Shrinking Binary and Planetary Orbits by Kozai Cycles with Tidal Friction

Abstract

At least two arguments suggest that the orbits of a large fraction of binary\nstars and extrasolar planets shrank by 1-2 orders of magnitude after formation:\n(i) the physical radius of a star shrinks by a large factor from birth to the\nmain sequence, yet many main-sequence stars have companions orbiting only a few\nstellar radii away, and (ii) in current theories of planet formation, the\nregion within ~0.1 AU of a protostar is too hot and rarefied for a Jupiter-mass\nplanet to form, yet many "hot Jupiters" are observed at such distances. We\ninvestigate orbital shrinkage by the combined effects of secular perturbations\nfrom a distant companion star (Kozai oscillations) and tidal friction. We\nintegrate the relevant equations of motion to predict the distribution of\norbital elements produced by this process. Binary stars with orbital periods of\n0.1 to 10 days, with a median of ~2 d, are produced from binaries with much\nlonger periods (10 d to 10^5 d), consistent with observations indicating that\nmost or all short-period binaries have distant companions (tertiaries). We also\nmake two new testable predictions: (1) For periods between 3 and 10 d, the\ndistribution of the mutual inclination between the inner binary and the\ntertiary orbit should peak strongly near 40 deg and 140 deg. (2) Extrasolar\nplanets whose host stars have a distant binary companion may also undergo this\nprocess, in which case the orbit of the resulting hot Jupiter will typically be\nmisaligned with the equator of its host star.\n