Numerical and Analytical Modelling of Transit Time Variations

TL;DR

This paper introduces analytic and numerical methods to extract planetary masses and eccentricities from transit time variations, applying them to Kepler planets and revealing generally low densities and small eccentricities.

Contribution

It provides new analytic formulas for TTVs including resonances and applies N-body MCMC to analyze previously unstudied Kepler planets.

Findings

Most planets have low densities.

Small eccentricities of a few percent or less are measured.

Analytic expressions help resolve degeneracies in TTV analysis.

Abstract

We develop and apply methods to extract planet masses and eccentricities from observed transit time variations (TTVs). First, we derive simple analytic expressions for the TTV that include the effects of both first- and second-order resonances. Second, we use N-body Markov chain Monte Carlo (MCMC) simulations, as well as the analytic formulae, to measure the masses and eccentricities of ten planets discovered by Kepler that have not previously been analyzed. Most of the ten planets have low densities. Using the analytic expressions to partially circumvent degeneracies, we measure small eccentricities of a few percent or less.