Hubert Klahr

Turbulence in accretion disks. Vorticity generation and angular momentum transport via the global baroclinic instability

In this paper we present the global baroclinic instability as a source for vigorous turbulence leading to angular momentum transport in Keplerian accretion disks. We show by analytical considerations and three-dimensional radiation-hydrodynamic simulations that, in particular, protoplanetary disks have a negative radial entropy gradient, which makes them baroclinic. Two-dimensional numerical simulations show that a baroclinic flow is unstable and produces turbulence. These findings are tested for numerical effects by performing a simulation with a barotropic initial condition, which shows that imposed turbulence rapidly decays. The turbulence in baroclinic disks transports angular momentum outward and creates a radially inward-bound accretion of matter. Potential energy is released, and excess kinetic energy is dissipated. Finally, the reheating of the gas supports the radial entropy gradient, forming a self-consistent process. We measure accretion rates in our two-dimensional and three-dimensional simulations of = -10-9 to -10-7 M? yr-1 and viscosity parameters of ? = 10-4 to 10-2, which fit perfectly together and agree reasonably with observations. The turbulence creates pressure waves, Rossby waves, and vortices in the (R, )-plane of the disk. We demonstrate in a global simulation that these vortices tend to form out of little background noise and to be long-lasting features, which have already been suggested to lead to the formation of planets.

Formation of giant planets by concurrent accretion of solids and gas inside an anticyclonic vortex

We study the formation of a giant gas planet by the core accretion and gas capture process, with numerical simulations, under the assumption that the planetary core forms in the center of an anticyclonic vortex. The presence of the vortex concentrates centimeter- to meter-sized particles from the surrounding disk and speeds up the core formation process. Assuming that a planet of Jupiter mass is forming at 5 AU from the star, the vortex enhancement results in considerably shorter formation times than are found in standard core-accretion gas-capture simulations. Also, formation of a gas giant is possible in a disk with mass comparable to that of the minimum mass solar nebula.

The Global Baroclinic Instability in Accretion Disks. II. Local Linear Analysis

This paper contains a local linear stability analysis for accretion disks under the influence of a global radial entropy gradient β = -d log T/d log r for constant surface density. Numerical simulations suggested the existence of an instability in two- and three-dimensional models of the solar nebula. The present paper tries to clarify, quantify, and explain such a global baroclinic instability for two-dimensional flat accretion disk models. As a result, linear theory predicts a transient linear instability that will amplify perturbations only for a limited time or up to a certain finite amplification. This can be understood as a result of the growth time of the instability being longer than the shear time, which destroys the modes that are able to grow. Thus, only nonlinear effects can lead to a relevant amplification. Nevertheless, a lower limit on the entropy gradient ∝β ≈ 0.22 for the transient linear instability is derived, which can be tested in future nonlinear simulations. This would help to explain the observed instability in numerical simulations as an ultimate result of the transient linear instability, i.e., the global baroclinic instability.

Dust Distribution in Gas Disks. II. Self-induced Ring Formation through a Clumping Instability

Debris rings of dust are found around young luminous stars such as HR 4796A and HD 141569. Some of these entities have sharp edges and gaps, which have been interpreted as evidence for the presence of shepherding and embedded planets. Here we show that gaps and sharp edges in the debris disks of dust can also be spontaneously self-generated if they are embedded in optically thin regions of gaseous disks. This clumping instability arises in regions where an enhancement in the dust density leads to local gas temperature and pressure increases. Consequently, the relative motion between the gas and the dust is modified. The subsequent hydrodynamic drag on the dust particles leads to further enhancement of their concentration. We show that this process is linearly unstable and leads to the formation of ringlike structures within the estimated lifetime of such young objects. Once the gas is removed (e.g., by photoevaporation), the structures are frozen and will persist, even when the gas might not be observable anymore.

Large-Scale Vortices in Protoplanetary Disks: On the Observability of Possible Early Stages of Planet Formation

We investigate the possibility of mapping large-scale anticyclonic vortices, resulting from a global baroclinic instability, as precursors of planet formation in protoplanetary disks with the planned Atacama Large Millimeter Array (ALMA). On the basis of three-dimensional radiative transfer simulations, images of a hydrodynamically calculated disk are derived that provide the basis for the simulation of ALMA. We find that ALMA will be able to trace the theoretically predicted large-scale anticyclonic vortex and will therefore allow testing of existing models of this very early stage of planet formation in circumstellar disks.