Pebble trapping backreaction does not destroy vortices

The formation of planets remains one of the most challenging problems of contemporary astrophysics. Starting with micron-sized dust grains, coagulation models predict growth up to centimeter (pebbles), but growth beyond this size is difficult because of fragmentation and drift. Ways to bypass this problem have focused on inhomogeneities in the flow, be that zonal flows, streaming instability, or vortices. Because vortices are in equilibrium between the Coriolis and the pressure force, the pressureless grains will orbit along a vortex streamline experiencing a drag force. This is a very effective mechanism to concentrate pebbles as also seen in numerical simulations and possibly in ALMA observations. Yet, a high pebble load is dangerous for the vortex, and we showed that in two-dimensional simulations the backreaction eventually leads to vortex disruption. We investigate whether the same happens in three dimensions. We perform 3D simulations with pebbles in a local box finding that, although the pebbles disturb the vortex around the midplane, the column does not get destroyed. This result is important because, based on the previous 2D result suggesting complete disruption, the vortex interpretation of ALMA observations has been called into question. We show instead that the vortex behaves like a Taylor column, and the pebbles as obstacles to the flow. Pebble accumulation in the center of the vortices proceeds to roughly the same concentration as in the control run without backreaction.Comment: AAS research note; 3 pages, 1 figur

Particle Trapping and Streaming Instability in Vortices in Protoplanetary Disks

We analyze the concentration of solid particles in vortices created and sustained by radial buoyancy in protoplanetary disks, e.g., 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 dust-to-gas ratio approaches unity. In our two-dimensional, 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 = 1.0. 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 a low initial dust-to-gas ratio of 1:10^4, e.g., much smaller than in the previously studied magnetohydrodynamic zonal flow case

Global Baroclinic Instability and its Implications on Planet Formation

In this thesis we analyze a form of non magneto hydrodynamic turbulence which could be described as disk weather since it forms vortices due to baroclinic effects. We want to find out if and how these vortices influences planet formation. The focus is on angular momentum transport and how efficient vortices can trap particles. We estimate disk properties from observations and derive radial Brunt-Väisälä frequencies as well as cooling time-scales. Then we analyze the baroclinic amplification of vortices and the particle concentration therein. We use 2D as well as 3D local shear- ing box simulations with the PENCIL CODE to investigate the problems. In 2D, we conduct a comprehensive study of a broad range of various entropy gradients, thermal cooling and thermal relaxation times covering the parameter space relevant for protoplanetary disks. We measure the Reynolds stresses as a function of our control parameters and see that there is angular momentum transport even for entropy gradients as low as β ≡ −d ln S/d ln r = 1/2. The amplification-rate of the perturbations appears to be proportional to β^2. The saturation level of Reynolds stresses on the other hand seems to be proportional to β^1/2. All entropy gradients will lead to Reynolds stresses of 10^−3 − 10^−2 which shows that baroclinic vortices are a feasible mechanism for transporting angular momentum. The concentration of particles of different sizes in baroclinic vortices is first analyzed in 2 dimensions. Because we expect strong particle accumulations, particle feedback onto the gas is included. Particles accumulate inside the vortices and the local dust-to-gas ratios become high enough to trigger the streaming instability even for initial dust-to-gas ratios as low as ε_0 = 10^−4. In 3 dimensional unstratified gas simulations we verify previous result. Once particles, that feel vertical gravity, with normalized friction times of St = 0.05and St = 1.0, and ε_0 = 0.01 are included, the vortex column in the mid-plane is strongly perturbed. Yet, when the initial dust-to-gas ratio is decreased the vortices remain stable and function as efficient particle traps. Streaming instability is triggered even for the lowest ε_0 = 10^−4 and smallest particle sizes (St = 0.05) we assumed, showing a path for planetesimal formation in vortex cores from even low global amounts of cm-sized particles

Disk Weather

Recent years have shown that accretion disks around young stars have extended regions, which are too low ionized to couple to magnetic fields and thus the nature of the underlying turbulence cannot be exclusively magnetic. We also found that disks have in general a baroclinic density and temperature structure which means that a typical disk is radially buoyant and has a vertical velocity gradient also known as thermal wind. Here we show that the expected entropy gradients in observed accretion disks around young stars are in fact steep enough and that the thermal relaxation times are sufficiently short to allow for efficient amplification of vortices

Disk Weather

Recent years have shown that accretion disks around young stars have extended regions, which are too low ionized to couple to magnetic fields and thus the nature of the underlying turbulence cannot be exclusively magnetic. We also found that disks have in general a baroclinic density and temperature structure which means that a typical disk is radially buoyant and has a vertical velocity gradient also known as thermal wind. Here we show that the expected entropy gradients in observed accretion disks around young stars are in fact steep enough and that the thermal relaxation times are sufficiently short to allow for efficient amplification of vortices