The resilience of Kepler systems to stellar obliquity

TL;DR

This paper investigates how stellar obliquity can destabilize Kepler planetary systems, potentially explaining the high number of single-transit systems and placing limits on stellar tilt in specific cases.

Contribution

It demonstrates that stellar obliquity-driven instability is common in Kepler systems, especially for stars with rapid rotation and significant tilt, and provides new constraints on stellar obliquity in certain systems.

Findings

Most analyzed systems become unstable with stellar spin periods below ~3 days and tilts around 30 degrees.

Upper limits on stellar obliquity are placed for systems like K2-38 (<20 degrees).

Up to half of super-Earth systems may experience this instability, aligning with the Kepler Dichotomy.

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 lead 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 (2016) 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 analysed, including those possessing only 2 planets, underwent instability for stellar spin periods below ~3 days and stellar tilts of order 30 degrees. Moreover, we are able to place upper limits on the stellar obliquity in systems such as K2-38 (obliquity <20 degrees), where other methods of measuring spin-orbit misalignment are not currently available. Given the known parameters of T-Tauri stars, we predict that up to 1/2 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.