Dynamical behaviour of multiplanet systems close to their stability limit

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 the 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.Comment: 7 pages, 3 figures, Accepted on MNRA

The influence of general-relativity effects, dynamical tides and collisions on planet-planet scattering close to the star

Planet--Planet scattering is an efficient and robust dynamical mechanism for producing eccentric exoplanets. Coupled to tidal interactions with the central star, it can also explain close--in giant planets on circularized and potentially misaligned orbits. We explore scattering events occurring close to the star and test if they can reproduce the main features of the observed orbital distribution of giant exoplanets on tight orbits.In our modeling we exploit a numerical integration code based on the Hermite algorithm and including the effects of general relativity, dynamical tides and two--body collisions.We find that P--P scattering events occurring in systems with three giant planets initially moving on circular orbits close to their star produce a population of planets similar to the presently observed one, including eccentric and misaligned close--in planets. The contribution of tides and general relativity is relevant in determining the final outcome of the chaotic phase. Even if two--body collisions dominate the chaotic evolution of three planets in crossing orbits close to their star, the final distribution shows a significant number of planets on eccentric orbits. The highly misaligned close--in giant planets are instead produced by systems where the initial semi--major axis of the inner planet was around 0.2 au or beyond.Comment: Accepted for publication on A&

Stability of multiplanet systems in binaries

When exploring the stability of multiplanet systems in binaries, two parameters are normally exploited: the critical semimajor axis ac computed by Holman and Wiegert (1999) within which planets are stable against the binary perturbations, and the Hill stability limit Delta determining the minimum separation beyond which two planets will avoid mutual close encounters. Our aim is to test whether these two parameters can be safely applied in multiplanet systems in binaries or if their predictions fail for particular binary orbital configurations. We have used the frequency map analysis (FMA) to measure the diffusion of orbits in the phase space as an indicator of chaotic behaviour. First we revisited the reliability of the empirical formula computing ac in the case of single planets in binaries and we find that, in some cases, it underestimates by 10-20% the real outer limit of stability. For two planet systems, the value of Delta is close to that computed for planets around single stars, but the level of chaoticity close to it substantially increases for smaller semimajor axes and higher eccentricities of the binary orbit. In these configurations ac also begins to be unreliable and non linear secular resonances with the stellar companion lead to chaotic behaviour well within ac, even for single planet systems. For two planet systems, the superposition of mean motion resonances, either mutual or with the binary companion, and non linear secular resonances may lead to chaotic behaviour in all cases. We have developed a parametric semiempirical formula determining the minimum value of the binary semimajor axis, for a given eccentricity of the binary orbit, below which stable two planet systems cannot exist.Comment: Accepted on A&

Dynamics of Jupiter Trojans during the 2:1 mean motion resonance crossing of Jupiter and Saturn

We study the dynamics of Jupiter Trojans in the early phase of the Solar system while the outer planets migrated due to their interaction with the planetesimal disk.Comment: 10 pages, 17 figure

Planet--planet scattering in circumstellar gas disks

Hydrodynamical simulations of two giant planets embedded in a gaseous disk have shown that in case of a smooth convergent migration they end up trapped into a mean motion resonance. These findings have led to the conviction that the onset of dynamical instability causing close encounters between the planets can occur only after the dissipation of the gas when the eccentricity damping is over. We show that a system of three giant planets may undergo planet-planet scattering when the gaseous disk, with density values comparable to that of the Minimum Mass Solar Nebula, is still interacting with the planets. The hydrodynamical code FARGO--2D--1D is used to model the evolution ofthe disk and planets, modified to properly handle close encounters between the massive bodies. Our simulations predict a variety of different outcomes of the scattering phase which includes orbital exchange, planet merging and scattering of a planet in a hyperbolic orbit. This implies thatthe final fate of a multiplanet system under the action of the disk torques is not necessarily a packed resonant configuration.Comment: Astronomy and Astrophysics Letters, in pres

Planets in binary systems: is the present configuration indicative of the formation process?

The present dynamical configuration of planets in binary star systems may not reflect their formation process since the binary orbit may have changed in the past after the planet formation process was completed. An observed binary system may have been part of a former hierarchical triple that became unstable after the planets completed their growth around the primary star. Alternatively, in a dense stellar environment even a single stellar encounter between the star pair and a singleton may singificantly alter the binary orbit. In both cases the planets we observe at present would have formed when the dynamical environment was different from the presently observed one. We have numerically integrated the trajectories of the stars (binary plus singleton) and of test planets to investigate the abovementioned mechanisms. Our simulations show that the circumstellar environment during planetary formation around the primary was gravitationally less perturbed when the binary was part of a hierarchical triple because the binary was necessarely wider and, possibly, less eccentric. This circumstance has consequences for the planetary system in terms of orbital spacing, eccentricity, and mass of the individual planets. Even in the case of a single stellar encounter the present appearance of a planetary system in a binary may significantly differ from what it had while planet formation was ongoing. However, while in the case of instability of a triple the trend is always towards a tighter and more eccentric binary system, when a single stellar encounter affects the system the orbit of the binary can become wider and be circularized.Comment: 5 pages, 5 figures Accepted for publication on A&

Dust-to-gas ratio resurgence in circumstellar disks due to the formation of giant planets: the case of HD 163296

The amount of dust present in circumstellar disks is expected to steadily decrease with age due to the growth from micron-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, non-equilibrium 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.Comment: 18 pages, 9 figures, 2 tables. Accepted for publication on The Astrophysical Journa

Asteroid detection at millimetric wavelengths with the Planck survey

The Planck mission, originally devised for cosmological studies, offers the opportunity to observe Solar System objects at millimetric and submillimetric wavelengths. We concentrate in this paper on the asteroids of the Main Belt. We intend to estimate the number of asteroids that can can be detected during the mission and to evaluate the strength of their signal. We have rescaled the instrument sensitivities, calculated by the LFI and HFI teams for sources fixed in the sky, introducing some degradation factors to properly account for moving objects. In this way a detection threshold is derived for asteroidal detection that is related to the diameter of the asteroid and its geocentric distance. We have developed a numerical code that models the detection of asteroids in the LFI and HFI channels during the mission. This code perfoprms a detailed integration of the orbits of the asteroids in the timespan of the mission and identifies those bodies that fall in the beams of Planck and their signal stenght. According to our simulations, a total of 397 objects will be observed by Planck and an asteroidal body will be detected in some beam in 30% of the total sky scan--circles. A significant fraction (in the range from ~50 to 100 objects) of the 397 asteroids will be observed with a high S/N ratio. Flux measurements of a large sample of asteroids in the submillimeter and millimeter range are relevant since they allow to analyze the thermal emission and its relation to the surface and regolith properties. Furthermore, it will be possible to check on a wider base the two standard thermal models, based on a nonrotating or rapidly rotating sphere. Our method can also be used to separate Solar System sources from cosmological sources in the survey. This work is based on Planck LFI activities.Comment: Contact person [email protected]. Accepted for pubblication in New Astronomy (2002). 1 figure in .eps format. Needs elsart.cls style + harvard.st