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 beta = - 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 which are able to grow. So only non-linear effects can lead to a relevant amplification. Nevertheless, a lower limit on the entropy gradient ~beta = 0.22 for the transient linear instability is derived, which can be tested in future non-linear 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.Comment: 35 pages, 11 figures; ApJ in pres

Formation of Giant Planets by Concurrent Accretion of Solids and Gas inside an Anti-Cyclonic Vortex

We study the formation of a giant gas planet by the core--accretion gas--capture process, with numerical simulations, under the assumption that the planetary core forms in the center of an anti-cyclonic vortex. The presence of the vortex concentrates particles of centimeter to meter size 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.Comment: 27 pages, 4 figures, ApJ in pres

Large-scale Vortices in Protoplanetary Disks: On the observability of possible early stages of planet formation

We investigate the possibility of mapping large-scale anti-cyclonic vortices, resulting from a global baroclinic instability, as pre-cursors of planet formation in proto-planetary 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 which provide the basis for the simulation of ALMA. We find that ALMA will be able to trace the theoretically predicted large-scale anti-cyclonic vortex and will therefore allow testing of existing models of this very early stage of planet formation in circumstellar disks.Comment: Accepted by ApJ (Letters section). A preprint version with high-quality figures can be downloaded from http://spider.ipac.caltech.edu/staff/swolf/homepage/public/preprints/ vortex.ps.g

Efficiency of thermal relaxation by radiative processes in protoplanetary discs: constraints on hydrodynamic turbulence

Hydrodynamic, non-magnetic instabilities can provide turbulent stress in the regions of protoplanetary discs, where the MRI can not develop. The induced motions influence the grain growth, from which formation of planetesimals begins. Thermal relaxation of the gas constrains origins of the identified hydrodynamic sources of turbulence in discs. We estimate the radiative relaxation timescale of temperature perturbations and study the dependence of this timescale on the perturbation wavelength, the location within the disc, the disc mass, and the dust-to-gas mass ratio. We then apply thermal relaxation criteria to localise modes of the convective overstability, the vertical shear instability, and the zombie vortex instability. Our calculations employed the latest tabulated dust and gas mean opacities and we account for the collisional coupling to the emitting species. The relaxation criterion defines the bulk of a typical T Tauri disc as unstable to the development of linear hydrodynamic instabilities. The midplane is unstable to the convective overstability from at most 2\mbox{ au} and up to 40\mbox{ au}, as well as beyond 140\mbox{ au}. The vertical shear instability can develop between 15\mbox{ au} and 180\mbox{ au}. The successive generation of (zombie) vortices from a seeded noise can work within the inner 0{.}8\mbox{ au}. Dynamic disc modelling with the evolution of dust and gas opacities is required to clearly localise the hydrodynamic turbulence, and especially its non-linear phase.Comment: 13 pages, 8 figure

Gaps, Rings, and Non-Axisymmetric Structures in Protoplanetary Disks - From Simulations to ALMA Observations

Recent observations by the Atacama Large Millimeter/submillimeter Array (ALMA) of disks around young stars revealed distinct asymmetries in the dust continuum emission. In this work we want to study axisymmetric and non-axisymmetric structures, evocated by the magneto-rotational instability in the outer regions of protoplanetary disks. We combine the results of state-of-the-art numerical simulations with post-processing radiative transfer (RT) to generate synthetic maps and predictions for ALMA. We performed non-ideal global 3D MHD stratified simulations of the dead-zone outer edge using the FARGO MHD code PLUTO. The stellar and disk parameters are taken from a parameterized disk model applied for fitting high-angular resolution multi-wavelength observations of circumstellar disks. The 2D temperature and density profiles are calculated consistently from a given surface density profile and Monte-Carlo radiative transfer. The 2D Ohmic resistivity profile is calculated using a dust chemistry model. The magnetic field is a vertical net flux field. The resulting dust reemission provides the basis for the simulation of observations with ALMA. The fiducial model develops a large gap followed by a jump in surface density located at the dead-zone outer edge. The jump in density and pressure is strong enough to stop the radial drift of particles. In addition, we observe the generation of vortices by the Rossby wave instability (RWI) at the jumps location close to 60 AU. The vortices are steadily generated and destroyed at a cycle of 40 local orbits. The RT results and simulated ALMA observations predict the feasibility to observe such large scale structures appearing in magnetized disks without having a planet.Comment: Language update, added comments, added citations, in press. (A&A

