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.
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 global non-axisymmetric stationary perturbations of aligned and unaligned logarithmic spiral configurations in an axisymmetric composite differentially rotating disc system of scale-free stellar and isopedically magnetized gas discs coupled
by gravity. The gas disc is threaded across by a vertical magnetic field $B_z$ with a constant dimensionless isopedic ratio $lambdaequiv 2pisqrt{G} Sigma^{(g)}/B_z$ of surface gas mass density $Sigma^{(g)}$ to $B_z$ with $G$ being the gravitational constant. Our exploration focuses on the relation between $lambda$ and the dark matter amount represented by a ratio $fequivbar{Phi}/Phi$ in order to sustain stationary perturbation configurations, where $bar{Phi}$ is the gravitational potential of a presumed axisymmetric halo of dark matter and $Phi$ is the gravitational potential of the composite disc matter. High and low $lambda$ values correspond to relatively weak and strong magnetic fields given the same gas surface mass density, respectively. The main goal of our model analysis is to reveal the relation between isopedic magnetic fields and dark matter halo in spiral galaxies with globally stationary perturbation configurations. Our results show that, fairly strong yet realistic magnetic fields require a considerably larger amount of dark matter in aligned and unaligned cases than weak or moderate magnetic field strengths. We discuss astrophysical and cosmological implications of our findings. For examples, patterns and pattern speeds of galaxies may change during the course of galactic evolution. Multiple-armed galaxies may be more numerous in the early Universe. Flocculent galaxies may represent the transitional phase of pattern variations in galaxies.
