Testing the Titius-Bode law predictions for Kepler multiplanet systems

Abstract

We use three and half years of Kepler long-cadence data to search for the 97 predicted planets of Bovaird & Lineweaver in 56 of the multiplanet systems, based on a general Titius–Bode (TB) relation. Our search yields null results in the majority of systems. We detect five planetary candidates around their predicted periods. We also find an additional transit signal beyond those predicted in these systems. We discuss the possibility that the remaining predicted planets are not detected in the Kepler data due to their non-coplanarity or small sizes. We find that the detection rate is beyond the lower boundary of the expected number of detections, which indicates that the prediction power of the TB relation in general extrasolar planetary systems is questionable. Our analysis of the distribution of the adjacent period ratios of the systems suggests that the general TB relation may overpredict the presence of planet pairs near the 3:2 resonance.