We have investigated the formation of close-in extrasolar giant planets through a coupling effect of mutual scattering, Kozai mechanism, and tidal circularization, by orbital integrations. We have carried out orbital integrations of three planets with Jupiter-mass, directly including the effect of tidal circularization. We have found that in about 30% runs close-in planets are formed, which is much higher than suggested by previous studies. We have found that Kozai mechanism by outer planets is responsible for the formation of close-in planets. During the three-planet orbital crossing, the 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 remain 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.
Based on a sample of 45 main-sequence solar-type spectroscopic binaries we find the tidal circularization cutoff in the open cluster NGC 188 (age 7 Gyr) to be well-defined at a period of 15.0 days. When compared to shorter tidal circularization cutoff periods in the younger clusters M67 and the Hyades, this result establishes that tidal circularization processes are effective in solar-type main-sequence binaries for timescales longer than 1 Gyr. This result is in contrast to the theoretical prediction by Zahn & Bouchet that tidal circularization due to equilibrium tides is ineffective for late…
We present a new homogeneous sample of 32 spectroscopic binary orbits in the young (~ 150 Myr) main-sequence open cluster M35. The distribution of orbital eccentricity vs. orbital period (e-log(P)) displays a distinct transition from eccentric to circular orbits at an orbital period of ~ 10 days. The transition is due to tidal circularization of the closest binaries. The population of binary orbits in M35 provide a significantly improved constraint on the rate of tidal circularization at an age of 150 Myr. We propose a new and more robust diagnostic of the degree of tidal circularization in a …
We present an ongoing study on tidal interactions in late-type close binary stars. New results on tidal circularization are combined with existing data to test and constrain theoretical predictions of tidal circularization in the pre-main-sequence (PMS) phase and throughout the main-sequence phase of stellar evolution. Current data suggest that tidal circularization during the PMS phase sets the tidal cutoff period for binary populations younger than ~1 Gyr. Binary populations older than ~1 Gyr show increasing tidal cutoff periods with age, consistent with active main-sequence tidal circulariz…
In recent years many binary minor planets (BMPs) have been discovered in the Solar system. Many models have been suggested for their formation, but these encounter difficulties explaining their observed characteristics. Here we show that secular perturbations by the Sun (Kozai mechanism) fundamentally change the evolution and the initial distribution of BMPs predicted by such models and lead to unique observational signatures. The Kozai mechanism can lead to a large periodic oscillations in the eccentricity and inclination of highly inclined BMP orbits, where we predict such effects to be obse…
We report on Keck and Hubble Space Telescope optical observations of the eclipsing binary pulsar system PSR B1718-19, in the direction of the globular cluster NGC 6342. These reveal a faint star ($m_{\rm F702W}=25.21\pm0.07$; Vega system) within the pulsar's 0\farcs5 radius positional error circle. This may be the companion. If it is a main-sequence star in the cluster, it has radius $\rcomp\simeq0.3 \rsun$, temperature $\teff\simeq3600 $K, and mass $\mcomp\simeq0.3 \msun$. In many formation models, however, the pulsar (spun up by accretion or newly formed) and its companion are initially in a…
A self-consistent model for binary evolution devised by Gingold \& Monaghan (1980) is used to show that two distinctly different types of behaviour are possible for close eccentric binaries. The model is based on a linear adiabatic normal mode analysis of the problem, which allows detailed examination of the transfer of energy from the orbit to the tides. We show that for most binaries, energy is exchanged quasi-periodically, with the system regulating itself so that the maximum tidal energy always remains small, and no circularization takes place. In contrast, for a range of eccentricities an…
This paper reviews the rich corpus of observational evidence for tidal effects in short-period binaries. We review the evidence for ellipsoidal variability and for the observational manifestation of apsidal motion in eclipsing binaries. Among the long-term effects, circularization was studied the most, and a transition period between circular and eccentric orbits has been derived for eight coeval samples of binaries. As binaries are supposed to reach synchronization before circularization, one can expect finding eccentric binaries in pseudo-synchronization state, the evidence for which is revi…
Strong tidal interaction with the central star can circularize the orbits of close-in planets. With the standard tidal quality factor Q of our solar system, estimated circularization times for close-in extrasolar planets are typically shorter than the ages of the host stars. While most extrasolar planets with orbital radii a < 0.1 AU indeed have circular orbits, some close-in planets with substantial orbital eccentricities have recently been discovered. This new class of eccentric close-in planets implies that either their tidal Q factor is considerably higher, or circularization is prevented …
