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Minoru Sekiya - One of the best experts on this subject based on the ideXlab platform.
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Shear instabilities in the Dust Layer of the solar nebula III. Effects of the Coriolis force
Earth Planets and Space, 2020Co-Authors: Naoki Ishitsu, Minoru SekiyaAbstract:In previous our papers (Sekiya and Ishitsu, 2000 and 2001), hydrodynamic stability of the Dust Layer in the solar nebula is investigated. However, these papers neglected the rotational effects, that is, the Coriolis and tidal forces. These forces may stabilize the shear instability of the Dust Layer. In this paper, the linear stability analysis with the Coriolis and without tidal force is done in order to elucidate the effects of the Coriolis force. Our results indicate that the growth rates of the instabilities are similar between the cases with and without the Coriolis force. However, we found a new type of instability which resembles the Lindblad resonance. This instability only emerges if the growth rate is similar to or smaller than the Keplerian angular frequency. The energy source of the instability is different from that of the shear instability.
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two key parameters controlling particle clumping caused by streaming instability in the dead zone Dust Layer of a protoplanetary disk
The Astrophysical Journal, 2018Co-Authors: Minoru Sekiya, Isamu K OnishiAbstract:The streaming instability and Kelvin?Helmholtz instability are considered the two major sources causing clumping of Dust particles and turbulence in the Dust Layer of a protoplanetary disk as long as we consider the dead zone where the magnetorotational instability does not grow. Extensive numerical simulations have been carried out in order to elucidate the condition for the development of particle clumping caused by the streaming instability. In this paper, a set of two parameters suitable for classifying the numerical results is proposed. One is the Stokes number that has been employed in previous works and the other is the Dust particle column density that is nondimensionalized using the gas density in the midplane, Keplerian angular velocity, and difference between the Keplerian and gaseous orbital velocities. The magnitude of Dust clumping is a measure of the behavior of the Dust Layer. Using three-dimensional numerical simulations of Dust particles and gas based on Athena code v. 4.2, it is confirmed that the magnitude of Dust clumping for two disk models are similar if the corresponding sets of values of the two parameters are identical to each other, even if the values of the metallicity (i.e., the ratio of the columns density of the Dust particles to that of the gas) are different.
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numerical simulations of the gravitational instability in the Dust Layer of a protoplanetary disk using a thin disk model
The Astrophysical Journal, 2008Co-Authors: Shigeru Wakita, Minoru SekiyaAbstract:The growth of the gravitational instability in the Dust Layer of a protoplanetary disk is investigated. In order to see the effects of only the gravitational instability, we assume a laminar disk which has no radial pressure gradient as an unperturbed state so that the shear and the streaming instabilities do not grow. We neglect the relative velocity between the Dust and gas parallel to the disk plane assuming that the Dust and gas couple firmly by the mutual friction. However, we take account of the Dust settling by using an analytic solution of Dust density growth. We construct a two-dimensional thin disk model in which the radial and azimuthal directions in the midplane are taken as independent variables. In order to keep a certain amount of a disturbance, which is considered to exist not only at the beginning but all through the time evolution, we give perturbations repeatedly per Keplerian shear time in a local frame of reference. We find that the gravitational instability grows for the Dust particle when the dimensionless gas friction time (the product of the gas friction time and the Keplerian angular velocity) is equal to 0.01. On the other hand, the gravitational instability does not grow sufficiently before the Dust Layer becomes infinitesimally thin if the dimensionless gas friction time is equal to 0.1. These results are consistent with the axisymmetric study by Yamoto and Sekiya. However, the gravitational instability grows nonaxisymmetrically, and trailing surface density patterns arise.
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Two evolutionary paths of an axisymmetric gravitational instability in the Dust Layer of a protoplanetary disk
The Astrophysical Journal, 2006Co-Authors: Fumiharu Yamoto, Minoru SekiyaAbstract:We perform nonlinear numerical simulations to investigate the density evolution in the Dust Layer of a protoplanetary disk due to gravitational instability and Dust settling toward the midplane. We restrict our study to the region where the radial pressure equilibrium is negligible so that the shear-induced instability is avoided, and we also restrict our model to an axisymmetric perturbation as a first step of nonlinear numerical simulations of the gravitational instability. We find that there are two different evolutionary paths of the gravitational instability, depending on the nondimensional gas friction time, which is defined as the product of the gas friction time and the Keplerian angular velocity. If the nondimensional gas friction time is equal to 0.01, the gravitational instability grows faster than Dust settling. On the other hand, if the nondimensional gas friction time is equal to 0.1, Dust aggregates settle sufficiently before the gravitational instability grows. In the latter case, an approximate analytical calculation reveals that Dust settling is faster than the growth of the gravitational instability, regardless of the Dust density at the midplane. Thus, the Dust Layer becomes extremely thin and may reach a few tenths of the material density of the Dust before the gravitational instability grows, as long as there is no turbulence.
