Dusty Vortices in Protoplanetary Disks (original) (raw)
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Monthly Notices of the Royal Astronomical Society, 2001
We investigate the response of dust particles in the mid-plane of a protoplanetary disc to the turbulent velocity field of long-lived, large-scale vortical circulation. The dynamical problem is studied through numerical integrations of the equations of motion for individual particles (the sizes of which range from centimetres to metres) subject to the solar gravity and the friction drag of the nebular gas. It is found, neglecting the thickness of the disc, that the particles do not drift inwards to the central star as occurs in a standard symmetrical nebula. Vortices tend to capture a large number of the particles. The effectiveness of this size-selective concentration mechanism depends not only on the value of the drag and the distance from the Sun, but also on the elongation of the vortex and its characteristic lifetime. Typical anticyclonic vortices with exponential decay times of 30 orbital periods and semiaxis ratios of 4 can increase the local surface density by a factor of 4 in a lifetime and accumulate 0:03±0:3 Earth masses. If the elongation is significant (.7), the vortex cannot concentrate any significant amount of solid material. Vortices with an elongation of about 2 are the most effective as regards trapping of dust. We have also found analytical expressions for the capture time as well as capture constraints as a function of the friction parameter, the elongation of the vortex and the impact parameter. By increasing the lifetime and the surface density of the solid particles, this confining mechanism can make the agglomeration of the solid material of the nebula (through collisional aggregation or gravitational instabilities) much more efficient than previously believed. This offers new possibilities for the formation of the planetesimals and the giant planet cores, and may explain the rapid formation of extrasolar giant planets.
Dust-trapping Rossby vortices in protoplanetary disks
Astronomy & Astrophysics, 2012
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-togas 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 pileup 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.
Simulations of dust-trapping vortices in protoplanetary discs
Astronomy and Astrophysics, 2004
Local three-dimensional shearing box simulations of the compressible coupled dust-gas equations are used in the fluid approximation to study the evolution of different initial vortex configurations in a protoplanetary disc and their dust-trapping capabilities. The initial conditions for the gas are derived from an analytic solution to the compressible Euler equation and the continuity equation. The solution is valid if there is a vacuum outside the vortex. In the simulations the vortex is either embedded in a hot corona, or it is extended in a cylindrical fashion in the vertical direction. Both configurations are found to survive for at least one orbit and lead to accumulation of dust inside the vortex. This confirms earlier findings that dust accumulates in anticyclonic vortices, indicating that this is a viable mechanism for planetesimal formation.
Particle Trapping and Streaming Instability in Vortices in Protoplanetary Disks
The Astrophysical Journal, 2015
We analyse the concentration of solid particles in vortices created and sustained by radial buoyancy in protoplanetary disks, i.e. baroclinic vortex growth. Besides the gas drag acting on particles we also allow for back-reaction from dust onto the gas. This becomes important when the local dustto-gas ratio approaches unity. In our 2D, local, shearing sheet simulations we see high concentrations of grains inside the vortices for a broad range of Stokes numbers, St. An initial dust-to-gas ratio of 1:100 can easily be reversed to 100:1 for St = 1. The increased dust-to-gas ratio triggers the streaming instability, thus counter-intuitively limiting the maximal achievable overdensities. We find that particle trapping inside vortices opens the possibility for gravity-assisted planetesimal formation even for small particles (St = 0.01) and low initial dust-to-gas ratios (1:10 4 ).
Astronomy and Astrophysics, 2009
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 1m s −1 . This result lends further support to previous studies showing that vortices provide a favorable environment for planet formation.
Structure, stability, and evolution of 3D Rossby vortices in protoplanetary disks
Astronomy & Astrophysics, 2013
Context. Large-scale persistent vortices could play a key role in the evolution of protoplanetary disks, particularly in the dead zone where no turbulence associated with a magnetic field is expected. These vortices are known to form easily in 2D disks via the Rossby wave or the baroclinic instability. In three dimensions, however, their formation and stability is a complex problem and still a matter of debate. Aims. We study the formation of vortices by the Rossby wave instability in a stratified inviscid disk and describe their 3D structure, stability, and long-term evolution. Methods. Numerical simulations were performed using a fully compressible hydrodynamical code based on a second-order finite volume method. We assumed a perfect-gas law and a non-homentropic adiabatic flow. Results. The Rossby wave instability is found to proceed in 3D in a similar way as in 2D. Vortices produced by the instability look like columns of vorticity in the whole disk thickness; the weak vertical motions are related to the weak inclination of the vortex axis that appears during the development of the RWI. Vortices with aspect ratios higher than 6 are unaffected by the elliptical instability. They relax into a quasi-steady columnar structure that survives hundreds of rotations while slowly migrating inward toward the star at a rate that reduces with the vortex aspect ratio. Vortices with a lower aspect ratio are by contrast affected by the elliptic instability. Short aspect ratio vortices (χ < 4) are completely destroyed in a few orbital periods. Vortices with an intermediate aspect ratio (4 < χ < 6) are partially destroyed by the elliptical instability in a region away from the midplane where the disk stratification is sufficiently strong. Conclusions. Elongated Rossby vortices can survive many orbital periods in protoplanetary disks in the form of vorticity columns. They could play a significant role in the evolution of the gas and the gathering of solid particles to form planetesimals or planetary cores, a possibility that receives a renewed interest with the recent discovery of a particle trap in the disk of Oph IRS 48.
