The Doppler technique measures the reflex radial motion of a star induced by the presence of companions and is the most successful method to detect exoplanets. If several planets are present, their signals will appear combined in the radial motion of the star, leading to potential misinterpretations of the data. Specifically, two planets in 2:1 resonant orbits can mimic the signal of a single planet in an eccentric orbit. We quantify the implications of this statistical degeneracy for a representative sample of the reported single exoplanets with available datasets, finding that 1) around 35 percent of the published eccentric one-planet solutions are statistically indistinguishable from planetary systems in 2:1 orbital resonance, 2) another 40 percent cannot be statistically distinguished from a circular orbital solution and 3) planets with masses comparable to Earth could be hidden in known orbital solutions of eccentric super-Earths and Neptune mass planets.
The high eccentricities of the known extrasolar planets remain largely unexplained. We explore the possibility that eccentricities are excited in the outer parts of an extended planetary disk by encounters with stars passing at a few hundreds of AU. After the encounter, eccentricity disturbances propagate inward due to secular interactions in the disks, eventually exciting the innermost planets. We study how the inward propagation of eccentricity in planetary disks depends on the number and masses of the planets and spacing between them and on the overall surface-density distribution in the di…
We investigate the existence and properties of equipotential surfaces and Lagrangian points in non-synchronous, eccentric binary star and planetary systems under the assumption of quasi-static equilibrium. We adopt a binary potential that accounts for non-synchronous rotation and eccentric orbits, and calculate the positions of the Lagrangian points as functions of the mass ratio, the degree of asynchronism, the orbital eccentricity, and the position of the stars or planets in their relative orbit. We find that the geometry of the equipotential surfaces may facilitate non-conservative mass tra…
We present high precision radial velocity observations of HD17156 during a transit of its eccentric Jovian planet. In these data, we detect the Rossiter-McLaughlin effect, which is an apparent perturbation in the velocity of the star due to the progressive occultation of part of the rotating stellar photosphere by the transiting planet. This system had previously been reported by Narita et al. (2008) to exhibit a lambda = 62 +/- 25 degree misalignment of the projected planetary orbital axis and the stellar rotation axis. We model our data, along with the Narita et al. data, and obtain lambda =…
The recent discovery of a planet in an orbit with eccentricity $e = 0.63 \pm 0.08$ around the Solar-type star 16 Cyg B, together with earlier discoveries of other planets in orbits of significant eccentricity, raises the question of the origin of these orbits, so unlike the nearly circular orbits of our Solar system. In this paper I consider close encounters between two planets, each initially in a nearly circular orbit (but with sufficient eccentricity to permit the encounter). Such encounters are described by a two-body approximation, in which the effect of the attracting star is neglected, …
The orbits of the outer two known planets orbiting Upsilon Andromedae are remarkably eccentric. Planet C possesses an orbital eccentricity of e1 = 0.253. For the more distant planet D, e2 = 0.308. Previous dynamical analyses strongly suggest that the two orbits are nearly co-planar and are trapped in an apsidal resonance in which the difference between their longitudes of periastron undergoes a bounded oscillation about 0 degrees. Here we elucidate the origin of these large eccentricities and of the apsidal alignment. Resonant interactions between a remnant circumstellar disk of gas lying exte…
The boundaries of the Uranian epsilon, alpha, and beta rings can be fitted by Keplerian ellipses. The pair of ellipses that outline a given ring share a common line of apsides. Apse alignment is surprising because the quadrupole moment of Uranus induces differential precession. We propose that rigid precession is maintained by a balance of forces due to ring self-gravity, planetary oblateness, and interparticle collisions. Collisional impulses play an especially dramatic role near ring edges. Pressure-induced accelerations are maximal near edges because there (1) velocity dispersions are enhan…
Most extrasolar planets are observed to have eccentricities much larger than those in the solar system. Some of these planets have sibling planets, with comparable masses, orbiting around the same host stars. In these multiple planetary systems, eccentricity is modulated by the planets' mutual secular interaction as a consequence of angular momentum exchange between them. For mature planets, the eigenfrequencies of this modulation are determined by their mass and semi-major axis ratios. But, prior to the disk depletion, self gravity of the planets' nascent disks dominates the precession eigenf…
