Dynamics of stellar spin driven by planets undergoing Lidov–Kozai migration: paths to spin–orbit misalignment

At least two arguments suggest that the orbits of a large fraction of binary stars and extrasolar planets shrank by 1-2 orders of magnitude after formation: (i) the physical radius of a star shrinks by a large factor from birth to the main sequence, yet many main-sequence stars have companions orbiting only a few stellar radii away, and (ii) in current theories of planet formation, the region within ~0.1 AU of a protostar is too hot and rarefied for a Jupiter-mass planet to form, yet many "hot Jupiters" are observed at such distances. We investigate orbital shrinkage by the combined effects of secular perturbations from a distant companion star (Kozai oscillations) and tidal friction. We integrate the relevant equations of motion to predict the distribution of orbital elements produced by this process. Binary stars with orbital periods of 0.1 to 10 days, with a median of ~2 d, are produced from binaries with much longer periods (10 d to 10^5 d), consistent with observations indicating that most or all short-period binaries have distant companions (tertiaries). We also make two new testable predictions: (1) For periods between 3 and 10 d, the distribution of the mutual inclination between the inner binary and the tertiary orbit should peak strongly near 40 deg and 140 deg. (2) Extrasolar planets whose host stars have a distant binary companion may also undergo this process, in which case the orbit of the resulting hot Jupiter will typically be misaligned with the equator of its host star.

The basic geometry of the Solar System -- the shapes, spacings, and orientations of the planetary orbits -- has long been a subject of fascination as well as inspiration for planet formation theories. For exoplanetary systems, those same properties have only recently come into focus. Here we review our current knowledge of the occurrence of planets around other stars, their orbital distances and eccentricities, the orbital spacings and mutual inclinations in multiplanet systems, the orientation of the host star's rotation axis, and the properties of planets in binary-star systems.

We provide evidence that the obliquities of stars with close-in giant planets were initially nearly random, and that the low obliquities that are often observed are a consequence of star-planet tidal interactions. The evidence is based on 14 new measurements of the Rossiter-McLaughlin effect (for the systems HAT-P-6, HAT-P-7, HAT-P-16, HAT-P-24, HAT-P-32, HAT-P-34, WASP-12, WASP-16, WASP-18, WASP-19, WASP-26, WASP-31, Gl 436, and Kepler-8), as well as a critical review of previous observations. The low-obliquity (well-aligned) systems are those for which the expected tidal timescale is short, and likewise the high-obliquity (misaligned and retrograde) systems are those for which the expected timescale is long. At face value, this finding indicates that the origin of hot Jupiters involves dynamical interactions like planet-planet interactions or the Kozai effect that tilt their orbits, rather than inspiraling due to interaction with a protoplanetary disk. We discuss the status of this hypothesis and the observations that are needed for a more definitive conclusion.