Evidence for a Non-Dichotomous Solution to the Kepler Dichotomy: Mutual Inclinations of Kepler Planetary Systems from Transit Duration Variations

Early analyses of exoplanet statistics from the Kepler Mission revealed that a model population of multiple-planet systems with low mutual inclinations (${\sim1^{\circ}-2^{\circ}}$) adequately describes the multiple-transiting systems but underpredicts the number of single-transiting systems. This so-called "Kepler dichotomy" signals the existence of a sub-population of multi-planet systems possessing larger mutual inclinations. However, the details of these inclinations remain uncertain. In this work, we derive constraints on the intrinsic mutual inclination distribution by statistically exploiting Transit Duration Variations (TDVs) of the Kepler planet population. When planetary orbits are mutually inclined, planet-planet interactions cause orbital precession, which can lead to detectable long-term changes in transit durations. These TDV signals are inclination-sensitive and have been detected for roughly two dozen Kepler planets. We compare the properties of the Kepler observed TDV detections to TDV detections of simulated planetary systems constructed from two population models with differing assumptions about the mutual inclination distribution. We find strong evidence for a continuous distribution of relatively low mutual inclinations that is well-characterized by a power law relationship between the median mutual inclination ($\tilde{\mu}_{i,n}$) and the intrinsic multiplicity ($n$): $\tilde{\mu}_{i,n} = \tilde{\mu}_{i,5}(n/5)^{\alpha}$, where $\tilde{\mu}_{i,5} = 1.10^{+0.15}_{-0.11}$ and $\alpha = -1.73^{+0.09}_{-0.08}$. These results suggest that late-stage planet assembly and possibly stellar oblateness are the dominant physical origins for the excitation of Kepler planet mutual inclinations.