Long time coverage and high radial velocity precision have allowed for the discovery of additional objects in known planetary systems. Many of the extrasolar planets detected have highly eccentric orbits, which raises the question of how likely those systems are to host additional planets. We investigate six systems which contain a very eccentric (e>0.6) planet: HD 3651, HD 37605, HD 45350, HD 80606, HD 89744, and 16 Cyg B. We present updated radial-velocity observations and orbital solutions, search for additional planets, and perform test particle simulations to find regions of dynamical sta…
The formation of resonant planets pairs in exoplanetary systems involves planetary migration inside the protoplanetary disc : an inwards migrating outer planet captures in Mean Motion Resonance an inner planet. During the migration of the resonant pair of planets, the eccentricities are expected to rise excessively, if no damping mechanism is applied on the inner planet. We express the required damping action to match the observations, and we show that the inner disk can play this role. This result applies for instance to the system GJ 876 : we reproduce the observed orbital elements through a…
Instabilities and strong dynamical interactions between multiple giant planets have been proposed as a possible explanation for the surprising orbital properties of extrasolar planetary systems. In particular, dynamical instabilities seem to provide a natural mechanism for producing the highly eccentric orbits seen in many systems. Previously, we performed numerical integrations for the dynamical evolution of planetary systems containing two giant planets of equal masses initially in nearly circular orbits very close to the dynamical stability limit. We found the ratio of collisions to ejectio…
More than 100 extrasolar planets have been discovered since 1990s. Different from the solar system, these planets' orbital eccentricities cover a huge range from 0 to 0.7. Incidently, the first Kuiper Belt Object was discovered in 1992. Thus, an interesting and important question will be whether extrasolar planetary systems could have structures like Kuiper Belt or asteroid belt. We investigate the stability of these planetary systems with different orbital eccentricities by the similar procedures in Rabl & Dvorak (1988) and Holman & Wiegert (1999). We claim that most extrasolar planetary syst…
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 towards a common final equilibrium distribution, well described by the fitting formula dn ~ e exp[-1/2 (e/0.3)^2] de. This distribution…
HD 69830 exhibits radial velocity variations attributed to three planets as well as infrared emission attributed to a warm debris disk. Previous studies have developed models for the planet migration and mass growth (Alibert et al. 2006) and the replenishment of warm grains (Wyatt et al. 2007). We perform n-body integrations in order to explore the implications of these models for: 1) the excitation of planetary eccentricity, 2) the accretion and clearing of a putative planetesimal disk, 3) the distribution of planetesimal orbits following migration, and 4) the implications for the origin of t…
High precision radial velocity observations of the solar-type star 16 Cygni B taken at McDonald Observatory and at Lick Observatory, have each independently discovered periodic radial-velocity variations indicating the presence of a Jovian-mass companion to this star. The orbital fit to the combined data gives a period of 800.8 days, a velocity amplitude of 43.9 m/s, and an eccentricity of 0.63. This is the largest eccentricity of any planetary system discovered so far. Assuming that 16 Cygni B has a mass of 1.0 Msun, this implies a mass for the companion of 1.5 sin i Jupiter masses. While the…
For centuries, our knowledge of planetary systems and ideas about planet formation were based on a single example, our solar system. During the last thirteen years, the discovery of ~170 planetary systems has ushered in a new era for astronomy. I review the surprising properties of extrasolar planetary systems and discuss how they are reshaping theories of planet formation. I focus on how multiple planet systems constrain the mechanisms proposed to explain the large eccentricities typical of extrasolar planets. I suggest that strong planet-planet scattering is common and most planetary systems…
We report the detection of a extrasolar planet candidate orbiting the G1 V star HD 39091. The orbital period is 2083 d and the eccentricity is 0.62. With a minimum (M sin $i$) mass of 10.3 M$_{\rm JUP}$ this object falls near the high mass end of the observed planet mass function, and may plausibly be a brown dwarf. Other characteristics of this system, including orbital eccentricity and metallicity, are typical of the well populated class of radial velocity planets in eccentric orbits around metal-rich stars.
