We investigate type I migration in a two-dimensional adiabatic disk. We find entropy perturbations that are advected in the planet's coorbital region. These entropy perturbations yield an excess of corotation torque that scales with the unperturbed entropy gradient at corotation. This torque excess can be large enough to slow down migration significantly, or even stop it.

We study the effect of poloidal magnetic field on type I planetary migration by linear perturbation analysis with the shearing-sheet approximation and the analytic results are compared with numerical calculation. We investigate the cases where magneto-rotational instability (MRI) does not occur: either the disk is two-dimensional, or a very strong field is exerted. We derive formulae for torque exerted on the planet for both cases. We find that two-dimensional torque is suppressed when plasma beta is less than 1 and three-dimensional modes dominate, in contrast to unmagnetized case.

We use a multi-dimensional hydrodynamics code to study the gravitational interaction between an embedded planet and a protoplanetary disk with emphasis on the generation of vortensity (Potential Vorticity or PV) through a Baroclinic Instability. We show that the generation of PV is very common and effective in non-barotropic disks through the Baroclinic Instability, especially within the coorbital region. Our results also complement previous work that non-axisymmetric Rossby-Wave Instabilities (RWIs) are likely to develop at local minima of PV distribution that are generated by the interaction between a planet and an inviscid barotropic disk. The development of RWIs results in non-axisymmetric density blobs, which exert stronger torques onto the planet when they move to the vicinity of the planet. Hence, large amplitude oscillations are introduced to the time behavior of the total torque acted on the planet by the disk. In current simulations, RWIs do not change the overall picture of inward orbital migration but cause a non-monotonic behavior to the migration speed. As a side effect, RWIs also introduce interesting structures into the disk. These structures may help the formation of Earth-like planets in the Habitable Zone or Hot Earths interior to a close-in giant planet.

We investigate the migration of two giant planets embedded in a proto-stellar disk. The inner planet(initially located at R10=1) is of 1 Jupiter mass and the outer one(R20=1.5) is of 1 Saturn mass. We find that due to the existence of the inner massive planet, the outer planet can not open a clear gap. Instead of an inward migration and being captured by the mean motion resonance of the inner planet, the outer planet undergoes an outward runaway migration. We conclude that this runaway migration is caused by the co-rotation torque in the co-orbital region of the outer planet and sustained by the wave(flow) driven by the inner massive planet.

We numerically investigate the conditions for planetesimal accretion in the circumprimary disk under the perturbing presence of a companion star, with focus on the γ Cephei system. Gas drag is included with a dissipating time scale of 105 years. We show at the beginning(within 103 ∼ 104 years), gas drag damps the ΔV between planetesimals of same sizes and increases ΔV between planetesimals of different sizes. However, after increasing to high values(300∼800m/s), we find the ΔV between bodies of different sizes decrease to very low values (below 10m/s) in a few 105yrs (depending on the gas-dissipating time scale Tdamp, radial size Rp and semi-major axis ap of planetesimals). Hence, the high ΔV is somewhat short-lived, and runaway accretion can be turned on later. We conclude that the conditions for planetary formation in binary systems (even close binary systems) are much better than what we expected before.

In this communication we review some properties and applications of mean-motion resonances in extrasolar planetary systems, with particular emphasis on the 2/1 commensurability. A first part is devoted to the dynamical structure of the 2/1 resonance, including (but not restricted to) the so-called apsidal corotations. In a second part we discuss the orbital evolution of resonant systems under the effects of non-conservative forces. Special attention is given to the use of apsidal corotations as markers of largescale orbital decay, possibly due to disk-planet interactions in primordial times. Finally, we analyze the interplay between dynamical analysis and orbital fitting. Using the HD82943 planetary system as an example, we discuss: (i) up to what point present orbital fits allow us to distinguish between different resonant configurations, and (ii) in what ways may the dynamical structure of resonances be used as a complementary part of the orbital fitting process.

