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Register a new userCoagulation Instability in Protoplanetary Disks: A Novel Mechanism Connecting Collisional Growth and Hydrodynamical Clumping of Dust Particles
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We present a new instability driven by a combination of coagulation and radial drift of dust particles. We refer to this instability as ``coagulation instability and regard it as a promising mechanism to concentrate dust particles and assist planetesimal formation in the very early stages of disk evolution. Because of dust-density dependence of collisional coagulation efficiency, dust particles efficiently (inefficiently) grow in a region of positive (negative) dust density perturbations, which lead to a small radial variation of dust sizes and as a result radial velocity perturbations. The resultant velocity perturbations lead to dust concentration and amplify dust density perturbations. This positive feedback makes a disk unstable. The growth timescale of coagulation instability is a few tens of orbital periods even when dust-to-gas mass ratio is of the order of $10^{-3}$. In a protoplanetary disk, radial drift and coagulation of dust particles tend to result in dust depletion. The present instability locally concentrates dust particles even in such a dust-depleted region. The resulting concentration provides preferable sites for dust-gas instabilities to develop, which leads to further concentration. Dust diffusion and aerodynamical feedback tend to stabilize short-wavelength modes, but do not completely suppress the growth of coagulation instability. Therefore, coagulation instability is expected to play an important role in setting up the next stage for other instabilities to further develop toward planetesimal formation, such as streaming instability or secular gravitational instability.
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In this work, we study how the dust coagulation/fragmentation will influence the evolution and observational appearances of vortices induced by a massive planet embedded in a low viscosity disk by performing global 2D high-resolution hydrodynamical simulations. Within the vortex, due to its higher gas surface density and steeper pressure gradients, dust coagulation, fragmentation and drift (to the vortex center) are all quite efficient, producing dust particles ranging from micron to $sim 1.0 {rm cm}$, as well as overall high dust-to-gas ratio (above unity). In addition, the dust size distribution is quite non-uniform inside the vortex, with the mass weighted average dust size at the vortex center ($sim 4.0$ mm) being a factor of $sim10$ larger than other vortex regions. Both large ($sim$ mm) and small (tens of micron) particles contribute strongly to affect the gas motion within the vortex. As such, we find that the inclusion of dust coagulation has a significant impact on the vortex lifetime and the typical vortex lifetime is about 1000 orbits. After the initial gaseous vortex is destroyed, the dust spreads into a ring with a few remaining smaller gaseous vortices with a high dust concentration and a large maximum size ($sim$ mm). At late time, the synthetic dust continuum images for the coagulation case show as a ring inlaid with several hot spots at 1.33 mm band, while only distinct hot spots remain at 7.0 mm.
We present the first 2D hydrodynamical finite volume simulations in which dust is fully coupled with the gas, including its back-reaction onto it, and at the same time the dust size is evolving according to coagulation and fragmentation based on a sub-grid model. The aim of this analysis is to present the differences occurring when dust evolution is included relative to simulations with fixed dust size, with and without an embedded Jupiter-mass planet that triggers gap formation. We use the two-fluid polar Godunov-type code RoSSBi developed by Surville et al. 2016 combined with a new local sub-grid method for dust evolution based on the model by Birnstiel et al. 2012. We find striking differences between simulations with variable and fixed dust sizes. The timescales for dust depletion differ significantly and yield a completely different evolution of the dust surface density. In general sharp features such as pile-ups of dust in the inner disk and near gap edges, when a massive planet is present, become much weaker. This has important implications on the interpretation of observed substructure in disks, suggesting that the presence of a massive planet does not necessarily cause sharp gaps and rings in the dust component. Also, particles with different dust sizes show a different distribution, pointing to the importance of multi-wavelength synthetic observations in order to compare with observations by ALMA and other instruments. We also find that simulations adopting fixed intermediate particle sizes, in the range $10^{-2} - 10^{-1}$ cm, best approximate the surface density evolution seen in simulations with dust evolution.
Turbulence is the dominant source of collisional velocities for grains with a wide range of sizes in protoplanetary disks. So far, only Kolmogorov turbulence has been considered for calculating grain collisional velocities, despite the evidence that turbulence in protoplanetary disks may be non-Kolmogorov. In this work, we present calculations of grain collisional velocities for arbitrary turbulence models characterized by power-law spectra and determined by three dimensionless parameters: the slope of the kinetic energy spectrum, the slope of the auto-correlation time, and the Reynolds number. The implications of our results are illustrated by numerical simulations of the grain size evolution for different turbulence models. We find that for the modeled cases of the Iroshnikov-Kraichnan turbulence and the turbulence induced by the magneto-rotational instabilities, collisional velocities of small grains are much larger than those for the standard Kolmogorov turbulence. This leads to faster grain coagulation in the outer regions of protoplanetary disks, resulting in rapid increase of dust opacity in mm-wavelength and possibly promoting planet formation in very young disks.
We discovered a new growth mode of dust grains to km-sized bodies in protoplanetary disks that evolve by viscous accretion and magnetically driven disk winds (MDWs). We solved an approximate coagulation equation of dust grains with time-evolving disks that consist of both gas and solid components by a one-dimensional model. With the grain growth, all solid particles initially drift inward toward the central star by the gas drag force. However, the radial profile of gas pressure, $P$, is modified by the MDW that disperses the gas in an inside-out manner. Consequently, a local concentration of solid particles is created by the converging radial flux of drifting dust grains at the location with the convex upward profile of $P$. When the dimensionless stopping time, ${rm St}$, there exceeds unity, the solid particles spontaneously reach the growth dominated state because of the positive feedback between the suppressed radial drift and the enhanced accumulation of dust particles that drift from the outer part. Once the solid particles are in the drift limited state, the above-mentioned condition of ${rm St} gtrsim 1$ for the dust growth is equivalent with begin{equation} Sigma_{rm d}/Sigma_{rm g}gtrsim eta, onumber end{equation} where $Sigma_{rm d}/Sigma_{rm g}$ is the dust-to-gas surface-density ratio and $eta$ is dimensionless radial pressure-gradient force. As a consequence of the successful growth of dust grains, a ring-like structure containing planetesimal-sized bodies is formed at the inner part of the protoplanetary disks. Such a ring-shaped concentration of planetesimals is expected to play a vital role in the subsequent planet formation.
Tidal interactions between the embedded planets and their surrounding protoplanetary disks are often postulated to produce the observed complex dust substructures, including rings, gaps, and asymmetries. In this Letter, we explore the consequences of dust coagulation on the dust dynamics and ring morphology. Coagulation of dust grains leads to dust size growth which, under typical disk conditions, produces faster radial drifts, potentially threatening the dust ring formation. Utilizing 2D hydrodynamical simulations of protoplanetary disks which include a full treatment of dust coagulation, we find that if the planet does not open a gap quickly enough, the formation of an inner ring is impeded due to dust coagulation and subsequent radial drift. Furthermore, we find that a buildup of sub-mm sized grains often appears in the dust emission at the outer edge of the dust disk.
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