A self-consistent, adiabatic model for the {\it long-time} behaviour of tidal capture binaries is presented. It is shown that most capture orbits behave chaotically, with the eccentricity following a quasi-random walk between the values of $\appless 1$ and some lower limit associated with the periastron separation at capture. If dissipation is taken into account, the binary goes through a short and violent chaotic phase, followed by a long quiescent phase in which it slowly circularizes from a high eccentricity on a much longer timescale than previously thought. A consequence is that merger is…
We investigate the possibility of substantial inflation of short-period Jupiter-mass planets, as a result of their internal tidal dissipation associated with the synchronization and circularization of their orbits. We employ the simplest prescription based on an equilibrium model with a constant lag angle for all components of the tide. We show that for young Jupiter-mass planets, with a period less than 3 days, an initial radius about 2 Jupiter radii, and an orbital eccentricity greater than 0.2, the energy dissipated during the circularization of their orbits is sufficiently intense and prot…
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…
The exo-solar 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 pericentre distances leads to gradual orbital decay. We call this migra…
Many recent observational studies have concluded that planetary systems commonly exist in multiple-star systems. At least ~20%, and presumably a larger fraction of the known extrasolar planetary systems are associated with one or more stellar companions. These stellar companions normally exist at large distances from the planetary systems (typical projected binary separations are on the orders 100-10000AU) and are often faint (ranging from F to T spectral types). Yet, secular cyclic angular momentum exchange with these distant stellar companions can significantly alter the orbital configuratio…
In this paper we develop a theory of disturbances induced by the stellar tidal field in a fully convective slowly rotating planet orbiting on a highly eccentric orbit around a central star. We show that there are two contributions to the mode energy and angular momentum gain due to impulsive tidal interaction: a) 'the quasi-static' contribution which requires dissipative processes operating in the planet; b) the dynamical contribution associated with excitation of modes of oscillation. These contributions are obtained self-consistently from a single set of the governing equations. We calculate…
We consider several processes operating during the late stages of planet formation that can affect observed orbital elements. Disk-planet interactions, tidal interactions with the central star, long term orbital instability and the Kozai mechanism are discussed.
A sample of spectroscopic binaries and a sample of single planetary systems, both having main-sequence solar-type primary components, are selected in order to compare their eccentricities. The positions of the objects in the (P.(1-e^2)^(3/2), e) plane is used to determine parts in the period-eccentricity diagram that are not affected by tidal circularization. The original eccentricities of binaries and planets are derived and compared. They seem to be weakly or not at all correlated with period in both samples, but two major differences are found :(1) The tidal circularization of planetary orb…
We present rotation periods for the solar-type primary stars in 13 close (a~< 5 AU) single-lined spectroscopic binaries with known orbital periods (P) and eccentricities (e). All binaries are members of the open clusters M35 (150Myr) and M34 (250Myr). The binary orbital parameters and the rotation periods of the primary stars were determined from time-series spectroscopy and time-series photometry, respectively. Knowledge of the ages, orbital periods, and eccentricities of these binaries combined with the rotation periods and masses of their primary stars makes them particularly interesting sy…
We consider the dynamical evolution of bound, hierarchical triples of supermassive black holes that might be formed in the nuclei of galaxies undergoing sequential mergers. The tidal force of the outer black hole on the inner binary produces eccentricity oscillations through the Kozai mechanism, and this can substantially reduce the gravitational wave merger time of the inner binary. We numerically calculate the merger time for a wide range of initial conditions and black hole mass ratios, including the effects of octupole interactions in the triple as well as general relativistic periastron p…
To first approximation, a binary system conserves its angular momentum while it evolves to its state of minimum kinetic energy: circular orbit, all spins aligned, and components rotating in synchronism with the orbital motion. The pace at which this final state is achieved depends on the physical processes that are responsible for the dissipation of the tidal kinetic energy. For stars (or planets) with an outer convection zone, the dominant mechanism identified so far is the viscous dissipation acting on the equilibrium tide. For stars with an outer radiation zone, it is the radiative damping …
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 grav…
We calculate the evolution of planets undergoing a strong tidal encounter using smoothed particle hydrodynamics (SPH), for a range of periastron separations. We find that outside the Roche limit, the evolution of the planet is well-described by the standard model of linear, non-radial, adiabatic oscillations. If the planet passes within the Roche limit at periastron, however, mass can be stripped from it, but in no case do we find enough energy transferred to the planet to lead to complete disruption. In light of the three new extrasolar planets discovered with periods shorter than two days, w…
