The Resilience of Kepler Systems to Stellar Obliquity

Abstract

The Kepler mission and its successor K2 have brought forth a cascade of transiting planets. Many of these planetary systems exhibit multiple members, but a large fraction possess only a single transiting example. This overabundance of singles has led to the suggestion that up to half of Kepler systems might possess significant mutual inclinations between orbits, reducing the transiting number (the so-called "Kepler Dichotomy"). In a recent paper, Spalding & Batygin demonstrated that the quadrupole moment arising from a young, oblate star is capable of misaligning the constituent orbits of a close-in planetary system enough to reduce their transit number, provided that the stellar spin axis is sufficiently misaligned with respect to the planetary orbital plane. Moreover, tightly packed planetary systems were shown to be susceptible to becoming destabilized during this process. Here, we investigate the ubiquity of the stellar obliquity-driven instability within systems with a range of multiplicities. We find that most planetary systems analyzed, including those possessing only two planets, underwent instability for stellar spin periods below ~3 days and stellar tilts of order 30°. Moreover, we are able to place upper limits on the stellar obliquity in systems such as K2-38 (obliquity lesssim20°), where other methods of measuring the spin–orbit misalignment are not currently available. Given the known parameters of T-Tauri stars, we predict that up to one-half of super-Earth-mass systems may encounter the instability, in general agreement with the fraction typically proposed to explain the observed abundance of single-transiting systems.