The distribution of mutual inclinations arising from the stellar quadrupole moment

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.

A General Origin for Multi-Planetary Systems With Significantly Misaligned USP Planets

“…In the TOI-125 system, the planets likely arrived into their observed locations early enough that the dynamics in this paper was allowed to operate. If the planets migrated inwards too late, then 𝐽 2 would have decayed sufficiently such that the inclination-exciting dynamics would no longer operate; see Figure 6, which shows that for this particular geometry, the dynamics no longer actively alters orbits after a 𝐽 2 of 10 −6 or so (see also discussion in Schultz et al 2021). The mechanism described in this paper will not occur for planets will sufficiently large orbital radii.…”

A General Origin for Multiplanetary Systems With Significantly Misaligned USP Planets

“…In the TOI-125 system, the planets likely arrived into their observed locations early enough that the dynamics in this paper was allowed to operate. If the planets migrated inwards too late, then J 2 would have decayed sufficiently such that the inclination-exciting dynamics would no longer operate; see Figure 6, which shows that for this particular geometry, the dynamics no longer actively alters orbits after a J 2 of 10 −6 or so (see also discussion in Schultz et al 2021). The mechanism described in this paper will not occur for planets will sufficiently large orbital radii.…”

Mutual Inclination of Ultra-Short-Period Planets with Time Varying Stellar J2-moment

“…USP orbits are typically circular due to fast tidal circularization timescales (Winn et al 2018), and the timescales of orbital decay and spin-alignment on the inner planet are much longer than those of planet-planet interaction (e.g., Rodriguez et al (2018); Becker et al (2020)), thus we assume the planets to be near circular and we neglect tidal effects in this work. We note that larger mutual inclination above ∼ 40 • could lead to eccentricity excitation of the USPs due to von Zeipel-Lidov-Kozai oscillations, and this could also lead to instability (e.g., Spalding & Batygin 2016;Schultz et al 2021), when the General Relativity (GR) effect is not sufficient to prevent the eccentricity excitation (e.g., Faridani et al 2021). Thus, we only consider lower mutual inclinations below 40 • with near circular orbits in our study.…”

“…Larger initial obliquity leads to larger final mutual inclination. Note that, if the final J 2 is small enough (∼ 10 −9 , close to 0), the final oscillation amplitude of the mutual inclination should be ∼ 0 (e.g., Schultz et al 2021) for both initial configurations regardless earlier or later arrival time.…”

“…Considering the stellar quadrupole moment and a planetary companion as two mechanisms, Becker et al (2020) suggested that these two processes can produce a misalignment between the USP and the tightly packed co-planar planets. Moreover, found that the stellar oblateness has a stronger influence than a distant giant and it is able to excite the mutual inclination with a rapid disk-dispersal, and Schultz et al (2021) found that a large J 2 could enhance mutual inclination and lead to orbital instability. For general planetary systems, Spalding & Batygin (2016) found that the significant misalignment between the orbital planes can be excited and the system can also undergo the dynamical instability for planets orbiting around a tilted star with a decreasing stellar oblateness (J 2 ).…”