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The Effect of Conjunctions on the Transit Timing Variations of Exoplanets

We develop an analytic model for transit timing variations produced by orbital conjunctions between gravitationally interacting planets. If the planetary orbits have tight orbital spacing, which is a common case among the Kepler planets, the effect of a single conjunction can be best described as: (1) a step-like change of the transit timing ephemeris with subsequent transits of the inner planet being delayed and those of the outer planet being sped up, and (2) a discrete change in sampling of the underlying oscillations from eccentricity-related interaction terms. In the limit of small orbital eccentricities, our analytic model gives explicit equations for these effects as a function of the mass and orbital separation of planets. We point out that a detection of the conjunction effect in real data is of crucial importance for the physical characterization of planetary systems from transit timing variations.