Context. In the early evolution of a planetary system, a pair of planets may be captured in a mean motion resonance while still embedded in their nesting circumstellar disk. Aims. The goal is to ...estimate the direction and amount of shift in the semimajor axis of the resonance location due to the disk gravity as a function of the gas density and mass of the planets. The stability of the resonance lock when the disk dissipates is also tested. Methods. The orbital evolution of a large number of systems is numerically integrated within a three-body problem in which the disk potential is computed as a series of expansion. This is a good approximation, at least over a limited amount of time. Results. Two different resonances are studied: the 2:1 and the 3:2. In both cases the shift is inwards, even if by a different amount, when the planets are massive and carve a gap in the disk. For super-Earths, the shift is instead outwards. Different disk densities, Σ, are considered and the resonance shift depends almost linearly on Σ. The gas dissipation leads to destabilization of a significant number of resonant systems, in particular if it is fast. Conclusions. The presence of a massive circumstellar disk may significantly affect the resonant behavior of a pair of planets by shifting the resonant location and by decreasing the size of the stability region. The disk dissipation may explain some systems found close to a resonance but not locked in it.
The dynamics of systems of two and three planets, initially placed on circular and nearly coplanar orbits, is explored in the proximity of their stability limit. The evolution of a large number of ...systems is numerically computed and their dynamical behaviour is investigated with the frequency map analysis as chaos indicator. Following the guidance of this analysis, it is found that for two-planet systems the dependence of the Hill limit on the planet mass, usually made explicit through Hill's radius parametrization, does not appear to be fully adequate. In addition, frequent cases of stable chaos are found in the proximity of the Hill limit. For three-planet systems, the usual approach adopted in numerical explorations of their stability, where the planets are initially separated by multiples of the mutual Hill radius, appears too reducing. A detailed sampling of the parameter space reveals that systems with more packed inner planets are stable well within previous estimates of the stability limit. This suggests that a two-dimensional approach is needed to outline when three-planet systems are dynamically stable.
Planet–planet scattering is a major dynamical mechanism able to significantly alter the architecture of a planetary system. In addition to that, it may also affect the formation and retention of a ...debris disc by the system. A violent chaotic evolution of the planets can easily clear leftover planetesimal belts preventing the ignition of a substantial collisional cascade that can give origin to a debris disc. On the other end, a mild evolution with limited steps in eccentricity and semimajor axis can trigger the formation of a debris disc by stirring an initially quiet planetesimal belt. The variety of possible effects that planet–planet scattering can have on the formation of debris discs is analysed and the statistical probability of the different outcomes is evaluated. This leads to the prediction that systems which underwent an episode of chaotic evolution might have a lower probability of harbouring a debris disc.
ABSTRACT We present two-dimensional hydrodynamic simulations using the Smoothed Particle Hydrodynamic code, VINE, to model a self-gravitating binary system. We model configurations in which a ...circumbinary torus+disk surrounds a pair of stars in orbit around each other and a circumstellar disk surrounds each star, similar to that observed for the GG Tau A system. We assume that the disks cool as blackbodies, using rates determined independently at each location in the disk by the time dependent temperature of the photosphere there. We assume heating due to hydrodynamical processes and to radiation from the two stars, using rates approximated from a measure of the radiation intercepted by the disk at its photosphere. We simulate a suite of systems configured with semimajor axes of either a = 62 AU ("wide") or a = 32 AU ("close"), and with assumed orbital eccentricity of either e = 0 or e = 0.3. Each simulation follows the evolution for ∼6500-7500 yr, corresponding to about three orbits of the torus around the center of mass. Our simulations show that strong, sharply defined spiral structures are generated from the stirring action of the binary and that, in some cases, these