We present a thorough study of the impact of a migrating planet on a planetesimal disk, by exploring a broad range of masses and eccentricities for the planet. We discuss the sensitivity of the structures generated in debris disks to the basic planet parameters. We perform many N-body numerical simulations, using the symplectic integrator SWIFT, taking into account the gravitational influence of the star and the planet on massless test particles. A constant migration rate is assumed for the planet. The effect of planetary migration on the trapping of particles in mean motion resonances is foun…
This paper studies the effects of dynamical interactions among the planets in observed extrasolar planetary systems, including hypothetical additional bodies, with a focus on secular perturbations. These interactions cause the eccentricities of the planets to explore a distribution of values over time scales that are long compared to observational time baselines, but short compared to the age of the systems. The same formalism determines the eccentricity forcing of hypothetical test bodies (terrestrial planets) in these systems and we find which systems allow for potentially habitable planets.…
The nonlinear stability domain of Lagrange's celebrated 1772 solution of a three-body problem is obtained numerically as a function of the masses of the bodies and the common eccentricity of their Keplerian orbits. This domain shows that this solution may be realized in extra-solar planetary systems similar to those that have been discovered recently with two Jupiter-size planets orbiting a solar-size star. For an exact 1:1 resonance, the Doppler shift variation in the emitted light would be the same as for stars which have only a single planetary companion. But it is more likely that in actua…
Half the known extrasolar planets have orbital eccentricities in excess of 0.3. Such large eccentricities are surprising as it is thought that planets form in a protoplanetary disk on nearly circular orbits much like the current states of the solar system planets. Possible explanations for the large planetary eccentricities include the perturbations that accompany planet-planet scattering, the tidal interaction between the gas disk and the planets, Kozai's secular eccentricity cycles, the eccentricity excitation during planetary pair migration in mean motion resonance, the perturbations by ste…
The dynamical evolution of nearly half of the known extrasolar planets in multiple-planet systems may be dominated by secular perturbations. The commonly high eccentricities of the planetary orbits calls into question the utility of the traditional Laplace-Lagrange (LL) secular theory in analyses of the motion. We analytically generalize this theory to fourth-order in the eccentricities, compare the result with the second-order theory and octupole-level theory, and apply these theories to the likely secularly-dominated HD 12661, HD 168443, HD 38529 and Ups And multi-planet systems. The fourth-…
The bright F8 V solar-type star upsilon Andromedae has recently been reported to have a system of three planets of Jovian masses. In order to investigate the orbital stability and mutual gravitational interactions among these extrasolar planets, both forward and backward integrations from the latest observed orbital elements for all three planets' orbits have been performed under the coplanar assumption. We reconfirm that the middle and the outer planet have strong interaction leading to large time variations in the eccentricities of these planets, which was shown by the previous studies. Howe…
(Abridged) A simple and general description of the dynamics of a narrow eccentric ring is presented.We view an eccentric ring which precesses uniformly at a slow rate as exhibiting a global $m=1$ mode originating from a standing wave superposed on an axisymmetric background.We adopt a continuum description using the language of fluid dynamics which gives equivalent results for the secular dynamics of thin rings as the the well known description using discrete elliptical streamlines formulated by Goldreich and Tremaine (1979). We use this to discuss the non linear mode interactions that appear …
We investigate the response of an accretion disk to the presence of a perturbing protoplanet embedded in the disk through time dependent hydrodynamical simulations. The disk is treated as a two-dimensional viscous fluid and the planet is kept on a fixed orbit. We run a set of simulations varying the planet mass, and the viscosity and temperature of the disk. All runs are followed until they reach a quasi-equilibrium state. We find that for planetary masses above a certain minimum mass, already 3 M_Jup for a viscosity of nu = 10^{-5}, the disk makes a transition from a nearly circular state int…
We examine the eccentricity evolution of a system of two planets locked in a mean motion resonance, in which the outer planet loses energy and angular momentum. The sink of energy and angular momentum could be either a gas or planetesimal disk. We show that the eccentricity of both planetary bodies can grow to large values, particularly if the inner body does not directly exchange energy or angular momentum with the disk. We analytically calculate the eccentricity damping rate in the case of a single planet migrating through a planetesimal disk. We present the results of numerical integrations…
