Tidal circularization

Abstract: Observations in the past decade have revealed extrasolar planets with a wide range of orbital semimajor axes and eccentricities. Based on the present understanding of planet formation via core accretion and oligarchic growth, we expect that giant planets often form in closely packed configurations. While the protoplanets are embedded in a protoplanetary gas disk, dissipation can prevent eccentricity growth and suppress instabilities from becoming manifest. However, once the disk dissipates, eccentricities can grow rapidly, leading to close encounters between planets. Strong planet-planet gravitational scattering could produce both high eccentricities and, after tidal circularization, very short period planets, as observed in the exoplanet population. We present new results for this scenario based on extensive dynamical integrations of systems containing three giant planets, both with and without residual gas disks. We assign the initial planetary masses and orbits in a realistic manner following the core accretion model of planet formation. We show that, with realistic initial conditions, planet-planet scattering can reproduce quite well the observed eccentricity distribution. Our results also make testable predictions for the orbital inclinations of short-period giant planets formed via strong planet scattering followed by tidal circularization.

Abstract: The exosolar planet HD 80606b has a highly eccentric (e = 0.93) and tight (a = 0.47 AU) orbit. We study how it might arrive at such an orbit and how it has avoided being tidally circularized until now. The presence of a stellar companion to the host star suggests the possibility that the Kozai mechanism and tidal dissipation combined to draw the planet inward well after it formed: Kozai oscillations produce periods of extreme eccentricity in the planet orbit, and the tidal dissipation that occurs during these periods of small pericenter distances leads to gradual orbital decay. We call this migration mechanism the "Kozai migration." It requires that the initial planet orbit be highly inclined relative to the binary orbit. For a companion at 1000 AU and an initial planet orbit at 5 AU, the minimum relative inclination required is ~85°. We discuss the efficiency of tidal dissipation inferred from the observations of exoplanets. Moreover, we investigate possible explanations for the velocity residual (after the motion induced by the planet is removed) observed on the host star: a second planet in the system is excluded over a large extent of semimajor axis space if Kozai migration is to work, and the tide raised on the star by HD 80606b is likely too small in amplitude. Last, we discuss the relevance of Kozai migration for other planetary systems.

Abstract: We have investigated the formation of close-in extrasolar giant planets through a coupling effect of mutual scattering, the Kozai mechanism, and tidal circularization, by orbital integrations. Close-in gas giants would have been originally formed at several AU beyond the ice lines in protoplanetary disks and migrated close to their host stars. Although type II migration due to planet-disk interactions may be a major channel for the migration, we show that this scattering process would also give a nonnegligible contribution. We carried out orbital integrations of three planets with Jupiter mass, directly including the effect of tidal circularization. We have found that in about 30% of the runs close-in planets are formed, which is much higher than suggested by previous studies. Three-planet orbit crossing usually results in the ejection of one or two planets. Tidal circularization often occurs during three-planet orbit crossing, but previous studies have monitored only the final stage after the ejection, significantly underestimating the formation probability. We have found that the Kozai mechanism in outer planets is responsible for the formation of close-in planets. During three-planet orbital crossing, Kozai excitation is repeated and the eccentricity is often increased secularly to values close enough to unity for tidal circularization to transform the inner planet to a close-in planet. Since a moderate eccentricity can retain for the close-in planet, this mechanism may account for the observed close-in planets with moderate eccentricities and without nearby secondary planets. Since these planets also remain a broad range of orbital inclinations (even retrograde ones), the contribution of this process would be clarified by more observations of Rossiter-McLaughlin effects for transiting planets.

Abstract: We explore the possibility that the observed eccentricity distribution of extrasolar planets arose through planet-planet interactions, after the initial stage of planet formation was complete. Our results are based on ~3250 numerical integrations of ensembles of randomly constructed planetary systems, each lasting 100 Myr. We find that for a remarkably wide range of initial conditions the eccentricity distributions of dynamically active planetary systems relax toward a common final equilibrium distribution, well described by the fitting formula $dn p eexp [ − f{1}{2}(e/0.3)2] de$ -->. This distribution agrees well with the observed eccentricity distribution for -->e 0.2 but predicts too few planets at lower eccentricities, even when we exclude planets subject to tidal circularization. These findings suggest that a period of large-scale dynamical instability has occurred in a significant fraction of newly formed planetary systems, lasting 1-2 orders of magnitude longer than the ~1 Myr interval in which gas giant planets are assembled. This mechanism predicts no (or weak) correlations between semimajor axis, eccentricity, inclination, and mass in dynamically relaxed planetary systems. An additional observational consequence of dynamical relaxation is a significant population of planets (10%) that are highly inclined (25?) with respect to the initial symmetry plane of the protoplanetary disk; this population may be detectable in transiting planets through the Rossiter-McLaughlin effect.