Degeneracy in the characterization of non-transiting planets from transit timing variations

Abstract

The transit timing variation (TTV) method allows the detection of non-transiting planets through their gravitational perturbations. Since TTVs are strongly enhanced in systems close to mean-motion resonances (MMR), even a low mass planet can produce an observable signal. This technique has thus been proposed to detect terrestrial planets. In this letter, we analyse TTV signals for systems in or close to MMR in order to illustrate the difficulties arising in the determination of planetary parameters. TTVs are computed numerically with an n-body integrator for a variety of systems close to MMR. The main features of these TTVs are also derived analytically. Systems deeply inside MMR do not produce particularly strong TTVs, while those close to MMR generate quasiperiodic TTVs characterised by a dominant long period term and a low amplitude remainder. If the remainder is too weak to be detected, then the signal is strongly degenerate and this prevents the determination of the planetary parameters. Even though an Earth mass planet can be detected by the TTV method if it is close to a MMR, it may not be possible to assert that this planet is actually an Earth mass planet. On the other hand, if the system is right in the center of a MMR, the high amplitude oscillation of the TTV signal vanishes and the detection of the perturber becomes as difficult as it is far from MMR.