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

Klahr, Hubert

doi:10.1086/383119

Cited by 75 publications

(100 citation statements)

References 18 publications

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“…Klahr & Bodenheimer (2003) and Klahr (2004) propose a non linear hydrodynamical instability growing in an entropy gradient (Petersen et al 2007a,b), called the baroclinic instability, to form such structures. show that these vortices are stable structures in 3D, whereas the MHD approach of Lyra & Klahr (2011) prove that this instability can form vortices only in the dead zone; however, the vortices migrate radially due to the radial pressure gradient (Paardekooper et al 2010), and their long-term stability is not clear.…”

Section: Introductionmentioning

confidence: 99%

Dust-trapping Rossby vortices in protoplanetary disks

Méheut¹,

Méliani²,

Varnière³

et al. 2012

A&A

111

108

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Context. One of the most challenging steps in planet formation theory is the one leading to the formation of planetesimals of kilometre size. A promising scenario involves the existence of vortices able to concentrate a large amount of dust and grains in their centres. Up to now this scenario has mostly been studied in 2D razor thin disks. A 3D study including, simultaneously, the formation and resulting dust concentration of the vortices with vertical settling, is still missing. Aims. The Rossby wave instability self-consistently forms 3D vortices, which have the unique quality of presenting a large-scale vertical velocity in their centre. Here we aim to study how this newly discovered effect can alter the dynamic evolution of the dust. Methods. We performed global 3D simulations of the RWI in a radially and vertically stratified disk using the code MPI-AMRVAC. After the growth phase of the instability, the gas and solid phases are modelled by a bi-fluid approach, where the dust is considered as a fluid without pressure. Both the drag force of the gas on the dust and the back reaction of the dust on the gas are included. Multiple grain sizes from 1 mm to 5 cm are used with a constant density distribution. Results. We obtain in a short timescale a high concentration of the largest grains in the vortices. Indeed, in 3 rotations the dust-to-gas density ratio grows from 10 −2 to unity leading to a concentration of mass up to that of Mars in one vortex. The presence of the radial drift is also at the origin of a dust pile-up at the radius of the vortices. Lastly, the vertical velocity of the gas in the vortex causes the sedimentation process to be reversed, the mm size dust is lifted and higher concentrations are obtained in the upper layer than in the midplane. Conclusions. The Rossby wave instability is a promising mechanism for planetesimal formation, and the results presented here can be of particular interest in the context of future observations of protoplanetary disks.

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Section: Introductionmentioning

confidence: 99%

Dust-trapping Rossby vortices in protoplanetary disks

Méheut¹,

Méliani²,

Varnière³

et al. 2012

A&A

111

108

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“…Therefore, the search for hydrodynamical sources of turbulence continues, if only to provide some residual accretion in the dead zone. A distinct possibility is the baroclinic instability (BI; Klahr & Bodenheimer 2003;Klahr 2004), the interest in which has been recently rekindled (Petersen et al 2007a,b;Lesur & Papaloizou 2010).…”

Section: Introductionmentioning

confidence: 99%

“…The difference between the baroclinic instability of weather patterns on planetary atmospheres and the baroclinic instability in accretion disks is that the former is linear, whereas the latter is nonlinear (Klahr 2004;Lesur & Papaloizou 2010). This is because in accretion disks, the disturbances have to overcome the strong Keplerian shear that causes perturbations to be heavily dominated by restoring forces in all Reynolds numbers.…”

