Mutually-inclined planetary companions may be identified by the torque they exert on transiting planets, inducing orbit precession that can cause change of transit duration. Systems with multiple planets and significant mutual inclinations have boosted probability of detection as a single transiting planet. So this method is biased towards highly inclined systems, just as the methods involving multiple transiting planets are biased towards low-inclination systems. Kepler's long time span and high photometric precision for a large sample of planets makes it an excellent dataset for detecting duration changes and studying the general features of the population of mutual inclinations in multiple systems. For the first time, we examined all Kepler transiting planets with high enough S/N, detecting about 30 significant duration changes out of 600 planets. We used our results to constrain the distribution of mutual inclinations of multiple planetary systems as a function of their different astrophysical parameters. For example, we find that planets with larger orbital periods display larger duration change rates, probably because they have companions with larger mutual inclinations. This correlation was not explicitly anticipated theoretically, but we discuss several possible interpretations.
