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

Impact of planet--planet scattering on the formation and survival of debris disks

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 disk 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 disk. On the other end, a mild evolution with limited steps in eccentricity and semimajor axis can trigger the formation of a debris disk by stirring an initially quiet planetesimal belt. The variety of possible effects that planet--planet scattering can have on the formation of debris disks 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 harboring a debris disk.Comment: Accepted for publication on MNRA

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

Shifting of the resonance location for planets embedded in circumstellar disks

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, Sigma, are considered and the resonance shift depends almost linearly on Sigma. 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.Comment: Accepted for publication on A&

Boltzmann Transport in Nanostructures as a Friction Effect

Surface scattering is the key limiting factor to thermal transport in dielectric crystals as the length scales are reduced or when temperature is lowered. To explain this phenomenon, it is commonly assumed that the mean free paths of heat carriers are bound by the crystal size and that thermal conductivity is reduced in a manner proportional to such mean free paths. We show here that these conclusions rely on simplifying assumptions and approximated transport models. Instead, starting from the linearized Boltzmann transport equation in the relaxon basis, we show how the problem can be reduced to a set of decoupled linear differential equations. Then, the heat flow can be interpreted as a hydrodynamic phenomenon, with the relaxon gas being slowed down in proximity of a surface by friction effects, similar to the flux of a viscous fluid in a pipe. As an example, we study a ribbon and a trench of monolayer molybdenum disulphide, describing the procedure to reconstruct the temperature and thermal conductivity profile in the sample interior and showing how to estimate the effect of nanostructuring. The approach is general and could be extended to other transport carriers, such as electrons, or extended to materials of higher dimensionality and to different geometries, such as thin films

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&

Three-dimensional modeling of radiative disks in binaries

Circumstellar disks in binaries are perturbed by the companion gravity causing significant alterations of the disk morphology. Spiral waves due to the companion tidal force also develop in the vertical direction and affect the disk temperature profile. These effects may significantly influence the process of planet formation. We perform 3D numerical simulations of disks in binaries with different initial dynamical configurations and physical parameters. Our goal is to investigate their evolution and their propensity to grow planets. We use an improved version of the SPH code VINE modified to better account for momentum and energy conservation. The energy equation includes a flux--limited radiative transfer algorithm and the disk cooling is obtained via "boundary particles". We model a system made of star/disk + star/disk where the secondary star (and relative disk) is less massive than the primary. The numerical simulations performed for different values of binary separation and disk density show that the disk morphology is substantially affected by the companion perturbations. Trailing spiral shock waves develop when the stars approach their pericenter. Strong hydraulic jumps occur at the shock front creating breaking waves and a consistent mass stream between the two disks, significantly heating them. The high gas temperature may prevent the ice condensation by moving outward the "snow line". The hydraulic jumps may slow down or even halt the dust coagulation process. At apocenter these perturbations are reduced and the disks are cooled down and less eccentric. The strength of the hydraulic jumps, disk heating, and mass exchange depends on the binary separation, and for larger semi-major axes, the tidal spiral pattern is substantially reduced.Comment: 15 pages, 17 figures, accepted for publication in A&

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&