In order to study the origin of the architectures of low mass planetary systems, we perform numerical surveys of the evolution of pairs of coplanar planets in the mass range $(1-4) rmn{M}_{oplus}.$ These evolve for up to $2times10^7 rmn{yr}$ under a
range of orbital migration torques and circularization rates assumed to arise through interaction with a protoplanetary disc. Near the inner disc boundary, significant variations of viscosity, interaction with density waves or with the stellar magnetic field could occur and halt migration, but allow ircularization to continue. This was modelled by modifying the migration and circularization rates. Runs terminated without an extended period of circularization in the absence of migration torques gave rise to either a collision, or a system close to a resonance. These were mostly first order with a few $%$ terminating in second order resonances. Both planetary eccentricities were small $< 0.1$ and all resonant angles liberated. This type of survey produced only a limited range of period ratios and cannot reproduce Kepler observations. When circularization alone operates in the final stages, divergent migration occurs causing period ratios to increase. Depending on its strength the whole period ratio range between $1$ and $2$ can be obtained. A few systems close to second order commensurabilities also occur. In contrast to when arising through convergent migration, resonant trapping does not occur and resonant angles circulate. Thus the behaviour of the resonant angles may indicate the form of migration that led to near resonance.
Supermassive black hole binaries may form as a consequence of galaxy mergers. Both prograde and retrograde orbits have been proposed. We study a binary of a small mass ratio, q, in a retrograde orbit immersed in and interacting with a gaseous accreti
on disk in order to estimate time scales for inward migration leading to coalescence and the accretion rate to the secondary component. We employ both semi-analytic methods and two dimensional numerical simulations, focusing on the case where the binary mass ratio is small but large enough to significantly perturb the disk. We develop the theory of type I migration for this case and determine conditions for gap formation finding that then inward migration occurs on a time scale equal to the time required for one half of the secondary mass to be accreted through the unperturbed disk, with accretion onto the secondary playing only a minor role. The semi-analytic and fully numerical approaches are in good agreement, the former being applicable over long time scales. Inward migration induced by interaction with the disk alleviates the final parsec problem. Accretion onto the secondary does not significantly affect the orbital evolution, but may have observational consequences for high accretion efficiency. The binary may then appear as two sources of radiation rotating around each other. This study should be extended to consider orbits with significant eccentricity and the effects of gravitational radiation at small length scales. Note too that torques acting between a circumbinary disk and a retrograde binary orbit may cause the mutual inclination to increase on a timescale that can be similar to, or smaller than that for orbital evolution, depending on detailed parameters. This is also an aspect for future study (abridged).
We study orbital inclination changes associated with the precession of a disc-planet system that occurs through gravitational interaction with a binary companion on an inclined orbit. We investigate whether this scenario can account for giant planets
on close orbits highly inclined to the stellar equatorial plane. We obtain conditions for maintaining approximate coplanarity and test them with SPH-simulations. For parameters of interest, the system undergoes approximate rigid body precession with modest warping while the planets migrate inwards. Because of pressure forces, disc self-gravity is not needed to maintain the configuration. We consider a disc and single planet for different initial inclinations of the binary orbit to the midplane of the combined system and a system of three planets for which migration leads to dynamical instability that reorders the planets. As the interaction is dominated by the time averaged quadrupole component of the binarys perturbing potential, results for a circular orbit can be scaled to apply to eccentric orbits. The system responded adiabatically when changes to binary orbital parameters occurred on time scales exceeding the orbital period. Accordingly inclination changes are maintained under its slow removal. Thus the scenario for generating high inclination planetary orbits studied here, is promising.
We study systems of close orbiting planets evolving under the influence of tidal circularization. It is supposed that a commensurability forms through the action of disk induced migration and orbital circularization. After the system enters an inner
cavity or the disk disperses the evolution continues under the influence of tides due to the central star which induce orbital circularization. We derive approximate analytic models that describe the evolution away from a general first order resonance that results from tidal circularization in a two planet system and which can be shown to be a direct consequence of the conservation of energy and angular momentum. We consider the situation when the system is initially very close to resonance and also when the system is between resonances. We also perform numerical simulations which confirm these models and then apply them to two and four planet systems chosen to have parameters related to the GJ581 and HD10180 systems. We also estimate the tidal dissipation rates through effective quality factors that could result in evolution to observed period ratios within the lifetimes of the systems. Thus the survival of, or degree of departure from, close commensurabilities in observed systems may be indicative of the effectiveness of tidal disipation, a feature which in turn may be related to the internal structure of the planets involved.
We consider the radial migration of vortices in two-dimensional isothermal gaseous disks. We find that a vortex core, orbiting at the local gas velocity, induces velocity perturbations that propagate away from the vortex as density waves. The resulti
ng spiral wave pattern is reminiscent of an embedded planet. There are two main causes for asymmetries in these wakes: geometrical effects tend to favor the outer wave, while a radial vortensity gradient leads to an asymmetric vortex core, which favors the wave at the side that has the lowest density. In the case of asymmetric waves, which we always find except for a disk of constant pressure, there is a net exchange of angular momentum between the vortex and the surrounding disk, which leads to orbital migration of the vortex. Numerical hydrodynamical simulations show that this migration can be very rapid, on a time scale of a few thousand orbits, for vortices with a size comparable to the scale height of the disk. We discuss the possible effects of vortex migration on planet formation scenarios.
