The Dust Subdisk in the Protoplanetary Nebula
TL;DR: In this article, a self-consistent computation of the structure of the dust subdisk in the protoplanetary nebula is presented, which is based on a competition between sedimentation processes due to gravity and diffusion due to turbulence.
About: This article is published in Icarus.The article was published on 1995-04-01. It has received 554 citations till now. The article focuses on the topics: Protoplanetary nebula & Turbulent diffusion.
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TL;DR: In this paper, the authors model the process of dust coagulation in protoplanetary disks and calculate how it affects their observational appearance, and they find that, even if only the very basic -and well understood -coagulation mechanisms are included, the grain growth is much too quick to be consistent with infrared observations of T Tauri disks.
Abstract: We model the process of dust coagulation in protoplanetary disks and calculate how it affects their observational appearance. Our model involves the detailed solution of the coagulation equation at every location in the disk. At regular time intervals we feed the resulting 3D dust distribution functions into a continuum radiative transfer code to obtain spectral energy distributions. We find that, even if only the very basic - and well understood - coagulation mechanisms are included, the process of grain growth is much too quick to be consistent with infrared observations of T Tauri disks. Small grains are removed so efficiently that, long before the disk reaches an age of 10 6 years typical of T Tauri stars, the SED shows only very weak infrared excess. This is inconsistent with observed SEDs of most classical T Tauri stars. Small grains must be replenished, for instance by aggregate fragmentation through high-speed collisions. A very simplified calculation shows that when aggregate fragmentation is included, a quasi-stationary grain size distribution is obtained in which growth and fragmentation are in equilibrium. This quasi-stationary state may last 10 6 years or even longer, depending on the circumstances in the disk, and may bring the time scales into the right regime. If this is indeed the case, or if other processes are responsible for the replenishment of small grains, then the typical grain sizes inferred from infrared spectral features of T Tauri disks do not necessarily reflect the age of the system (small grains → young, larger grains → older), as is often proposed. Indeed, there is evidence reported in the literature that the typical inferred grain sizes do not correlate with the age of the star. Instead, it is more likely that the typical grain sizes found in T Tauri star (and Herbig Ae/Be star and Brown Dwarf) disks reflect the state of the disk in some more complicated way, e.g. the strength of the turbulence, the amount of dust mass transformed into planetesimals, the amount of gas lost via evaporation etc. A simple evolutionary scenario in which grains slowly grow from pristine 0.1 µm grains to larger grains over a period of a few Myr is most likely incorrect.
789 citations
TL;DR: In this article, the authors presented the results of numerical simulations with more and more realistic physics involved, including various effects, such as particle growth, radial/vertical particle motion and dust particle fragmentation in their simulations.
Abstract: The growth of solid particles towards meter sizes in protoplanetary disks has to circumvent at least two hurdles, namely the rapid loss of material due to radial drift and particle fragmentation due to destructive collisions. In this paper, we present the results of numerical simulations with more and more realistic physics involved. Step by step, we include various effects, such as particle growth, radial/vertical particle motion and dust particle fragmentation in our simulations. We demonstrate that the initial dust-to-gas ratio is essential for the particles to overcome the radial drift barrier. If this value is increased by a factor of 2 compared with the canonical value for the interstellar medium, km-sized bodies can form in the inner disk ( yrs. However, we find that solid particles get destroyed through collisional fragmentation. Only with the unrealistically high-threshold velocities needed for fragmentation to occur (>30 m/s), particles are able to grow to larger sizes in disks with low α values. We also find that less than 5% of the small dust grains remain in the disk after 1 Myr due to radial drift, no matter whether fragmentation is included in the simulations or not. In this paper, we also present considerable improvements to existing algorithms for dust-particle coagulation, which speed up the coagulation scheme by a factor of ~ 104 .
741 citations
Cites background or methods from "The Dust Subdisk in the Protoplanet..."
...With the two dimensionless numbers, α and St, the scale height of the dust hk of a certain grain mass mk is given by (Dubrulle et al. 1995; Cuzzi & Weidenschilling 2006; Brauer et al. 2007)( hk H )2 = α min(Stk, 1/2)(1 + Stk) · (15) Since the dust scale height hk can not exceed the gas scale height…...
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...In the vertical direction, we will always assume that each particle species is in vertical sedimentation/mixing equilibrium (Dubrulle et al. 1995; Cuzzi & Weidenschilling 2006)....
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...While Morfill (1988), Weidenschilling (1988) or Weidenschilling & Cuzzi (1993) use turbulent gas velocities of αcs, which implies q = 1, more recent publications explicitly derived q = 1/2 which leads to vt = √ αcs (Dubrulle et al. 1995; Cuzzi et al. 2001; Cuzzi & Weidenschilling 2006)....
