ALBERT

Description: Pairs of extrasolar giant planets in a mean motion commensurability are common with 2:1 resonance occurring most frequently. Disc–planet interaction provides a mechanism for their origin. However, the time-scale on which this could operate in particular cases is unclear. We perform 2D and 3D numerical simulations of pairs of giant planets in a protoplanetary disc as they form and maintain a mean motion commensurability. We consider systems with current parameters similar to those of HD 155358, 24 Sextantis and HD 60532, and disc models of varying mass, decreasing mass corresponding to increasing age. For the lowest mass discs, systems with planets in the Jovian mass range migrate inwards maintaining a 2:1 commensurability. Systems with the inner planet currently at around 1 au from the central star could have originated at a few au and migrated inwards on a time-scale comparable to protoplanetary disc lifetimes. Systems of larger mass planets such as HD 60532 attain 3:1 resonance as observed. For a given mass accretion rate, results are insensitive to the disc model for the range of viscosity prescriptions adopted, there being good agreement between 2D and 3D simulations. However, in a higher mass disc a pair of Jovian mass planets passes through 2:1 resonance before attaining a temporary phase lasting a few thousand orbits in an unstable 5:3 resonance prior to undergoing a scattering. Thus, finding systems in this commensurability is unlikely.

Description: We determine the response of a uniformly rotating star to tidal perturbations due to a companion. General periodic orbits and parabolic flybys are considered. We evaluate energy and angular momentum exchange rates as a sum of contributions from normal modes allowing for dissipative processes. We consider the case when the response is dominated by the contribution of an identifiable regular spectrum of low-frequency modes, such as rotationally modified gravity modes. We evaluate this response in the limit of very weak dissipation, where individual resonances can be significant and also when dissipative effects are strong enough to prevent wave reflection from the neighbourhood of either the stellar surface or stellar centre, making radiation conditions more appropriate. The former situation may apply to Sun-like stars with radiative cores and convective envelopes and the latter to more massive stars with convective cores and radiative envelopes. We provide general expressions for transfer of energy and angular momentum that can be applied to an orbit with any eccentricity. Detailed calculations require knowledge of the mode spectrum and evaluation of the mode overlap integrals that measure the strength of the tidal interaction. These are evaluated for Sun-like stars in the slow rotation regime where centrifugal distortion is neglected in the equilibrium and the traditional approximation is made for the normal modes. We use both a Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) procedure and a direct numerical evaluation which are found to be in good agreement for regimes of interest. The former is used to provide expressions for the mode spectrum and overlap integrals as a function of mode frequency and stellar rotation rate. These can be used to find the tidal energy and angular momentum exchange rates and hence the orbital evolution. Finally we use our formalism to determine the evolution time scales for an object, in an orbit of small eccentricity, around a Sun-like star in which the tidal response is assumed to occur. Systems with either no rotation or synchronous rotation are considered. Only rotationally modified gravity modes are taken into account under the assumption that wave dissipation proceeds close to the stellar centre. It is noted that inertial waves excited in the convective envelope may produce a comparable amount of tidal dissipation in the latter case for sufficiently large orbital periods.

Description: 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 per cent 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.

Description: 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 a single planet for different initial inclinations of the binary orbit to the mid-plane 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.

Description: In order to circumvent the loss of solid material through radial drift towards the central star, the trapping of dust inside persistent vortices in protoplanetary discs has often been suggested as a process that can eventually lead to planetesimal formation. Although a few special cases have been discussed, exhaustive studies of possible quasi-steady configurations available for dust-laden vortices and their stability are yet to be undertaken, thus their viability or otherwise as locations for the gravitational instability to take hold and seed planet formation is unclear. In this paper we generalize and extend the well-known Kida solution to obtain a series of steady-state solutions with varying vorticity and dust density distributions in their cores, in the limit of perfectly coupled dust and gas. We then present a local stability analysis of these configurations, considering perturbations localized on streamlines. Typical parametric instabilities found have growth rates of 0.05 P , where P is the angular velocity at the centre of the vortex. Models with density excess can exhibit many narrow parametric instability bands while those with a concentrated vorticity source display internal shear which significantly affects their stability. However, the existence of these parametric instabilities may not necessarily prevent the possibility of dust accumulation in vortices.

Description: The migration of low-mass planets, or type I planetary migration, has been studied in hydrodynamical disc models for more than three decades. For a long time, it was thought to be very rapid and directed inwards due to Lindblad torques. More recently, it has been shown that the corotation torque, linked to the horseshoe motion of the gas near the planet, may slow down or even reverse migration. How is this picture modified by the expected presence of a magnetic field in the protoplanetary disc? When the magnetic field is strong enough to prevent horseshoe motion, the corotation torque is replaced by a torque arising from magnetic resonances which may significantly alter the migration rate. In the case of a weaker magnetic field, the magnetic field is not strong enough to prevent horseshoe motion and a corotation torque then exists. In this regime, recent turbulent magnetohydrodynamical (MHD) simulations have reported the existence of an additional component of the corotation torque due to the presence of the magnetic field. The aim of this paper is to investigate the physical origin and the properties of this additional corotation torque. We performed MHD simulations of a low-mass planet embedded in a 2D laminar disc threaded by a weak toroidal magnetic field, where the effects of turbulence are modelled by a viscosity and a resistivity. We confirm that the interaction between the magnetic field and the horseshoe motion of the gas results in an additional corotation torque on the planet, which we dub the MHD torque excess. We demonstrate that it is caused by the accumulation of the magnetic field along the downstream separatrices of the horseshoe region, which gives rise to an azimuthally asymmetric underdense region at that location. The properties of the MHD torque excess are characterized by varying the slope of the density, temperature and magnetic field profiles, as well as the diffusion coefficients and the strength of the magnetic field. The sign of the torque excess and its radial distribution are found to be in agreement with the earlier full magnetorotational instability simulations. This sign depends on the density and temperature gradients only and is positive for profiles expected in protoplanetary discs. The magnitude of the torque excess is in turn mainly determined by the strength of the magnetic field and the turbulent resistivity. It can be strong enough to reverse migration even when the magnetic pressure is less than 1 per cent of the thermal pressure. The MHD torque excess can therefore lead to outward planetary migration in the radiatively efficient outer parts of protoplanetary discs, where the hydrodynamical corotation torque is too weak to prevent fast inward migration.

Description: We study, by means of numerical simulations and analysis, the details of the accretion process from a disc on to a binary system. We show that energy is dissipated at the edge of a circumbinary disc and this is associated with the tidal torque that maintains the cavity: angular momentum is transferred from the binary to the disc through the action of compressional shocks and viscous friction. These shocks can be viewed as being produced by fluid elements that drift into the cavity and, before being accreted, are accelerated on to trajectories that send them back to impact the disc. The rate of energy dissipation is approximately equal to the product of potential energy per unit mass at the disc's inner edge and the accretion rate, estimated from the disc parameters just beyond the cavity edge, that would occur without the binary. For very thin discs, the actual accretion rate on to the binary may be significantly less. We calculate the energy emitted by a circumbinary disc taking into account energy dissipation at the inner edge and also irradiation arising there from reprocessing of light from the stars. We find that, for tight PMS binaries, the SED is dominated by emission from the inner edge at wavelengths between 1–4 and 10 μm. This may apply to systems like CoRoT 223992193 and V1481 Ori.