Transit Timing Variations for Inclined and Retrograde Exoplanetary Systems

TL;DR

This study investigates how transit timing variations (TTVs) caused by Earth-mass perturbers on Hot-Jupiters depend on planetary inclination, revealing that retrograde and highly inclined systems often produce undetectable TTV signals, affecting exoplanet detection strategies.

Contribution

It provides a detailed analysis of TTV amplitude variations across a wide range of inclinations, including retrograde systems, highlighting the importance of inclination effects in exoplanet detection.

Findings

Low order MMRs maintain constant TTV amplitudes up to 170° inclination.

High order MMRs show increased TTV amplitude around 45° inclination.

Retrograde systems generally have undetectable TTV signals unless high eccentricity or near resonance.

Abstract

We perform numerical calculations of the expected transit timing variations (TTVs) induced on a Hot-Jupiter by an Earth-mass perturber. Motivated by the recent discoveries of retrograde transiting planets, we concentrate on an investigation of the effect of varying relative planetary inclinations, up to and including completely retrograde systems. We find that planets in low order (E.g. 2:1) mean-motion resonances (MMRs) retain approximately constant TTV amplitudes for $0<\,^{\circ}i<170\,^{\circ}$, only reducing in amplitude for $i > 170\,^{\circ}$. Systems in higher order MMRs (E.g. 5:1) increase in TTV amplitude as inclinations increase towards $45\,^{\circ}$, becoming approximately constant for $45 < i < 135$, and then declining for $i > 135\,^{\circ}$. Planets away from resonance slowly decrease in TTV amplitude as inclinations increase from 0 to 180, where-as planets adjacent to resonances can exhibit a huge range of variability in TTV amplitude as a function of both eccentricity and inclination. For highly retrograde systems ($135\,^{\circ} < i \leq 180\,^{\circ}$), TTV signals will be undetectable across almost the entirety of parameter space, with the exceptions occurring when the perturber has high eccentricity or is very close to a MMR. This high inclination decrease in TTV amplitude (on and away from resonance) is important for the analysis of the known retrograde and multi-planet transiting systems, as inclination effects need to be considered if TTVs are to be used to exclude the presence of any putative planetary companions: absence of evidence is not evidence of absence.