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Register a new userDetailed Model of the Growth of Fluffy Dust Aggregates in a Protoplanetary Disk: Effects of Nebular Conditions
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Coagulation of dust aggregates plays an important role in the formation of planets and is of key importance to the evolution of protoplanetary disks (PPDs). Characteristics of dust, such as the diversity of particle size, porosity, charge, and the manner in which dust couples to turbulent gas, affect the collision outcome and the rate of dust growth. Here we present a numerical model of the evolution of the dust population within a PPD which incorporates all of these effects. The probability that any two particles collide depends on the particle charge, cross-sectional area and their relative velocity. The actual collision outcome is determined by a detailed collision model which takes into account the aggregate morphology, trajectory, orientation, and electrostatic forces acting between charged grains. The data obtained in this research reveal the characteristics of dust populations in different environments at the end of the hit-and-stick growth, which establishes the foundation for the onset of the next growth stage where bouncing, mass transfer and fragmentation become important. For a given level of turbulence, neutral and weakly charged particles collide more frequently and grow faster than highly charged particles. However, highly charged particles grow to a larger size before reaching the bouncing barrier, and exhibit a Runaway growth, in which a few large particles grow quickly by accreting smaller particles while the rest of the population grows very slowly. In general, highly charged aggregates have a more compact structure and are comprised of larger monomers than neutral/weakly charged aggregates. The differences in the particle structure/composition not only affect the threshold velocities for bouncing and fragmentation, but also change the scattering and absorption opacity of dust, influencing the appearance of PPDs.
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Planetesimal formation is one of the most important unsolved problems in planet formation theory. In particular, rocky planetesimal formation is difficult because silicate dust grains are easily broken when they collide. Recently, it has been proposed that they can grow as porous aggregates when their monomer radius is smaller than $sim$ 10 nm, which can also avoid the radial drift toward the central star. However, the stability of a layer composed of such porous silicate dust aggregates has not been investigated. Therefore, we investigate the gravitational instability of this dust layer. To evaluate the disk stability, we calculate Toomres stability parameter $Q$, for which we need to evaluate the equilibrium random velocity of dust aggregates. We calculate the equilibrium random velocity considering gravitational scattering and collisions between dust aggregates, drag by mean flow of gas, stirring by gas turbulence, and gravitational scattering by gas density fluctuation due to turbulence. We derive the condition of the gravitational instability using the disk mass, dust-to-gas ratio, turbulent strength, orbital radius, and dust monomer radius. We find that, for the minimum mass solar nebula model at 1 au, the dust layer becomes gravitationally unstable when the turbulent strength $alphalesssim10^{-5}$. If the dust-to-gas ratio is increased twice, the gravitational instability occurs for $alphalesssim10^{-4}$. We also find that the dust layer is more unstable in disks with larger mass, higher dust-to-gas ratio, and weaker turbulent strength, at larger orbital radius, and with a larger monomer radius.
Context. The growth process of dust particles in protoplanetary disks can be modeled via numerical dust coagulation codes. In this approach, physical effects that dominate the dust growth process often must be implemented in a parameterized form. Due to a lack of these parameterizations, existing studies of dust coagulation have ignored the effects a hydrodynamical gas flow can have on grain growth, even though it is often argued that the flow could significantly contribute either positively or negatively to the growth process. Aims. We intend to provide a quantification of hydrodynamical effects on the growth of dust particles, such that these effects can be parameterized and implemented in a dust coagulation code. Methods. We numerically integrate the trajectories of small dust particles in the flow of disk gas around a proto-planetesimal, sampling a large parameter space in proto-planetesimal radii, headwind velocities, and dust stopping times. Results. The gas flow deflects most particles away from the proto-planetesimal, such that its effective collisional cross section, and therefore the mass accretion rate, is reduced. The gas flow however also reduces the impact velocity of small dust particles onto a proto-planetesimal. This can be beneficial for its growth, since large impact velocities are known to lead to erosion. We also demonstrate why such a gas flow does not return collisional debris to the surface of a proto-planetesimal. Conclusions. We predict that a laminar hydrodynamical flow around a proto-planetesimal will have a significant effect on its growth. However, we cannot easily predict which result, the reduction of the impact velocity or the sweep-up cross section, will be more important. Therefore, we provide parameterizations ready for implementation into a dust coagulation code.
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.
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.
The growth of solids from sub-micron to millimeter and centimeter sizes is the early step toward the formation of planets inside protoplanetary disks (PPDs). However, such processes and their potential impact on the later stages of solid growth are still poorly understood. In this work, we test the hypothesis that most disks contain at least one ringed structure with a relative small radius. We have carried out a large family of 1D two-fluid (gas+dust) hydrodynamical simulations by evolving the gas and dust motion self-consistently while allowing dust size to evolve via coagulation and fragmentation. We investigate the joint effects of ringed structures and dust size growth on the overall sub-millimeter and millimeter (mm) flux and spectral index of PPDs. Ringed structures slow down the dust radial drift and speed up the dust growth. In particular, we find that those unresolved disks with a high fragmentation velocity ($sim10 {rm m~s^{-1}}$) and a high dust surface density ($sim10 {rm g cm^{-2}}$ in the ring) can have mm spectral indices as low as $sim2.0$, consistent with mm observations of faint disks in nearby star forming regions. Furthermore, disks with more than one ringed structure can potentially reproduce brighter disks with spectral indices lower than $sim2.5$. Future multi-wavelength high-resolution observations of these low spectral index sources can be used to test the existence of the ringed structures in the unresolved disks and differentiate the effects of dust size growth from optical depth.
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