Measurement of planet masses with transit timing variations due to synodic "chopping" effects

TL;DR

This paper introduces simple analytic formulas for transit timing variation 'chopping' signals caused by planetary interactions, enabling mass measurements of exoplanets without complex dynamical modeling, especially near mean motion resonances.

Contribution

The authors derive and validate analytic formulae for TTV chopping signals that allow for direct planetary mass determination without full dynamical simulations.

Findings

Chopping signals can uniquely determine planetary masses.

Formulas are accurate for eccentricities e <~ 0.1.

Application to Kepler systems confirms the method's effectiveness.

Abstract

Gravitational interactions between planets in transiting exoplanetary systems lead to variations in the times of transit that are diagnostic of the planetary masses and the dynamical state of the system. Here we show that synodic "chopping" contributions to these transit timing variations (TTVs) can be used to uniquely measure the masses of planets without full dynamical analyses involving direct integration of the equations of motion. We present simple analytic formulae for the chopping signal, which are valid (generally <10% error) for modest eccentricities e <~ 0.1. Importantly, these formulae primarily depend on the mass of the perturbing planet, and therefore the chopping signal can be used to break the mass/free-eccentricity degeneracy which can appear for systems near first order mean motion resonances. Using a harmonic analysis, we apply these TTV formulae to a number of Kepler systems which had been previously analyzed with full dynamical analyses. We show that when chopping is measured, the masses of both planets can be determined uniquely, in agreement with previous results, but without the need for numerical orbit integrations. This demonstrates how mass measurements from TTVs may primarily arise from an observable chopping signal. The formula for chopping can also be used to predict the number of transits and timing precision required for future observations, such as those made by TESS or PLATO, in order to infer planetary masses through analysis of TTVs.