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Stabilization of the Shear Instability in a Dust Layer of a Protoplanetary Disk and Possible Formation of Planetesimals due to Gravitational Fragmentation of the Dust Layer
arXiv: Astrophysics, 2004Co-Authors: Naoki Ishitsu, Minoru SekiyaAbstract:We show that the planetesimal formation due to the gravitational fragmentation of a Dust Layer in a protoplanetary disk is possible. The Dust density distribution in the Dust Layer would approach the constant Richardson number distribution due to the Dust stirring by the shear instability and Dust settling. We perform the analysis of the shear instability of Dust Layer in a protoplanetary disk with the constant Richardson number density distribution. Our study revealed that this distribution is stable against the shear instability even if the Dust density at the midplane reaches the critical density of the gravitational instability, and the planetesimal formation through the gravitational fragmentation of the Dust Layer can occur even for the Dust to gas surface density ratio with the solar composition.
Naoki Ishitsu - One of the best experts on this subject based on the ideXlab platform.
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Shear instabilities in the Dust Layer of the solar nebula III. Effects of the Coriolis force
Earth Planets and Space, 2020Co-Authors: Naoki Ishitsu, Minoru SekiyaAbstract:In previous our papers (Sekiya and Ishitsu, 2000 and 2001), hydrodynamic stability of the Dust Layer in the solar nebula is investigated. However, these papers neglected the rotational effects, that is, the Coriolis and tidal forces. These forces may stabilize the shear instability of the Dust Layer. In this paper, the linear stability analysis with the Coriolis and without tidal force is done in order to elucidate the effects of the Coriolis force. Our results indicate that the growth rates of the instabilities are similar between the cases with and without the Coriolis force. However, we found a new type of instability which resembles the Lindblad resonance. This instability only emerges if the growth rate is similar to or smaller than the Keplerian angular frequency. The energy source of the instability is different from that of the shear instability.
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induced turbulence and the density structure of the Dust Layer in a protoplanetary disk
The Astrophysical Journal, 2012Co-Authors: Taku Takeuchi, Takayuki Muto, Satoshi Okuzumi, Naoki IshitsuAbstract:We study the turbulence induced in the Dust Layer of a protoplanetary disk based on the energetics of Dust accretion due to gas drag. We estimate turbulence strength from the energy supplied by Dust accretion, using the radial drift velocity of the Dust particles in a laminar disk. Our estimate of the turbulence strength agrees with previous analytical and numerical research on the turbulence induced by Kelvin-Helmholtz and/or streaming instabilities for particles with stopping time less than the Keplerian time. For such small particles, the strongest turbulence is expected to occur when the Dust-to-gas ratio of the disk is ~C 1/2 eff(hg /r) ~ 10–2, where C eff ≈ 0.2 represents the energy supply efficiency to turbulence and hg /r ~ 5 × 10–2 is the aspect ratio of the gas disk. The maximum viscosity parameter is αmax ~ C eff Ts (hg /r)2 ~ 10–4 Ts , where Ts (< 1) is the non-dimensional stopping time of the Dust particles. Modification to the Dust-to-gas ratio from the standard value, 10–2, by any process, results in weaker turbulence and a thinner Dust Layer, and consequently may accelerate the growth process of the Dust particles.
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Stabilization of the Shear Instability in a Dust Layer of a Protoplanetary Disk and Possible Formation of Planetesimals due to Gravitational Fragmentation of the Dust Layer
arXiv: Astrophysics, 2004Co-Authors: Naoki Ishitsu, Minoru SekiyaAbstract:We show that the planetesimal formation due to the gravitational fragmentation of a Dust Layer in a protoplanetary disk is possible. The Dust density distribution in the Dust Layer would approach the constant Richardson number distribution due to the Dust stirring by the shear instability and Dust settling. We perform the analysis of the shear instability of Dust Layer in a protoplanetary disk with the constant Richardson number density distribution. Our study revealed that this distribution is stable against the shear instability even if the Dust density at the midplane reaches the critical density of the gravitational instability, and the planetesimal formation through the gravitational fragmentation of the Dust Layer can occur even for the Dust to gas surface density ratio with the solar composition.