Precision radial velocity measurements of the Gamma Cephei (HR8974) binary system suggest the existence of a planetary companion with a minimum mass of 1.7 Jupiter-mass on an elliptical orbit with a ~2.14 AU semimajor axis and 0.12 eccentricity (hatzes et al. 2003). I present in this paper a summary of the results of an extensive numerical study of the orbital stability of this three-body system for different values of the semimajor axis and orbital eccentricity of the binary, and also the orbital inclination of the planet. Numerical integrations indicate that the system is stable for the plan…
We show that interaction with a gas disk may produce young planetary systems with closely-spaced orbits, stabilized by mean-motion resonances between neighbors. On longer timescales, after the gas is gone, interaction with a remnant planetesimal disk tends to pull these configurations apart, eventually inducing dynamical instability. We show that this can lead to a variety of outcomes; some cases resemble the Solar System, while others end up with high-eccentricity orbits reminiscent of the observed exoplanets. A similar mechanism has been previously suggested as the cause of the lunar Late He…
The two planets about the star GJ 876 appear to have undergone extensive migration from their point of origin in the protoplanetary disk -- both because of their close proximity to the star (30 and 60 day orbital periods) and because of their occupying three stable orbital resonances at the 2:1 mean-motion commensurability. The resonances were most likely established by converging differential migration of the planets leading to capture into the resonances. A problem with this scenario is that continued migration of the system while it is trapped in the resonances leads to orbital eccentriciti…
We investigate the dynamics of putative Earth-mass planets in the habitable zone (HZ) of the extrasolar planetary system OGLE-2006-BLG-109L, a close analog of the Solar system. Our work is inspired by work of Malhotra and Minton (2008). Using the linear Laplace-Lagrange theory, they identified a strong secular resonance that may excite large eccentricity of orbits in the HZ. However, due to uncertain or unconstrained orbital parameters, the sub-system of Jupiters may be found in dynamically active region of the phase space spanned by low-order mean-motion resonances. To generalize this secular…
Instabilities and strong dynamical interactions between several giant planets have been proposed as a possible explanation for the surprising orbital properties of extrasolar planetary systems. In particular, dynamical instabilities would seem to provide a natural mechanism for producing the highly eccentric orbits seen in many systems. Here we present results from numerical integrations for the dynamical evolution of planetary systems containing two identical giant planets in nearly circular orbits very close to the dynamical stability limit. We determine the statistical properties of the thr…
The three-dimensional secular behavior of a system composed of a central star and two massive planets is modeled semi-analytically in the frame of the general three-body problem. The main dynamical features of the system are presented in geometrical pictures allowing us to investigate a large domain of the phase space of this problem without time-expensive numerical integrations of the equations of motion and without any restriction on the magnitude of the planetary eccentricities, inclinations and mutual distance. Several regimes of motion of the system are observed. With respect to the secul…
We perform numerical simulations to study the secular orbital evolution and dynamical structure in the HD 69830 system with the best-fit orbital solutions by Lovis and coworkers (2006). In the simulations, we show that the triplet Neptunian system can be stable at least for 2 Gyr and the stability would not be greatly influenced even if we vary the planetary masses. In addition, we employ the Laplace-Lagrange secular theory to investigate the long-term behaviors of the system, and the outcomes demonstrate that this theory can well describe the secular orbital evolution for all planets, where t…
The orbital eccentricity of a single planet around a component of a stellar binary system with a sufficiently large mutual inclination angle is known to oscillate on a secular timescale through the Kozai mechanism. We have investigated the effects of the Kozai mechanism on double-planet systems in binaries. The evolutionary sequence of a pair of planets under the influence of a binary companion is fairly complex. Various dynamical outcomes are seen in numerical simulations. One interesting outcome is the rigid rotation of the planetary orbits in which the planetary orbital planes secularly pre…
We report the detection of two planetary mass companions to the solar-type star HD 155358. The two planets have orbital periods of 195.0 and 530.3 days, with eccentricities of 0.11 and 0.18. The minimum masses for these planets are 0.89 and 0.50 Jupiter masses respectively. The orbits are close enough to each other, and the planets are sufficiently massive, that the planets are gravitationally interacting with each other, with their eccentricities and arguments of periastron varying with periods of 2300--2700 years. While large uncertainties remain in the orbital eccentricities, our orbital in…
Two planets with orbital period ratio approximately 10:1 have been discovered around the star HD 83443. The inner and more massive planet, HD 83443b, has the smallest semi-major axis among all currently known exoplanets. Unlike other short period exoplanets, it maintains a substantial orbital eccentricity, e_1=0.079+/- 0.008, in spite of efficient tidal damping. This is a consequence of its secular interactions with HD 83443c whose orbital eccentricity e_2=0.42+/-0.06. Dissipation, associated with tides the star raises in the inner planet, removes energy but not angular momentum from its orbit…
