Transit Timing Observations from Kepler: IV. Confirmation of 4 Multiple Planet Systems by Simple Physical Models

TL;DR

This paper confirms four multi-planet systems observed by Kepler through transit timing variations, demonstrating planetary interactions and constraining their masses and orbital parameters using simple physical models.

Contribution

It provides the first confirmation of multiple planets in these systems via transit timing variations and introduces a method to estimate planetary masses and orbits without Doppler data.

Findings

Transit timing variations confirm planetary nature of the systems.

Dynamical models constrain planetary masses and eccentricities.

Systems remain stable over long timescales.

Abstract

Eighty planetary systems of two or more planets are known to orbit stars other than the Sun. For most, the data can be sufficiently explained by non-interacting Keplerian orbits, so the dynamical interactions of these systems have not been observed. Here we present 4 sets of lightcurves from the Kepler spacecraft, which each show multiple planets transiting the same star. Departure of the timing of these transits from strict periodicity indicates the planets are perturbing each other: the observed timing variations match the forcing frequency of the other planet. This confirms that these objects are in the same system. Next we limit their masses to the planetary regime by requiring the system remain stable for astronomical timescales. Finally, we report dynamical fits to the transit times, yielding possible values for the planets' masses and eccentricities. As the timespan of timing data increases, dynamical fits may allow detailed constraints on the systems' architectures, even in cases for which high-precision Doppler follow-up is impractical.