Quasi-steady vortices in protoplanetary disks
Astronomy & Astrophysics, 2015
Aims. We determine the size, structure, and evolution of persistent vortices in 2D and inviscid Keplerian flows. Methods. A Gaussian model of the vortices is built and compared with numerical solutions issued from non-linear hydrodynamical simulations. Test vortices are also produced using a fiducial method based on the Rossby wave instability to help explore the vortex parameters. Numerical simulations are performed using a second order finite volume method. We assume a perfect-gas law and a non-homentropic adiabatic flow. Results. The new model nicely fits the numerical vortex solution. In the vortex centre it is consistent with existing models, whereas in the outer regions it enables the vortex to be connected with the background flow. Two families of vortices can be distinguished following the importance of the compressional effects. The model also permitted a new class of vortices to be discovered corresponding to huge perturbations of pressure and density and whose radial sizes are significantly larger than the disk scale height, in contrast with the standard way to define the maximum vortex size. Conclusions. Our Gaussian model of the vortex solutions of the 2D Euler's equations is a useful tool for studying vortex properties. Among the large number of vortex solutions, the possible existence of giant vortices could open interesting perspectives in planetary formation, particularly during the building stage of the giant gas planets.
Vortex generation in protoplanetary disks with an embedded giant planet
Astronomy & Astrophysics, 2007
Context: Vortices in protoplanetary disks can capture solid particles and form planetary cores within shorter timescales than those involved in the standard core-accretion model. Aims: We investigate vortex generation in thin unmagnetized protoplanetary disks with an embedded giant planet with planet to star mass ratio 10-4 and 10-3. Methods: Two-dimensional hydrodynamical simulations of a protoplanetary disk with a planet are performed using two different numerical methods. The results of the non-linear simulations are compared with a time-resolved modal analysis of the azimuthally averaged surface density profiles using linear perturbation theory. Results: Finite-difference methods implemented in polar coordinates generate vortices moving along the gap created by Neptune-mass to Jupiter-mass planets. The modal analysis shows that unstable modes are generated with growth rate of order 0.3 ΩK for azimuthal numbers m=4,5,6, where ΩK is the local Keplerian frequency. Shock-capturing Cartesian-grid codes do not generate very much vorticity around a giant planet in a standard protoplanetary disk. Modal calculations confirm that the obtained radial profiles of density are less susceptible to the growth of linear modes on timescales of several hundreds of orbital periods. Navier-Stokes viscosity of the order ν=10-5 (in units of a2 Ωp) is found to have a stabilizing effect and prevents the formation of vortices. This result holds at high resolution runs and using different types of boundary conditions. Conclusions: Giant protoplanets of Neptune-mass to Jupiter-mass can excite the Rossby wave instability and generate vortices in thin disks. The presence of vortices in protoplanetary disks has implications for planet formation, orbital migration, and angular momentum transport in disks.
Did planet formation begin inside persistent gaseous vortices?
Arxiv preprint astro-ph/9501050, 1995
We explore here the idea, reminiscent in some respect of Von Weizsäcker's (1944) and Alfvèn's (1976) outmoded cosmogonies, that long-lived vortices in a turbulent protoplanetary nebula can capture large amount of solid particles and initiate the formation of planets. Some puzzling features of the solar system appear as natural consequences of our simple model:-The captured mass presents a maximum near Jupiter's orbit.-Outside this optimal orbit, the collected material, mainly composed of low density particles, sinks deeply into the vortices and rapidly collapses into massive bodies at the origin of the solid core of the giant planets.-Inside this orbit, by contrast, the high density particles are preferentially selected by the vortices and assembled by local gravitational instabilities into planetesimals, massive enough to be released by the vortices and to grow later, in successive collisions, to form the terrestrial planets.
Rapid planetesimal formation in turbulent circumstellar disks
Nature, 2007
The initial stages of planet formation in circumstellar gas discs proceed via dust grains that collide and build up larger and larger bodies 1 . How this process continues from metre-sized boulders to kilometre-scale planetesimals is a major unsolved problem 2 : boulders stick together poorly 3 , and spiral into the protostar in a few hundred orbits due to a head wind from the slower rotating gas 4 . Gravitational collapse of the solid component has been suggested to overcome this barrier 1, 5, 6 . Even low levels of turbulence, however, inhibit sedimentation of solids to a sufficiently dense midplane layer 2, 7 , but turbulence must be present to explain observed gas accretion in protostellar discs 8 . Here we report the discovery of efficient gravitational collapse of boulders in locally overdense regions in the midplane. The boulders concentrate initially in transient high pressures in the turbulent gas 9 , and these concentra-1 arXiv:0708.3890v1 [astro-ph]