Stability and nonlinear adjustment of vortices in Keplerian flows

We investigate the stability, nonlinear development and equilibrium structure of vortices in a background shearing Keplerian flow. We make use of high-resolution global two-dimensional compressible hydrodynamic simulations. We introduce the concept of nonlinear adjustment to describe the transition of unbalanced vortical fields to a long-lived configuration. We discuss the conditions under which vortical perturbations evolve into long-lived persistent structures and we describe the properties of these equilibrium vortices. The properties of equilibrium vortices appear to be independent from the initial conditions and depend only on the local disk parameters. In particular we find that the ratio of the vortex size to the local disk scale height increases with the decrease of the sound speed, reaching values well above the unity. The process of spiral density wave generation by the vortex, discussed in our previous work, appear to maintain its efficiency also at nonlinear amplitudes and we observe the formation of spiral shocks attached to the vortex. The shocks may have important consequences on the long term vortex evolution and possibly on the global disk dynamics. Our study strengthens the arguments in favor of anticyclonic vortices as the candidates for the promotion of planetary formation. Hydrodynamic shocks that are an intrinsic property of persistent vortices in compressible Keplerian flows are an important contributor to the overall balance. These shocks support vortices against viscous dissipation by generating local potential vorticity and should be responsible for the eventual fate of the persistent anticyclonic vortices. Numerical codes have be able to resolve shock waves to describe the vortex dynamics correctly.Comment: 12 pages, 10 figure

Survival of the mm-cm size grain population observed in protoplanetary disks

Millimeter interferometry provides evidence for the presence of mm to cm size "pebbles" in the outer parts of disks around pre-main-sequence stars. The observations suggest that large grains are produced relatively early in disk evolution (< 1 Myr) and remain at large radii for longer periods of time (5 to 10 Myr). Simple theoretical estimates of the radial drift time of solid particles, however, imply that they would drift inward over a time scale of less than 0.1 Myr. In this paper, we address this conflict between theory and observation, using more detailed theoretical models, including the effects of sedimentation, collective drag forces and turbulent viscosity. We find that, although these effects slow down the radial drift of the dust particles, this reduction is not sufficient to explain the observationally determined long survival time of mm/cm-sized grains in protoplanetary disks. However, if for some reason the gas to dust ratio in the disk is reduced by at least a factor of 20 from the canonical value of 100 (for instance through photoevaporation of the gas), then the radial drift time scales become sufficiently large to be in agreement with observations.Comment: Accepted for publication in Astronomy and Astrophysic

Dust sedimentation and self-sustained Kelvin-Helmholtz turbulence in protoplanetary disk mid-planes. I. Radially symmetric simulations

We perform numerical simulations of the Kelvin-Helmholtz instability in the mid-plane of a protoplanetary disk. A two-dimensional corotating slice in the azimuthal--vertical plane of the disk is considered where we include the Coriolis force and the radial advection of the Keplerian rotation flow. Dust grains, treated as individual particles, move under the influence of friction with the gas, while the gas is treated as a compressible fluid. The friction force from the dust grains on the gas leads to a vertical shear in the gas rotation velocity. As the particles settle around the mid-plane due to gravity, the shear increases, and eventually the flow becomes unstable to the Kelvin-Helmholtz instability. The Kelvin-Helmholtz turbulence saturates when the vertical settling of the dust is balanced by the turbulent diffusion away from the mid-plane. The azimuthally averaged state of the self-sustained Kelvin-Helmholtz turbulence is found to have a constant Richardson number in the region around the mid-plane where the dust-to-gas ratio is significant. Nevertheless the dust density has a strong non-axisymmetric component. We identify a powerful clumping mechanism, caused by the dependence of the rotation velocity of the dust grains on the dust-to-gas ratio, as the source of the non-axisymmetry. Our simulations confirm recent findings that the critical Richardson number for Kelvin-Helmholtz instability is around unity or larger, rather than the classical value of 1/4Comment: Accepted for publication in ApJ. Some minor changes due to referee report, most notably that the clumping mechanism has been identified as the streaming instability of Youdin & Goodman (2005). Movies of the simulations are still available at http://www.mpia.de/homes/johansen/research_en.ph

Linear coupling of modes in 2D radially stratified astrophysical discs

We investigate mode coupling in a two dimensional compressible disc with radial stratification and differential rotation. We employ the global radial scaling of linear perturbations and study the linear modes in the local shearing sheet approximation. We employ a three-mode formalism and study the vorticity (W), entropy (S) and compressional (P) modes and their coupling properties. The system exhibits asymmetric three-mode coupling: these include mutual coupling of S and P-modes, S and W-modes, and asymmetric coupling between the W and P-modes. P-mode perturbations are able to generate potential vorticity through indirect three-mode coupling. This process indicates that compressional perturbations can lead to the development of vortical structures and influence the dynamics of radially stratified hydrodynamic accretion and protoplanetary discs.Comment: 10 pages, 10 figures, MNRAS (accepted