Ultra Short Period Planets and their Nearby Companions
Systems of tightly packed inner planets (STIPs) occur in about 20-30% of systems (Muirhead 2015, Zhu 2018). STIPs generally have many planets residing within 0.5 AU or so of their host stars, and are fairly well-confined in orbital inclination. Ultra-short period planets (USPs), defined as those with orbital periods less than a day, occur in roughly 0.5% of systems (Sanchis-Ojeda 2014). Once a sufficiently large sample of both types of planets had been assembled by Kepler, Dai et al. (2018) showed that USPs tend to have a larger range of mutual inclination with their nearby planets than longer-period planets. Sometimes, a STIP will host an USP, and these systems serve as prime case studies to examine this effect.
The K2-266 system, discovered in Rodriguez, Becker, et al. (2018), is a perfect example of the overlap between USPs and STIPs, where the USP shows a large mutual inclination with respect to the STIP while the STIP internally has low mutual inclination. In this way, K2-266 resides in two dynamical states, with the outer system being compact with a low range in orbital inclination, and the inner planet being misaligned with respect to the STIP by a significant 14-17 degrees. Additionally, two of the planets in this system are close to a 4:3 mean motion resonance, which is suggestive of a disk-driven migratory history.
this work, please see my 2020 DDA talk.
In Becker, Batygin, Fabrycky, et al. (2020), we consider how the geometry described above could have arisen. Starting from a totally coplanar system (if the USP and STIP all form in an unbroken protoplanetary disk, then this should have been the initial condition), then some mechanism must misalign the USP from the STIP while still keeping the mutual inclinations of the STIP low. We find that there are two options that can cause the system geometry we see today: an additional unseen companion, or a slight stellar obliquity. In the former option, some particular choices of orbital parameters for an additional companion would cause the USP to decouple from the STIP while still allowing the STIP inclinations to remain similar to each other. It is possible that this unseen companion could be detected observationally in the future, so we will have to wait and see. For the latter option (the stellar obliquity), a slight misalignment of the stellar spin axis with the planetary orbital angular momenta could allow the USP and STIP to reside in dynamically distinct states. For some values of the stellar quadrupole moment, this could also recreate the geometry of the K2-266 system.
Although at the current time we cannot determine which of these mechanisms was more important in the K2-266 systems, future observations and more theoretical work will make it easier to figure out! For more on applying the ideas described above (stellar obliquity and the stellar quadrupole moment affecting the inclinations of close-in planets) to a larger set of systems, also see Li, Dai, and Becker (2020).