We report precise Doppler measurements of HD 142022 obtained during the past six years with the CORALIE echelle spectrograph at La Silla Observatory together with a few additional observations made recently with the HARPS echelle spectrograph. Our radial velocities reveal evidence of a planetary companion with an orbital period P = 1928 +53-39 days, an eccentricity e = 0.53 +0.23-0.18, and a velocity semiamplitude K = 92 +102-29 m/s. The inferred companion minimum mass is M2sini = 5.1 +2.6-1.5 MJup and the semimajor axis a = 3.03+/-0.05 AU. Only one full orbital revolution has been monitored y…
Habitability is usually defined as the requirement for a terrestrial planet's atmosphere to sustain liquid water. This definition can be complemented by the dynamical requirement that other planets in the system do not gravitationally perturb terrestrial planets outside of their habitable zone, the orbital region allowing the existence of liquid water. We quantify the dynamical habitability of 85 known extrasolar planetary systems via simulations of their orbital dynamics in the presence of potentially habitable terrestrial planets. When requiring that habitable planets remain strictly within …
We address the occurrence of narrow planetary rings under the interaction with shepherds. Our approach is based on a Hamiltonian framework of non-interacting particles where open motion (escape) takes place, and includes the quasi-periodic perturbations of the shepherd's Kepler motion with small and zero eccentricity. We concentrate in the phase-space structure and establish connections with properties like the eccentricity, sharp edges and narrowness of the ring. Within our scattering approach, the organizing centers necessary for the occurrence of the rings are stable periodic orbits, or mor…
The formation of resonant pairs of planets in exoplanetary systems involves planetary migration in the protoplanetary disc. After a resonant capture, the subsequent migration in this configuration leads to a large increase of planetary eccentricities if no damping mechanism is applied. This has led to the conclusion that the migration of resonant planetary systems cannot occur over large radial distances and has to be terminated sufficiently rapidly through disc dissipation. In this study, we investigate whether the presence of an inner disc might supply an eccentricity damping of the inner pl…
We review the orbital dynamics exhibited by the first extra-solar planetary system discovered, Upsilon Andromedae. This system is unique in combining all of the surprising architectural features displayed individually by extrasolar planetary systems found today: (1) a hot Jupiter, (2) two planets on highly eccentric orbits, and (3) a stellar companion. We discuss the system's stability properties and its possible origin. Planet-disk interactions seem critical to the emerging story.
Recent discoveries of extrasolar planets at small orbital radii, or with significant eccentricities, indicate that interactions between massive planets and the disks of gas and dust from which they formed are vital for determining the final shape of planetary systems. We show that if this interaction occurs at an early epoch, when the protoplanetary disc was still massive, then rapid planet growth through accretion causes an otherwise stable disc to fragment into additional planetary mass bodies when the planetary mass reaches 4-5 Jupiter masses. We suggest that such catastrophic planet format…
We investigate the secular resonances for massless small bodies and Earth-like planets in several planetary systems. We further compare the results with those of Solar System. For example, in the GJ 876 planetary system, we show that the secular resonances $ν_1$ and $ν_2$ (respectively, resulting from the inner and outer giant planets) can excite the eccentricities of the Earth-like planets with orbits 0.21 AU $\leq a <$ 0.50 AU and eject them out of the system in a short timescale. However, in a dynamical sense, the potential zones for the existence of Earth-like planets are in the area 0.50 …
The known extrasolar planets exhibit many interesting and surprising features--extremely short-period orbits, high-eccentricity orbits, mean-motion and secular resonances, etc.--and have dramatically expanded our appreciation of the diversity of possible planetary systems. In this review we summarize the orbital properties of extrasolar planets. One of the most remarkable features of extrasolar planets is their high eccentricities, far larger than seen in the solar system. We review theoretical explanations for large eccentricities and point out the successes and shortcomings of existing theor…
This paper studies the long term evolution of planetary systems containing short-period planets, including the effects of tidal circularization, secular excitation of eccentricity by companion planets, and stellar damping. For planetary systems subject to all of these effects, analytic solutions (or approximations) are presented for the time evolution of the semi-major axes and eccentricities. Secular interactions enhance the inward migration and accretion of hot Jupiters, while general relativity tends to act in opposition by reducing the effectiveness of the secular perturbations. The analyt…
