Systemic: A Testbed for Characterizing the Detection of Extrasolar Planets. II. Numerical approaches to the Transit Timing Inverse Problem

TL;DR

This paper explores numerical methods to solve the inverse problem of determining orbital elements of perturbing bodies from transit timing variations, emphasizing the role of radial velocity data in resolving degeneracies.

Contribution

It introduces approaches for analyzing transit timing variations to infer properties of unseen planets, highlighting the importance of combined radial velocity measurements.

Findings

Radial velocity data can significantly reduce solution degeneracies.

Numerical methods can effectively characterize non-resonant and resonant planetary systems.

Insights into planetary interior structures can be gained through transit timing analysis.

Abstract

Transit timing variations - deviations from strict periodicity between successive passages of a transiting planet - can be used to probe the structure and dynamics of multiple-planet systems. In this paper, we examine prospects for numerically solving the so-called inverse problem, the determination of the orbital elements of a perturbing body from the transit timing variations it induces. We assume that the planetary systems under examination have a limited number of Doppler velocity measurements, and show that a more extensive radial velocity characterization with precision comparable to the semiamplitude of the perturber may remove degeneracies in the solution. We examine several configurations of interest, including (1) a prototypical non-resonant system, modeled after HD40307 b and c, which contains multiple super-Earth mass planets, (2) a hypothetical system containing a transiting giant planet with a terrestrial-mass companion trapped in low-order mean motion resonance, and (3) the HAT-P-13 system, in which forced precession by an outer perturbing body that is well characterized by Doppler radial velocity measurements can give insight into the interior structure of a perturbing planet, and for which the determination of mutual inclination between the transiting planet and its perturber is a key issue.