Planet formation and dynamics

Abstract:

According to current theories, tidal interactions between a disk and an embedded planet may lead to the rapid migration of the protoplanet on a timescale shorter than the disk lifetime or estimated planetary formation timescales. Therefore, planets can form only if there is a mechanism to hold at least some of the cores back on their way in. Once a giant planet has assembled, there also has to be a mechanism to prevent it from migrating down to the disk center. This paper reviews the different mechanisms that have been proposed to stop or slow down migration.

Abstract:

We calculate the linear torque exerted by a planet on a circular orbit on a disc containing a toroidal magnetic field. All fluid perturbations are singular at the so-called magnetic resonances, where the Doppler shifted frequency of the perturbation matches that of a slow MHD wave propagating along the field line. These lie on both sides of the corotation radius. Waves propagate outside the Lindblad resonances, and also in a restricted region around the magnetic resonances. The magnetic resonances contribute to a significant global torque which, like the Lindblad torque, is negative (positive) inside (outside) the planet's orbit. As these resonances are closer to the planet than the Lindblad resonances, the torque they contribute dominates over the Lindblad torque if the magnetic field is large enough. In addition, if β ≡ c2/vA2 increases fast enough with radius, the outer magnetic resonance becomes less important and the total torque is then negative, dominated by the inner magnetic resonance. This leads to outward migration of the planet. Even for β ∼ 100 at corotation, a negative torque may be obtained. A planet migrating inward through a non-magnetized region of a disc would then stall when reaching a magnetized region. It would then be able to grow to become a terrestrial planet or the core of a giant planet. In a turbulent magnetized disc in which the large-scale field structure changes sufficiently slowly, a planet may alternate between inward and outward migration, depending on the gradients of the field encountered. Its migration could then become diffusive, or be limited only to small scales.

Abstract:

We consider the evolution of a system containing a population of massive planets formed rapidly through a fragmentation process occurring on a scale on the order of 100 au and a lower mass planet that assembles in a disc on a much longer time-scale. During the formation phase, the inner planet is kept on a circular orbit owing to tidal interaction with the disc, while the outer planets undergo dynamical relaxation. Interaction with the massive planets left in the system after the inner planet forms may increase the eccentricity of the inner orbit to high values, producing systems similar to those observed.

Abstract:

Following the suggestion of Black that some massive extrasolar planets may be associated with the tail of the distribution of stellar companions, we investigate a scenario in which 5 ≤ N ≤ 100 planetary mass objects are assumed to form rapidly through a fragmentation process occuring in a disc or protostellar envelope on a scale of 100 au. These are assumed to have formed rapidly enough through gravitational instability or fragmentation that their orbits can undergo dynamical relaxation on a time-scale of ∼100 orbits. Under a wide range of initial conditions and assumptions, the relaxation process ends with either (i) one potential 'hot Jupiter' plus up to two 'external' companions, i.e. planets orbiting near the outer edge of the initial distribution; (ii) one or two 'external' planets or even none at all; (iii) one planet on an orbit with a semi-major axis of 10 to 100 times smaller than the outer boundary radius of the inital distribution together with an 'external' companion. Most of the other objects are ejected and could contribute to a population of free-floating planets. Apart from the potential 'hot Jupiters', all the bound objects are on orbits with high eccentricity, and also with a range of inclination with respect to the stellar equatorial plane. We found that, apart from the close orbiters, the probability of ending up with a planet orbiting at a given distance from the central star increases with the distance. This is because of the tendency of the relaxation process to lead to collisions with the central star. The scenario we envision here does not impose any upper limit on the mass of the planets. We discuss the application of these results to some of the more massive extrasolar planets.