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TL;DR: In this paper, the authors introduce a new model similar to Brauer et al. (2008, A&A, 480, 859) in which they include the time-dependent viscous evolution of the gas disk, and in which more advanced input physics and numerical integration methods are implemented.
Abstract: Context. Current models of the size- and radial evolution of dust in protoplanetary disks generally oversimplify either the radial evolution of the disk (by focussing at one single radius or by using steady state disk models) or they assume particle growth to proceed monodispersely or without fragmentation. Further studies of protoplanetary disks – such as observations, disk chemistry and structure calculations or planet population synthesis models – depend on the distribution of dust as a function of grain size and radial position in the disk.Aims. We attempt to improve upon current models to be able to investigate how the initial conditions, the build-up phase, and the evolution of the protoplanetary disk influence growth and transport of dust.Methods. We introduce a new model similar to Brauer et al. (2008, A&A, 480, 859) in which we now include the time-dependent viscous evolution of the gas disk, and in which more advanced input physics and numerical integration methods are implemented.Results. We show that grain properties, the gas pressure gradient, and the amount of turbulence are much more influencing the evolution of dust than the initial conditions or the build-up phase of the protoplanetary disk. We quantify which conditions or environments are favorable for growth beyond the meter size barrier. High gas surface densities or zonal flows may help to overcome the problem of radial drift, however already a small amount of turbulence poses a much stronger obstacle for grain growth.
645 citations
TL;DR: In this article, the Schmidt number (ratio of gas to particle diusivity) is shown to rise quadratically, not linearly, with stopping time, and the particle layer becomes thinner with the strength of turbulent diusion held xed.
621 citations
Cites background or result from "The Dust Subdisk in the Protoplanet..."
...(53)) and Dubrulle et al. (1995) for tight particle coupling, and Carballido et al. (2006) for loose particle coupling....
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...Turbulent diffusion balances the vertical settling of dust grains and larger solids to the midplane (Cuzzi et al., 1993; Sekiya, 1998; Dubrulle et al., 1995; Carballido et al., 2006), thereby setting the midplane volume density for a given surface density....
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...We compare our result with the standard value derived by Dubrulle et al. (1995) for tightly coupled 5 With 〈w2g〉 instead of 〈u2g〉....
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...In stratified models, Hp Hg is imposed by the hypothesis that the quantity diffused by turbulence is not the absolute particle density, but the particle concentration relative to gas7 (Dubrulle et al., 1995, their Eq....
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...We compare our result with the standard value derived by Dubrulle et al. (1995) for tightly coupled...
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TL;DR: In this paper, the effects of gas drag on the impact radii and the accretion rates of these particles were investigated, and a laminar disk characterized by a smooth pressure gradient that causes particles to drift in radially.
Abstract: Planetary bodies form by accretion of smaller bodies. It has been suggested that a very efficient way to grow protoplanets is by ac- creting particles of sizekm (e.g., chondrules, boulders, or fragments of larger bodies) as they can be kept dynamically cold. We investigate the effects of gas drag on the impact radii and the accretion rates of these particles. As simplifying assumptions we restrict our analysis to 2D settings, a gas drag law linear in velocity, and a laminar disk characterized by a smooth (global) pressure gradient that causes particles to drift in radially. These approximations, however, enable us to cover an arbitrary large parameter space. The framework of the circularly restricted three body problem is used to numerically integrate particle trajectories and to derive their impact parameters. Three accretion modes can be distinguished: hyperbolic encounters, where the 2-body gravitational focusing en- hances the impact parameter; three-body encounters, where gas drag enhances the capture probability; and settling encounters ,w here particles settle towards the protoplanet. An analysis of the observed behavior is presented; and we provide a recipe to analytically calculate the impact radius, which confirms the numerical findings. We apply our results to the sweepup of fragments by a protoplanet at a distance of 5 AU. Accretion of debris on small protoplanets (<50 km) is found to be slow, because the fragments are distributed over a rather thick layer. However, the newly found settling mechanism, which is characterized by much larger impact radii, becomes relevant for protoplanets of ∼10 3 km in size and provides a much faster channel for growth.
572 citations
Cites background from "The Dust Subdisk in the Protoplanet..."
...The height of the particle layer may be obtained by equating particle diffusion and settling timescale; i.e., Hp Hg ≈ min ( 1, √ αt St ) , (35) (Dubrulle et al. 1995; Carballido et al. 2006; Youdin & Lithwick 2007) where αt is the Shakura & Sunyaev (1973) viscosity parameter for turbulent diffusion....
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