Tidally-induced angular momentum transport in disks

We discuss the transport of angular momentum induced by tidal effects in a disk surrounding a star in a pre-main sequence binary system. We consider the effect of both density and bending waves. Although tidal effects are important for truncating protostellar disks and for determining their size, it is unlikely that tidally-induced angular momentum transport plays a dominant role in the evolution of protostellar disks. Where the disk is magnetized, transport of angular momentum is probably governed by MHD turbulence. In a non self-gravitating laminar disk, the amount of transport provided by tidal waves is probably too small to account for the lifetime of protostellar disks. In addition, tidal effects tend to be localized in the disk outer regions.Comment: 4 pages, LaTeX, uses newpasp.sty, to be published in 'The Formation of Binary Stars', eds. R.D. Mathieu and H. Zinnecker (ASP Conference Series

Theory of Turbulent Accretion Disks

In low-mass disks, turbulent torques are probably the most important way of redistributing angular momentum. Here we present the theory of turbulent accretion disks. We show the molecular viscosity is far too small to account for the evolutionary timescale of disks, and we describe how turbulence may result in enhanced transport of (angular) momentum. We then turn to the magnetorotational instability, which thus far is the only mechanism that has been shown to initiate and sustain turbulence in disks. Finally, we present both the basis and the structure of alpha disk models.Comment: 25 pages, LaTex, To appear in the proceedings of the Aussois 2000 summer school ``Formation Stellaire et Physique des Etoiles Jeunes'

New composite models of partially ionized protoplanetary disks

We study an accretion disk in which three different regions may coexist: MHD turbulent regions, dead zones and gravitationally unstable regions. Although the dead zones are stable, there is some transport due to the Reynolds stress associated with waves emitted from the turbulent layers. We model the transport in each of the different regions by its own $\alpha$ parameter, this being 10 to $10^{3}$ times smaller in dead zones than in active layers. In gravitationally unstable regions, $\alpha$ is determined by the fact that the disk self-adjusts to a state of marginal stability. We construct steady-state models of such disks. We find that for uniform mass flow, the disk has to be more massive, hotter and thicker at the radii where there is a dead zone. In disks in which the dead zone is very massive, gravitational instabilities are present. Whether such models are realistic or not depends on whether hydrodynamical fluctuations driven by the turbulent layers can penetrate all the way inside the dead zone. This may be more easily achieved when the ratio of the mass of the active layer to that of the dead zone is relatively large, which in our models corresponds to $\alpha$ in the dead zone being about 10% of $\alpha$ in the active layers. If the disk is at some stage of its evolution not in steady-state, then the surface density will evolve toward the steady-state solution. However, if $\alpha$ in the dead zone is much smaller than in the active zone, the timescale for the parts of the disk beyond a few AU to reach steady-state may become longer than the disk lifetime. Steady-state disks with dead zones are a more favorable environment for planet formation than standard disks, since the dead zone is typically 10 times more massive than a corresponding turbulent zone at the same location.Comment: 13 pages, 5 figures, accepted for publication in Ap

Is Planetary Migration Inevitable?

International audienceAccording 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

Stopping inward planetary migration by a toroidal magnetic field

25 pages including 10 figures, Latex in the MN style -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. Since 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 beta=c^2/v_A^2 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 beta=100 at corotation, a negative torque may be obtained. A planet migrating inward through a nonmagnetized 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