The Kepler Mission has detected dozens of compact planetary systems with more than four transiting planets. This sample provides a collection of close-packed planetary systems with relatively little spread in the inclination angles of the inferred orbits. A large fraction of the observational sample contains limited multiplicity, begging the question whether there is a true diversity of multi transiting systems, or if some systems merely possess high mutual inclinations, allowing them to appear as single-transiting systems in a transit-based survey. This paper begins an exploration of the effectiveness of dynamical mechanisms in exciting orbital inclination within exoplanetary systems of this class. For these tightly packed systems, we determine that the orbital inclination angles are not spread out appreciably through self-excitation. In contrast, the two Kepler multi-planet systems with additional non-transiting planets are susceptible to oscillations of their inclination angles, which means their currently observed configurations could be due to planet-planet interactions alone. We also provide constraints and predictions for the expected transit duration variations (TDVs) for each planet. In these multi-planet compact Kepler systems, oscillations of their inclination angles are remarkably hard to excite; as a result, they tend to remain continually mutually transiting (CMT-stable). We study this issue further by augmenting the planet masses and determining the enhancement factor required for oscillations to move the systems out of transit. The oscillations of inclination found here inform the recently suggested dichotomy in the sample of solar systems observed by Kepler.
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