The distribution of mutual inclinations arising from the stellar quadrupole moment

TL;DR

This paper investigates how the stellar quadrupole moment influences mutual inclinations in planetary systems, explaining observed trends and predicting that a subset of systems may be intrinsically single due to dynamical instabilities.

Contribution

It introduces a simulation of planetary systems affected by stellar quadrupolar potential, revealing its role in mutual inclination distribution and potential for inducing dynamical instabilities.

Findings

Reproduces the increase in mutual inclinations with proximity to the star.

Suggests 5-10% of low-mass Kepler systems are prone to instability.

Links stellar obliquity reduction to dynamical instability.

Abstract

A large proportion of transiting planetary systems appear to possess only a single planet as opposed to multiple transiting planets. This excess of singles is indicative of significant mutual inclinations existing within a large number of planetary systems, but the origin of these misalignments is unclear. Moreover, recent observational characterization reveals that mutual inclinations tend to increase with proximity to the host star. These trends are both consistent with the dynamical influence of a strong quadrupolar potential arising from the host star during its early phase of rapid rotation, coupled with a non-zero stellar obliquity. Here, we simulate a population of planetary systems subject to the secular perturbation arising from a tilted, oblate host star as it contracts and spins down subsequent to planet formation. We demonstrate that this mechanism can reproduce the general increase in planet-planet mutual inclinations with proximity to the host star, and delineate a parameter space wherein the host star can drive dynamical instabilities. We suggest that approximately 5-10\% of low-mass Kepler systems are susceptible to this instability mechanism, suggesting that a significant number of single-transiting planets may truly be intrinsically single. We also report a novel connection between instability and stellar obliquity reduction and make predictions that can be tested within upcoming TESS observations.