Turbulence in Accretion Disks: Vorticity Generation and Angular Momentum Transport via the Global Baroclinic Instability

By H. Klahr, Peter Bodenheimer UCOLick Observatory, C. Physics, I. F. A. U. Astrophysik, U. Tuebingen, Heidelberg · Germany. 2002

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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 Ṁ = -10-9 to -10-7 M☉ yr-1 and viscosity parameters of α = 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, ϕ)-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.

Subfields: Astronomy and Astrophysics, Fluid Flow and Transfer Processes, Spectroscopy

View Paper: https://www.semanticscholar.org/paper/665defa2b248b0e10a49f17da877b00774502f32

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Citations in the corpus

Dust Evolution and the Formation of Planetesimals (2016, background): “Alternatively, other hydrodynamical concentration mechanisms may be are able to bridge the gap, e.g. the baroclinic instability/convective overstability (Klahr & Bodenheimer 2003) or the vertical shear instability (Nelson et al. 2013).”
On the Corotation Torque in a Radiatively Inefficient Disk (2007, background): “We comment also that in such systems, a negative entropy gradient may render the disk unstable to a baroclinic instability (Klahr 2004; Klahr & Bodenheimer 2003).”
Semi-global simulations of the magneto-rotational instability in core collapse supernovae (2008, methodology): “We have used a recently developed highresolution MHD code, and employedshearing-diskboundary conditions (Klahr & Bodenheimer 2003).”
The great dichotomy of the Solar System: Small terrestrial embryos and massive giant planet cores (2015, background): “, 2007), baroclynic instability (Klahr and Bodenheimer, 2003), vertical shear instability (Nelson et al.”
The subcritical baroclinic instability in local accretion disc models (2009, methodology): “This suggests that either the global baroclinic instability described by Klahr & Bodenheimer (2003) and the SBI are two separate instabilities, or strong numerical artefacts have produced an artificially large thermal diffusion in Klahr & Bodenheimer (2003) simulations.”
Gravoturbulent Formation of Planetesimals (2005, background): “Giant long-lived vortices may form in protoplanetary disc due to a baroclinic instability (Klahr & Bodenheimer 2003), but the conditions for the baroclinic instability in protoplanetary discs are still not clear (Klahr 2004).”
Breaking the chains: hot super-Earth systems from migration and disruption of compact resonant chains (2017, background): “Instabilities include the Rossby-wave instability (Lovelace et al. 1999), the global baroclinic instability (Klahr & Bodenheimer 2003), the Kelvin–Helmholtz instability generated during dust vertical sedimentation towards the disc mid-plane (Johansen, Henning & Klahr 2006) and the vertical shear…”
Grain Retention and Formation of Planetesimals near the Snow Line in MRI-driven Turbulent Protoplanetary Disks (2007, background): “…(Lin & Papaloizaou 1980), gravitational torques (Laughlin & Rozycza 1996), linear Rossby wave instability (Li et al. 2000), baroclinic instability (Klahr & Bodenheimer 2003; Klahr 2004), linear stratorotational instability (Dubrulle et al. 2005; Shalybkov & Rüdiger 2005), etc.) so that it is…”
The structure of protoplanetary discs around evolving young stars (2014, background): “Additionally, hydrodynamical instabilities, such as the baroclinic instability (Klahr & Bodenheimer 2003) or the vertical shear instability (Nelson et al. 2013; Stoll & Kley 2014), can act as a source of turbulence in the weakly ionised regions of the disc.”
Two‐dimensional adiabatic flows on to a black hole – I. Fluid accretion (2003, background): “In particular, baroclinic discs (i.e. discs in which ∇ P ×∇ρ̄ = 0) can be susceptible to non-axisymmetric modes even when the second Høiland criterion is satisfied (see, e.g., Klahr & Bodenheimer 2003).”
Planet formation bursts at the borders of the dead zone in 2D numerical simulations of circumstellar disks (2009, background): “Vortices in disks can be the result of the baroclinic instability (Klahr & Bodenheimer 2003; Klahr 2004; Petersen et al. 2007), the Rossby wave instability (Lovelace et al. 1999; Li et al. 2000; Li et al. 2001) or, perhaps, the MRI (Fromang and Nelson 2005).”
Linear and non-linear evolution of the vertical shear instability in accretion discs (2012, background): “In the context of protoplanetary discs, for example, the formation of vortices is believed to have potential importance for planet formation (e.g. Barge & Sommeria 1995; Klahr & Bodenheimer 2003).”
Ice Condensation as a Planet Formation Mechanism (2013, background): “Particles also concentrate in long-lived vortices (Barge & Sommeria, 1995; Klahr & Bodenheimer, 2003) and pressure bumps (Johansen et al., 2009) excited in the turbulent flow.”
Pebble-isolation mass: Scaling law and implications for the formation of super-Earths and gas giants (2018, background): “Simulations with hydrodynamical instabilities in regions of the disc that are not subject to MRI-driven turbulence show α values of a few times 10−4, which probably sets a lower limit on turbulence (Klahr & Bodenheimer 2003; Nelson et al. 2013; Stoll & Kley 2016).”
Heating Protoplanetary Disk Atmospheres (2004, background): “…enhanced line width include turbulence associated with in situ angular momentum transport (e.g., via the magnetorotational instability [Balbus & Hawley 1991] or the global baroclinic instability [Klahr & Bodenheimer 2003]) or turbulence induced at the disk surface by a wind blowing over the disk.”
THREE-DIMENSIONAL SIMULATION OF MASSIVE STAR FORMATION IN THE DISK ACCRETION SCENARIO (2011, background): “Developing convective (Kley et al. 1993a; Lin et al. 1993), radiation hydrodynamical (Klahr & Bodenheimer 2003), magneto-rotational (Balbus & Hawley 1991; Hawley & Balbus 1991; Flock et al. 2010; Dzyurkevich et al. 2010) and self-gravitating instabilities (Yang et al. 1991; Laughlin & Bodenheimer…”
On the relevance of subcritical hydrodynamic turbulence to accretion disk transport (2005, neutral): “A local, baroclinic-like instability has been observed in global simulations by Klahr & Bodenheimer (2003).”
Toward Planetesimals: Dense Chondrule Clumps in the Protoplanetary Nebula (2008, background): “Baroclinic instabilities require substantial opacity at thermal wavelengths, but might be suitable to generate turbulence during the fairly opaque chondrule-CAI epoch in the inner solar system (Klahr and Bodenheimer 2003).”