structures fragment into 1-2 massive clumps. The torus quickly fragments into several dozen such fragments in configurations in which either the binary is replaced by a single star of equal mass, or radiative heating is neglected. The spiral structures extend inwards to the circumstellar environment as large scale material streams for which most material is found on trajectories that return it to the torus on a timescale of 1-200 yr, with only a small fraction accreting into the circumstellar environment. The spiral structures also propagate outwards through the torus, generating net outwards mass flow, and eventually losing coherence at large distances from the stars. The torus becomes significantly eccentric in shape over most of its evolution. In all configurations, accretion onto the stars occurs at a steady rate of a few ×10−8 M yr−1, with the net result that, without replenishment, the disk lifetimes would be shorter than ∼104 yr. Our simulations show that only wide orbit configurations are able to retain circumstellar disks, by virtue of accretion driven from the robust material streams generated in wide configurations, which are very weak in close configurations. In wide, eccentric orbit configurations, accretion is episodic and occurs preferentially onto the secondary, with rates strongly peaked near the binary periapse. Based on our results, we conclude that the GG Tau A torus is strongly self gravitating and that a major contribution to its thermal energy input is the shock dissipation associated with spiral structures generated both by self gravitating disturbances and by the stirring action of the binary. We interpret the sharply defined features observed in the torus as manifestations of such spiral structures. We interpret the low density disk surrounding it as an excretion disk created by the outward mass flux generated by the spiral arms as they propagate outwards. Typical eccentricities calculated for the shape of the tori modeled in our simulations are large enough to account for the supposed ∼20° mutual inclination between the stellar orbit plane of GG Tau A and its surrounding torus through a degeneracy between the interpretation of inclination of the torus and its eccentricity. We therefore interpret the observations in favor of a coplanar system with an eccentric torus. Because accretion onto the disks occurs at rates sufficient to sustain them only in wide orbit configurations, we conclude that the gas currently resident in the circumstellar disks of the GG Tau A system has been accreted from the torus within the past few thousand years. Although circumstellar disks will persist over time spans long enough to permit planet formation, the overall environment remains unfavorable due to high temperatures and other conditions. Given the presence of circumstellar disks, robust accretion streams, and our interpretation of the GG Tau A stellar orbit plane as coplanar with the torus surrounding it, we conclude that the GG Tau A system is in an eccentric, a ∼ 62 AU orbit, resolving questions in the literature regarding its orbit parameters.
The amount of dust present in circumstellar disks is expected to steadily decrease with age due to the growth from m-sized particles to planetesimals and planets. Mature circumstellar disks, however, ...can be observed to contain significant amounts of dust and possess high dust-to-gas ratios. Using HD 163296 as our case study, we explore how the formation of giant planets in disks can create the conditions for collisionally rejuvenating the dust population, halting or reversing the expected trend. We combine N-body simulations with statistical methods and impact scaling laws to estimate the dynamical and collisional excitation of the planetesimals due to the formation of HD 163296's giant planets. We show that this process creates a violent collisional environment across the disk that can inject collisionally produced second-generation dust into it, significantly contributing to the observed dust-to-gas ratio. The spatial distribution of the dust production can explain the observed local enrichments in HD 163296's inner regions. The results obtained for HD 163296 can be extended to any disk with embedded forming giant planets and may indicate a common evolutionary stage in the life of such circumstellar disks. Furthermore, the dynamical excitation of the planetesimals could result in the release of transient, nonequilibrium gas species like H2O, CO2, NH3, and CO in the disk due to ice sublimation during impacts and, due to the excited planetesimals being supersonic with respect to the gas, could produce bow shocks in the latter that could heat it and cause a broadening of its emission lines.
