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Abstract We fit a dynamical model to Kepler systems that contain four or more transiting planets using the analytic method AnalyticLC and obtain physical and orbital parameters for 101 planets in 23 systems, of which 95 are of mass significance better than 3 σ , and 46 are without previously reported mass constraints or upper limits. In addition, we compile a list of 71 Kepler objects of interest that display significant transit impact parameter variations (TbVs), complementing our previously published work on two- and three-transiting-planet systems. Together, these works include the detection of significant TbV signals of 130 planets, which is, to our knowledge, the largest catalog of this type to date. The results indicate that the typical detectable TbV rate in the Kepler population is of order 10 −2 yr −1 and that rapid TbV rates (≳0.05 yr −1 ) are observed only in systems that contain a transiting planet with an orbital period less than ∼20 days. The observed TbV rates are only weakly correlated with orbital period within Kepler’s ≲100-day-period planets. If this extends to longer periods, it implies a limit on the utility of the transit technique for long-period planets. The TbVs we find may not be detectable in direct impact parameter measurements, but rather are inferred from the full dynamics of the system, encoded in all types of transit variations. Finally, we find evidence that the mutual inclination distribution is qualitatively consistent with the previously suggested angular momentum deficit model using an independent approach.
Judkovsky et al. (Mon,) studied this question.