We study the tidal evolution of a binary system consisting of a 1.4 Msun compact object in elliptic orbit about a 10 Msun uniformly rotating main sequence star for various values of the initial orbital parameters. We apply our previously published results of 2D non-adiabatic calculations of the non-radial g- and r-mode oscillations of the uniformly rotating MS star, and include the effects of resonant excitation of these modes in the tidal evolution calculations. A high orbital eccentricity enhances the effectiveness of the tidal interaction because of the large number of harmonic components o…
Pluto's recently discovered minor moons, Nix and Hydra, have almost circular orbits, and are nearly coplanar with Charon, Pluto's major moon. This is surprising because tidal interactions with Pluto are too weak to damp their eccentricities. We consider an alternative possibility: that Nix and Hydra circularize their orbits by exciting Charon's eccentricity via secular interactions, and Charon in turn damps its own eccentricity by tidal interaction with Pluto. The timescale for this process can be less than the age of the Solar System, for plausible tidal parameters and moon masses. However, a…
The short-period exoplanet HD 147506b (also known as HAT-P-2b) has an eccentric orbit, raising the possibility that it migrated through planet-planet scattering or Kozai oscillations accompanied by tidal dissipation. Either of these scenarios could have significantly tilted the orbit relative to the host star's equatorial plane. Here we present spectroscopy of a transit of HD 147506b, and assess the spin-orbit alignment via the Rossiter-McLaughlin effect. We find the sky projections of the stellar spin axis and orbital axis to be aligned within 14 deg. Thus we find no corroborating evidence fo…
In order to explain the significant orbital eccentricity of the short-period transiting Neptune-mass planet GJ 436b and at the same time satisfy various observational constraints and anomalies, Ribas, Font-Ribera and Beaulieu have proposed the existence of an eccentric low-mass companion planet at the position of the outer 2:1 resonance. The authors demonstrate the viability of their proposal using point-mass three-body integrations, arguing that as long as the system appears to be dynamically stable, the short-term secular variations ought to dominate the long-term dissipative evolution. Here…
[Abridged] Tides may play an important role in determining the observed distributions of mass, orbital period, and eccentricity of the extrasolar planets. In addition, tidal interactions between giant planets in the solar system and their moons are thought to be responsible for the orbital migration of the satellites, leading to their capture into resonant configurations. We treat the underlying fluid dynamical problem with the aim of determining the efficiency of tidal dissipation in gaseous giant planets. In cases of interest, the tidal forcing frequencies are comparable to the spin frequenc…
Several short-period Jupiter-mass planets have been discovered around nearby solar-type stars. During the circularization of their orbits, the dissipation of tidal disturbance by their host stars heats the interior and inflates the sizes of these planets. Based on a series of internal structure calculations for giant planets, we examine the physical processes which determine their luminosity-radius relation. In order for young or intensely heated gas giant planets to attain quasi-hydrostatic equilibria, with sizes comparable to or larger than two Jupiter radii, their interiors must have suffic…
To date, two planetary systems have been discovered with close-in, terrestrial-mass planets (< 5-10 Earth masses). Many more such discoveries are anticipated in the coming years with radial velocity and transit searches. Here we investigate the different mechanisms that could form "hot Earths" and their observable predictions. Models include: 1) in situ accretion; 2) formation at larger orbital distance followed by inward "type 1" migration; 3) formation from material being "shepherded" inward by a migrating gas giant planet; 4) formation from material being shepherded by moving secular resona…
Radial velocity surveys find Jupiter mass planets with semi-major axes a less than 0.1 AU around ~1% of solar-type stars; counting planets with $a$ as large as 5 AU, the fraction of stars having planets reaches ~ 10% {Marcy,Butler}. An examination of the distribution of semi-major axes shows that there is a clear excess of planets with orbital periods around 3 or 4 days, corresponding to a~0.03$ AU, with a sharp cutoff at shorter periods (see Figure 1). It is believed that Jupiter mass planets form at large distances from their parent stars; some fraction then migrate in to produce the short p…
We present a rapid binary evolution algorithm that enables modelling of even the most complex binary systems. In addition to all aspects of single star evolution, features such as mass transfer, mass accretion, common-envelope evolution, collisions, supernova kicks and angular momentum loss mechanisms are included. In particular, circularization and synchronization of the orbit by tidal interactions are calculated for convective, radiative and degenerate damping mechanisms. We use this algorithm to study the formation and evolution of various binary systems. We also investigate the effect that…