ABSTRACT
Pairs of planets in a system may end up close to their host star on eccentric orbits as a consequence of planet–planet scattering, Kozai, or secular migration. In this scenario, general ...relativity and secular perturbations have comparable time-scales and may interfere with each other with relevant effects on the eccentricity and pericenter evolution of the two planets. We explore, both analytically and via numerical integration, how the secular evolution is changed by general relativity for a wide range of different initial conditions. We find that when the faster secular frequency approaches the general relativity precession rate, which typically occurs when the outer planet moves away from the inner one, it relaxes to it and a significant damping of the proper eccentricity of the inner planet occurs. The proper eccentricity of the outer planet is reduced as well due to the changes in the secular interaction of the bodies. The lowering of the peak eccentricities of the two planets during their secular evolution has important implications on their stability. A significant number of two-planet systems, otherwise chaotic because of the mutual secular perturbations, are found stable when general relativity is included.
Context. We explore the dynamical evolution of a planet that is embedded in a circumstellar disk, as part of a binary system where the orbital plane of the companion star is significantly tilted with ...respect to the initial disk plane. Aims. Our aim is to test whether the planet remains within the disk and continues to migrate towards the star in a Type I/II mode, in spite of the secular perturbations of the companion star. Our findings, could explain why observed exoplanets have significant inclination in relation to the equatorial plane of their host star. Methods. We used two different smoothed particle hydrodynamic codes, VINE and PHANTOM, to model the evolution of a star+disk+planet system with a companion star over time. Results. After an initial coupled evolution, the inclinations of the disk and the planet begin to differ significantly. The period of oscillation of the disk inclination, in relation to the initial plane, becomes shorter for the planet, which evolves independently after about 104 yr, following a perturbed N-body behaviour. However, the planet continues to migrate towards the star because, during its orbital motion, it crosses the disk plane, and friction with the gas causes angular momentum loss. Conclusions. In a significantly inclined binary system, disks and planets are not dynamically coupled for small binary separations but evolve almost independently. The planet abandons the disk, and because of the onset of a significant mutual inclination, it interacts with the gas only when its orbit intersects the disk plane. The drift of the planet towards the star is not due to Type I/II, where the planet is embedded in the disk, but to the friction with the gas while crossing the disk.
I explore the dynamics of small dust particles in transport-dominated circumstellar debris discs in binary star systems. In these tenuous discs the effects of mutual collisions are negligible and ...their morphology is determined by Poynting-Robertson drag and, possibly, by the strong perturbations induced by the interaction with the interstellar medium (ISM) flux of neutral atoms. The force due to the ISM flux can significantly affect the dynamical behaviour of the dust grains, causing a fast inward drift and a large periodic oscillation of both eccentricity and inclination. If the disc is around a star in a binary system, the gravity of the companion star competes with the ISM force and the dynamics is complex. The balance between the two forces depends strongly on the binary semimajor axis a
B and eccentricity e
B. In a scenario with an ISM flux similar to that observed in the Solar system neighbourhood, the binary secular perturbations, assuming a mass ratio of 0.5, dominate over the ISM force when a
B < 600 au and e
B= 0.2. This occurs when the dust disc is generated by a parent body ring encompassed between 50 and 60 aufrom the primary star. For a larger binary eccentricity e
B= 0.6, the limit moves to a
B < 700 au.
Within these values of a
B, the time-scale of the binary secular perturbations is much shorter than the period of the ISM-induced orbital variations, and the disc shape and density distribution are dominated by the companion gravity. It appears slightly eccentric and, if the binary is coplanar with the disc, only a limited warping due to the ISM perturbations is observed. In this scenario, the strong ISM perturbations, which may significantly affect debris discs around single stars embedded in strong ISM winds, are almost completely silenced.
For larger semimajor axes, the scenario is reversed with the ISM perturbations ruling the dynamics of the dust. The disc develops a large clump oriented at 90° with respect to the direction of the ISM flux and it appears highly warped in space. Since the period of the two perturbations can be analytically estimated, it is possible to deduce by easy computations when a given system is governed either by the binary gravity or by the ISM perturbations.
