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

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.