Shrinking binary and planetary orbits by Kozai cycles with tidal friction

TL;DR

This paper explores how Kozai cycles combined with tidal friction can cause binary stars and exoplanets to migrate inward, explaining observed short-period systems and predicting specific orbital inclination distributions.

Contribution

It provides a detailed integration of equations showing how Kozai cycles with tidal friction can produce short-period binaries and hot Jupiters, with new testable predictions.

Findings

Short-period binaries likely formed from wider binaries via Kozai cycles and tidal friction.

Predicted inclination distribution peaks near 40° and 140° for certain periods.

Hot Jupiters may be misaligned with their host stars due to this process.

Abstract

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.