Detection of Laplace-resonant three-planet systems from transit timing variations

TL;DR

This paper investigates how transit timing variations (TTVs) can reveal the presence of Laplace-resonant three-planet systems, emphasizing the detection of characteristic periods and the importance of long-term observations.

Contribution

It provides a dynamical analysis of TTVs in Laplace-resonant three-planet systems, identifying key periods and their detectability based on system configurations.

Findings

Three characteristic periods are identified in TTVs for certain configurations.

TTVs can distinguish between different resonant planetary arrangements.

Long-term TTV observations are crucial for detecting and constraining resonant systems.

Abstract

Transit timing variations (TTVs) are useful to constrain the existence of perturbing planets, especially in resonant systems where the variations are strongly enhanced. Here we focus on Laplace-resonant three-planet systems, and assume the inner planet transits the star. A dynamical study is performed for different masses of the three bodies, with a special attention to terrestrial planets. We consider a maximal time-span of ~ 100 years and discuss the shape of the inner planet TTVs curve. Using frequency analysis, we highlight the three periods related to the evolution of the system: two periods associated with the Laplace-resonant angle and the third one with the precession of the pericenters. These three periods are clearly detected in the TTVs of an inner giant planet perturbed by two terrestrial companions. Only two periods are detected for a Jupiter-Jupiter-Earth configuration (the ones associated with the giant interactions) or for three terrestrial planets (the Laplace periods). However, the latter system can be constrained from the inner planet TTVs. We finally remark that the TTVs of resonant three or two Jupiter systems mix up, when the period of the Laplace resonant angle matches the pericenter precession of the two-body configuration. This study highlights the importance of TTVs long-term observational programs for the detection of multiple-planet resonant systems.