Extrasolar planet surveys have discovered over two dozen multiple planet systems. As radial velocity searches push towards higher precisions and longer survey durations, they can be expected to discover an even higher fraction of multiple planet systems. Combined with radial velocity data, dynamical studies of these systems can constrain planet masses and inclinations, measure the significance of resonant and secular interactions, and provide insights into the formation and evolution of these systems. Here, we review the dynamical properties of known extrasolar multiple planet systems and their implications for planet formation theory. We conclude by outlining pressing questions to be addressed by a combination of future observations and theoretical research.

We present an analysis of high precision radial velocity (RV) observations of stars hosting multi-planet systems with Jovian companions. We use dynamical stability constraints and quasi-global methods of optimization. As an illustration, we present new results derived for the RV data of the Sun-like dwarfs HD 155358 and τ1 Gruis.

In this article we examine the motion of fictitious Trojan planets close to the equilateral Lagrangean equilibrium points in extrasolar planetary systems. Whether there exist stable motion in this area or not depends on the massratio of the primariy bodies in the restricted three body problem, namely the host star and the gasgiant. Taking into account also the eccentricity of the primaries we show via results of extensive numerical integrations that Trojan planets may survive only for e < 0.25. We also show first results of a mapping in the 1:1 resonance with a gas giant on an eccentric orbit which is applied to the extrasolar planetary systems HD 17051. We furthermore study the influence of an additional outer planet which perturbs the motion of the gasgiant as well as the Trojan cloud around its L4 Lagrangean point.

The dynamical interactions of planetary systems may be a clue to their formation histories. Therefore, the distribution of these interactions provides important constraints on models of planet formation. We focus on each system's apsidal motion and proximity to dynamical instability. Although only ∼25 multiple planet systems have been discovered to date, our analyses in these terms have revealed several important features of planetary interactions. 1) Many systems interact such that they are near the boundary between stability and instability. 2) Planets tend to form such that at least one planet's eccentricity periodically drops to near zero. 3) Mean-motion resonant pairs would be unstable if not for the resonance. 4) Scattering of approximately equal mass planets is unlikely to produce the observed distribution of apsidal behavior. 5) Resonant interactions may be identified through calculating a system's proximity to instability, regardless of knowledge of angles such as mean longitude and longitude of periastron (e.g. GJ 317 b and c are probably in a 4:1 resonance). These properties of planetary systems have been identified through calculation of two parameters that describe the interaction. The apsidal interaction can be quantified by determining how close a planet is to an apsidal separatrix (a boundary between qualitatively different types of apsidal oscillations, e.g. libration or circulation of the major axes). This value can be calculated through short numerical integrations. The proximity to instability can be measured by comparing the observed orbital elements to an analytic boundary that describes a type of stability known as Hill stability. We have set up a website dedicated to presenting the most up-to-date information on dynamical interactions: http://www.lpl.arizona.edu/~rory/research/xsp/dynamics.

We investigate the secular evolution of non-resonant exoplanetary systems consisting of a central star and two co-planar planets using a semi-numerical averaging method of the first order in planetary masses (in this case equivalent to “averaging by scissors” or simply dropping the fast periodic terms). The resulting Hamiltonian level curves for different exoplanetary systems were compared to those obtained by direct numerical integration. Studying the dependence of the reliability of the averaging method (as well as chaoticity of numerically integrated trajectories) upon the initial conditions, we found that the averaging methods fails even for Hill stable systems. Based on the Hill stability criterion we introduced empirically a more restrictive stability condition, that enabled us to give an estimate for the region of validity of the averaging method in the plane of initial conditions.

We report in this paper the numerical simulations of the capture into the 3:1 mean-motion resonance between the planets b and c in the 55 Cancri system. The results show that this resonance can be obtained by a differential planetary migration. The moderate initial eccentricities, relatively slower migration and suitable eccentricity damping rate increase significantly the probability of being trapped in this resonance. Otherwise, the system crosses the 3:1 commensurability avoiding resonance capture, to be eventually captured into a 2:1 resonance or some other higher-order resonances. After capture into resonance, the system can jump from one orbital configuration to another one if the migration continues, making a large region of the configuration space accessible for a resonance system. These investigations help us understand the diversity of resonance configurations and put some constraints on the early dynamical evolution of orbits in the extra-solar planetary systems.