Section: Introductionmentioning

confidence: 99%

The baroclinic instability in the context of layered accretion

Lyra

Klahr

2011

A&A

126

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Context. Turbulence and angular momentum transport in accretion disks remains a topic of debate. With the realization that dead zones are robust features of protoplanetary disks, the search for hydrodynamical sources of turbulence continues. A possible source is the baroclinic instability (BI), which has been shown to exist in unmagnetized non-barotropic disks. Aims. We aim to verify the existence of the baroclinic instability in 3D magnetized disks, as well as its interplay with other instabilities, namely the magneto-rotational instability (MRI) and the magneto-elliptical instability. Methods. We performed local simulations of non-isothermal accretion disks with the Pencil Code. The entropy gradient that generates the baroclinic instability is linearized and included in the momentum and energy equations in the shearing box approximation. The model is compressible, so excitation of spiral density waves is allowed and angular momentum transport can be measured. Results. We find that the vortices generated and sustained by the baroclinic instability in the purely hydrodynamical regime do not survive when magnetic fields are included. The MRI by far supersedes the BI in growth rate and strength at saturation. The resulting turbulence is virtually identical to an MRI-only scenario. We measured the intrinsic vorticity profile of the vortex, finding little radial variation in the vortex core. Nevertheless, the core is disrupted by an MHD instability, which we identify with the magneto-elliptic instability. This instability has nearly the same range of unstable wavelengths as the MRI, but has higher growth rates. In fact, we identify the MRI as a limiting case of the magneto-elliptic instability, when the vortex aspect ratio tends to infinity (pure shear flow). We isolated its effect on the vortex, finding that a strong but unstable vertical magnetic field leads to channel flows inside the vortex, which stretch it apart. When the field is decreased or resistivity is used, we find that the vortex survives until the MRI develops in the box. The vortex is then destroyed by the strain of the surrounding turbulence. Constant azimuthal fields and zero net flux fields also lead to vortex destruction. Resistivity quenches both instabilities when the magnetic Reynolds number of the longest vertical wavelength of the box is near unity. Conclusions. We conclude that vortex excitation and self-sustenance by the baroclinic instability in protoplanetary disks is viable only in low ionization, i.e., the dead zone. Our results are thus in accordance with the layered accretion paradigm. A baroclinicly unstable dead zone should be characterized by the presence of large-scale vortices whose cores are elliptically unstable, yet sustained by the baroclinic feedback. Since magnetic fields destroy the vortices and the MRI outweighs the BI, the active layers are unmodified.

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“…Klahr & Bodenheimer (2006) further argue that anticyclonic vortices would be less turbulent than the ambient gas, which in turn would lead to velocity dispersions that are low enough to prevent fragmentation. 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 & Nelson 2005).…”

Section: Introductionmentioning

confidence: 99%

Planet formation bursts at the borders of the dead zone in 2D numerical simulations of circumstellar disks

Lyra¹,

Johansen

Zsom

et al. 2009

A&A

167

188

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Context. As accretion in protoplanetary disks is enabled by turbulent viscosity, the border between active and inactive (dead) zones constitutes a location where there is an abrupt change in the accretion flow. The gas accumulation that ensues triggers the Rossby wave instability, which in turn saturates into anticyclonic vortices. It has been suggested that the trapping of solids within them leads to a burst of planet formation on very short timescales. Aims. We study in the formation and evolution of the vortices in greater detail, focusing on the implications for the dynamics of embedded solid particles and planet formation. Methods. We performed two-dimensional global simulations of the dynamics of gas and solids in a non-magnetized thin protoplanetary disk with the Pencil code. We used multiple particle species of radius 1, 10, 30, and 100 cm. We computed the particles' gravitational interaction by a particle-mesh method, translating the particles' number density into surface density and computing the corresponding self-gravitational potential via fast Fourier transforms. The dead zone is modeled as a region of low viscosity. Adiabatic and locally isothermal equations of state are used. Results. The Rossby wave instability is triggered under a variety of conditions, thus making vortex formation a robust process. Inside the vortices, fast accumulation of solids occurs and the particles collapse into objects of planetary mass on timescales as short as five orbits. Because the drag force is size-dependent, aerodynamical sorting ensues within the vortical motion, and the first bound structures formed are composed primarily of similarly-sized particles. In addition to erosion due to ram pressure, we identify gas tides from the massive vortices as a disrupting agent of formed protoplanetary embryos. We find evidence that the backreaction of the drag force from the particles onto the gas modifies the evolution of the Rossby wave instability, with vortices being launched only at later times if this term is excluded from the momentum equation. Even though the gas is not initially gravitationally unstable, the vortices can grow to Q ≈ 1 in locally isothermal runs, which halts the inverse cascade of energy towards smaller wavenumbers. As a result, vortices in models without self-gravity tend to rapidly merge towards a m = 2 or m = 1 mode, while models with self-gravity retain dominant higher order modes (m = 4 or m = 3) for longer times. Non-selfgravitating disks thus show fewer and stronger vortices. We also estimate the collisional velocity history of the particles that compose the most massive embryo by the end of the simulation, finding that the vast majority of them never experienced a collision with another particle at speeds faster than 1 m s −1 . This result lends further support to previous studies showing that vortices provide a favorable environment for planet formation.

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

Cited by 75 publications

References 18 publications

Dust-trapping Rossby vortices in protoplanetary disks

Dust-trapping Rossby vortices in protoplanetary disks

The baroclinic instability in the context of layered accretion

Planet formation bursts at the borders of the dead zone in 2D numerical simulations of circumstellar disks

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