We study the interaction between massive planets and a gas disc with a mass in the range expected for protoplanetary discs. We use SPH simulations to study the orbital evolution of a massive planet as well as the dynamical response of the disc for planet masses between 1 and 6 M J and the full range of initial relative orbital inclinations.We find that gap formation can occur for planets in inclined orbits as well as for coplanar orbits as expected. For given planet mass, a threshold relative orbital inclination exists under which a gap forms. This threshold increases with planet mass. Orbital migration manifest through a decreasing semi-major axis is seen in all cases.At high relative inclinations, the inclination decay rate increases for increasing planet mass and decreasing initial relative inclination as is expected from estimates based on dynamical friction between planet and disc. For an initial semi-major axis of 5 AU and relative inclination of i 0 = 80 • , the times required for the inclination to decay by 10 • is ∼ 10 6 yr and ∼ 10 5 yr for 1 M J and 6 M J respectively, these times scaling in the usual way for larger initial orbits. For retrograde planets, the inclination always evolves towards coplanarity with the disc, with the rate of evolution being fastest for orbits with i 0 → 180 • . The indication is thus that, without taking account of subsequent operation of phenomena such as the Lidov-Kozai effect, planets with mass 1 M J initiated in circular orbits with semi-major axis ∼ 5 AU and i 0 ∼ 90 • might only just become coplanar, as a result of frictional effects, within the disc lifetime. In other cases highly inclined orbits will survive only if they are formed after the disc has mostly dispersed.Planets on inclined orbits warp the disc by an extent that is negligible for 1 M J but increases with increasing mass becoming quite significant for a planet of mass 6 M J . In that case, the disc can gain a total inclination of up to 15 • together with a warped inner structure with an inclination of up to ∼ 20 • relative to the outer part. We also find a solid body precession of both the total disc angular momentum vector and the planet orbital momentum vector about the total angular momentum vector, with the angular velocity of precession decreasing with increasing relative inclination as expected in that case.Our results illustrate that the influence of an inclined massive planet on a protoplanetary disc can lead to significant changes of the disc structure and orientation which can in turn affect the orbital evolution of the planet significantly. A threedimensional treatment of the disc is then essential in order to capture all relevant dynamical processes in the composite system.

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 binary's 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 the three-dimensional evolution of a viscous protoplanetary disc which is perturbed by a passing star on a parabolic orbit. The aim is to test whether a single stellar flyby is capable to excite significant disc inclinations which would favour the formation of so-called misaligned planets. We use smoothed particle hydrodynamics to study inclination, disc mass and angular momentum changes of the disc for passing stars with different masses. We explore different orbital configurations for the perturber's orbit to find the parameter spaces which allow significant disc inclination generation. Prograde inclined parabolic orbits are most destructive leading to significant disc mass and angular momentum loss. In the remaining disc, the final disc inclination is only below 20 • . This is due to the removal of disc particles which have experienced the strongest perturbing effects. Retrograde inclined parabolic orbits are less destructive and can generate disc inclinations up to 60 • . The final disc orientation is determined by the precession of the disc angular momentum vector about the perturber's orbital angular momentum vector and by disc orbital inclination changes.We propose a sequence of stellar flybys for the generation of misalignment angles above 60 • . The results taken together show that stellar flybys are promising and realistic for the explanation of misaligned Hot Jupiters with misalignment angles up to 60 • .

We investigate misaligned accretion discs formed after tidal disruption events that occur when a star encounters a supermassive black hole. We employ the linear theory of warped accretion discs to find the shape of a disc for which the stream arising from the disrupted star provides a source of angular momentum that is misaligned with that of the black hole. For quasi-steady configurations we find that when the warp diffusion or propagation time is large compared to the local mass accretion time and/or the natural disc alignment radius is small, misalignment is favoured.These results have been verified using SPH simulations. We also simulated 1D model discs including gas and radiation pressure. As accretion rates initially exceed the Eddington limit the disc is initially advection dominated. Assuming the α model for the disc, where it can be thermally unstable it subsequently undergoes cyclic transitions between high and low states. During these transitions the aspect ratio varies from ∼ 1 to ∼ 10 −3 which is reflected in changes in the degree of disc misalignment at the stream impact location. For maximal black hole rotation and sufficiently large values of viscosity parameter α >∼ 0.01 − 0.1 the ratio of the disc inclination to that of the initial stellar orbit is estimated to be 0.1 − 0.2 in the advection dominated state, while reaching of order unity in the low state. Misalignment descreases with decrease of α, but increases as the black hole rotation parameter decreases. Thus, it is always significant when the latter is small.

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) M ⊕ . These evolve for up to 2 × 10 7 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 circularization 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.