Near-separatrix motion is a kind of motion of two planets with their relative apsidal longitude near the boundary between libration and circulation. Observed multiple planetary systems seem to favor near-separatrix motions between neighboring planets. In this report, we study the probability that near-separatrix motion occurs with both the linear secular system and full three-body systems. We find that generally the ratio of near-separatrix motion is small unless the eccentricities of the two planets differ from each other by an order of magintude, or they are in mean motion resonance. To explore the dynamical procedures causing the near-separatrix motion, we suppose a modification to scattering model by adding a mass-accretion process during the protoplanet growth. Statistics on the modified scattering model indicate that the probability of the final planet pairs in near-separatrix motion is high (∼ 85%), which may explain the high occurrence of near-separatrix motions in observed planetary systems.

We perform numerical simulations to study the Habitable zones (HZs) and dynamical structure for Earth-mass planets in multiple planetary systems. For example, in the HD 69830 system, we extensively explore the planetary configuration of three Neptune-mass companions with one massive terrestrial planet residing in 0.07 AU ≤ a ≤ 1.20 AU, to examine the asteroid structure in this system. We underline that there are stable zones of at least 105 yr for low-mass terrestrial planets locating between 0.3 and 0.5 AU, and 0.8 and 1.2 AU with final eccentricities of e < 0.20. Moreover, we also find that the accumulation or depletion of the asteroid belt are also shaped by orbital resonances of the outer planets, for example, the asteroidal gaps at 2:1 and 3:2 mean motion resonances (MMRs) with Planet C, and 5:2 and 1:2 MMRs with Planet D. In a dynamical sense, the proper candidate regions for the existence of the potential terrestrial planets or HZs are 0.35 AU < a < 0.50 AU, and 0.80 AU < a < 1.00 AU for relatively low eccentricities, which makes sense to have the possible asteroidal structure in this system.

The unexpected diversity of exoplanets includes a growing number of super-Earth planets, i.e., exoplanets with masses smaller than 10 Earth masses. Unlike the larger exoplanets previously found, these smaller planets are more likely to have similar chemical and mineralogical composition to the Earth. We present a thermal evolution model for super-Earth planets to identify the sources and sinks of atmospheric carbon dioxide. The photosynthesis-sustaining habitable zone (pHZ) is determined by the limits of biological productivity on the planetary surface. We apply our model to calculate the habitability of the two super-Earths in the Gliese 581 system. The super-Earth Gl 581c is clearly outside the pHZ, while Gl 581d is at the outer edge of the pHZ. Therefore, it could at least harbor some primitive forms of life.

About half of all known stellar systems with Sun-like stars consist of two or more stars, significantly affecting the orbital stability of any planet in these systems. This observational evidence has prompted a large array of theoretical research, including the derivation of mathematically stringent criteria for the orbital stability of planets in stellar binary systems, valid for the “coplanar circular restricted three-body problem”. In the following, we use these criteria to explore the validity of results from previous theoretical studies.

Multi-planet systems detected until now are in most cases characterized by hot-Jupiters close to their central star as well as high eccentricities. As a consequence, from a dynamical point of view, compact multi-planetary systems form a variety of the general N-body problem (with N ≥ 3), whose solutions are not necessarily known. Extrasolar planets are up to now found in prograde (i.e. direct) orbital motions about their host star and often in mean-motion resonances (MMR). In the present paper, we investigate a theoretical alternative suitable for the stability of compact multi-planetary systems. When the outer planet moves on a retrograde orbit in MMR with respect to the inner planet, we find that the so-called retrograde resonances present fine and characteristic structures particularly relevant for dynamical stability. We show that retrograde resonances and their resources open a family of stabilizing mechanisms involving specific behaviors of apsidal precessions. We also point up that for particular orbital data, retrograde MMRs may provide more robust stability compared to the corresponding prograde MMRs.