systems, accurate to first order in eccentricity and mass ratios, aiding characterization of exoplanets.

Contribution

It introduces novel first-order analytic formulae for TTVs applicable near and away from resonances, validated against N-body simulations and real Kepler data.

Findings

Formulas accurately predict TTVs in low eccentricity, low mass-ratio systems.

Validated formulas against N-body simulations and Kepler data.

Code implementation provided for practical use.

Abstract

Characterization of transiting planets with transit timing variations (TTVs) requires understanding how to translate the observed TTVs into masses and orbital elements of the planets. This can be challenging in multi-planet transiting systems, but fortunately these systems tend to be nearly plane-parallel and low eccentricity. Here we present a novel derivation of analytic formulae for TTVs that are accurate to first order in the planet-star mass ratios and in the orbital eccentricities. These formulae are accurate in proximity to first order resonances, as well as away from resonance, and compare well with more computationally expensive N-body integrations in the low eccentricity, low mass-ratio regime when applied to simulated and to actual multi-transiting Kepler planet systems. We make code available for implementing these formulae.