Context. Stellar flybys in star clusters are suspected of affecting the orbital architecture of planetary systems causing eccentricity excitation and orbital misalignment between the planet orbit and ...the equatorial plane of the star. Aims. We explore whether the impulsive changes in the orbital elements of planets, caused by a hyperbolic stellar flyby, can be fully damped by the circumstellar disk surrounding the star. The time required to disperse stellar clusters is comparable to the circumstellar disk’s lifetime. Since we perform 3D simulations, we can also test the inclination, excitation, and damping. Methods. We have modeled in 3D with the SPH code VINE, a system made of a solar-type star surrounded by a low density disk with a giant planet embedded in it approached on a hyperbolic encounter trajectory by a second star of similar mass and with its own disk. Different inclinations between the disks, planet orbit, and star trajectory have been considered to explore various encounter geometries. We focus on an extreme configuration where a very deep stellar flyby perturbs a Jovian planet on an external orbit. This allows us to test in full the ability of the disk to erase the effects of the stellar encounter. Results. We find that the amount of mass lost by the disk during the stellar flyby is less than in 2D models where a single disk was considered. This is mostly related to the mass exchange between the two disks at the encounter. The damping in eccentricity is slightly faster than in 2D models and it occurs on timescales on the order of a few kyr. During the flyby both the disks are warped owing to the mutual interaction and to the stellar gravitational perturbations, but they quickly relax to a new orbital plane. The planet is quickly dragged back within the disk by the tidal interaction with the gas. The only trace of the flyby left in the planet system, after about 104 yr, is a small misalignment, lower than 9°, between the star equatorial plane and the planet orbit. Conclusions. In a realistic model based on 3D simulations of star-planet-disk interactions, we find that stellar flybys cannot excite significant eccentricities and inclinations of planets in stellar clusters. The circumstellar disks hosting the planets damp on a short timescale all the step changes in the two orbital parameters produced during any stellar encounter. All records of past encounters are erased.
Context. Planetesimals and planets embedded in a circumstellar disk are dynamically perturbed by the disk gravity. It causes an apsidal line precession at a rate that depends on the disk density ...profile and on the distance of the massive body from the star. Aims. Different analytical models are exploited to compute the precession rate of the perihelion ϖ̇. We compare them to verify their equivalence, in particular after analytical manipulations performed to derive handy formulas, and test their predictions against numerical models in some selected cases. Methods. The theoretical precession rates were computed with analytical algorithms found in the literature using the Mathematica symbolic code, while the numerical simulations were performed with the hydrodynamical code FARGO. Results. For low-mass bodies (planetesimals) the analytical approaches described in Binney & Tremaine (2008, Galactic Dynamics, p. 96), Ward (1981, Icarus, 47, 234), and Silsbee & Rafikov (2015a, ApJ, 798, 71) are equivalent under the same initial conditions for the disk in terms of mass, density profile, and inner and outer borders. They also match the numerical values computed with FARGO away from the outer border of the disk reasonably well. On the other hand, the predictions of the classical Mestel disk (Mestel 1963, MNRAS, 126, 553) for disks with p = 1 significantly depart from the numerical solution for radial distances beyond one-third of the disk extension because of the underlying assumption of the Mestel disk is that the outer disk border is equal to infinity. For massive bodies such as terrestrial and giant planets, the agreement of the analytical approaches is progressively poorer because of the changes in the disk structure that are induced by the planet gravity. For giant planets the precession rate changes sign and is higher than the modulus of the theoretical value by a factor ranging from 1.5 to 1.8. In this case, the correction of the formula proposed by Ward (1981) to account for the presence of a gap is a better approximation, at least in predicting a positive precession rate. Conclusions. Analytical modeling of the precession rate of massive bodies embedded in a circumstellar disk is accurate for planetesimals and terrestrial planets, but it becomes inaccurate when Jupiter-sized planets are considered. The changes they induce in the disk reverse the precession rate and increase it by more than 50%. This discrepancy can be partly solved by including the effects of a gap in the disk density profile in the analytical equations, as done in Ward (1981).
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