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the effects of the tidal force on shear instabilities in the Dust Layer of the solar nebula
Icarus, 2003Co-Authors: Naoki Ishitsu, Minoru SekiyaAbstract:Abstract The linear analysis of the instability due to vertical shear in the Dust Layer of the solar nebula is performed. The following assumptions are adopted throughout this paper: (1) The self-gravity of the Dust Layer is neglected. (2) One fluid model is adopted, where the Dust aggregates have the same velocity with the gas due to strong coupling by the drag force. (3) The gas is incompressible. The calculations with both the Coriolis and the tidal forces show that the tidal force has a stabilizing effect. The tidal force causes the radial shear in the disk. This radial shear changes the wave number of the mode which is at first unstable, and the mode is eventually stabilized. Thus the behavior of the mode is divided into two stages: (1) the first growth of the unstable mode which is similar to the results without the tidal force, and (2) the subsequent stabilization due to an increase of the wave number by the radial shear. If the midplane Dust/gas density ratio is smaller than 2, the stabilization occurs before the unstable mode grows largely. On the other hand, the mode grows faster by one hundred orders of magnitude, if this ratio is larger than 20. Because the critical density of the gravitational instability is a few hundreds times as large as the gas density, the hydrodynamic instability investigated in this paper grows largely before the onset of the gravitational instability. It is expected that the hydrodynamic instability develops turbulence in the Dust Layer and the Dust aggregates are stirred up to prevent from settling further. The formation of planetesimals through the gravitational instabilities is difficult to occur as long as the Dust/gas surface density ratio is equal to that for the solar abundance. On the other hand, the shear instability is suppressed and the planetesimal formation through the gravitational instability may occur, if Dust/gas surface density ratio is hundreds times as large as that for the solar abundance.
Shuichiro Inutsuka - One of the best experts on this subject based on the ideXlab platform.
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secular gravitational instability of a Dust Layer in shear turbulence
The Astrophysical Journal, 2012Co-Authors: Shugo Michikoshi, Eiichiro Kokubo, Shuichiro InutsukaAbstract:We perform a linear stability analysis of a Dust Layer in a turbulent gas disk. Youdin investigated the secular gravitational instability (GI) of a Dust Layer using hydrodynamic equations with a turbulent diffusion term. We obtain essentially the same result independently of Youdin. In the present analysis, we restrict the area of interest to small Dust particles, while investigating the secular GI in a more rigorous manner. We discuss the time evolution of the Dust surface density distribution using a stochastic model and derive the advection-diffusion equation. The validity of the analysis by Youdin is confirmed in the strong drag limit. We demonstrate quantitatively that the finite thickness of a Dust Layer weakens the secular GI and that the density-dependent diffusion coefficient changes the growth rate. We apply the results obtained to the turbulence driven by the shear instability and find that the secular GI is faster than the radial drift when the gas density is three times as large as that in the minimum-mass disk model. If the Dust particles are larger than chondrules, the secular GI grows within the lifetime of a protoplanetary disk.
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n body simulation of planetesimal formation through gravitational instability of a Dust Layer in laminar gas disk
The Astrophysical Journal, 2010Co-Authors: Shugo Michikoshi, Eiichiro Kokubo, Shuichiro InutsukaAbstract:We investigate the formation process of planetesimals from the Dust Layer by the gravitational instability in the gas disk using local N-body simulations. The gas is modeled as a background laminar flow. We study the formation process of planetesimals and its dependence on the strength of the gas drag. Our simulation results show that the formation process is divided into three stages qualitatively: the formation of wake-like density structures, the creation of planetesimal seeds, and their collisional growth. The linear analysis of the dissipative gravitational instability shows that the Dust Layer is secularly unstable although Toomre's Q value is larger than unity. However, in the initial stage, the growth time of the gravitational instability is longer than that of the Dust sedimentation and the decrease in the velocity dispersion. Thus, the velocity dispersion decreases and the disk shrinks vertically. As the velocity dispersion becomes sufficiently small, the gravitational instability finally becomes dominant. Then wake-like density structures are formed by the gravitational instability. These structures fragment into planetesimal seeds. The seeds grow rapidly owing to mutual collisions.
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N-Body Simulation of Planetesimal Formation through Gravitational Instability of a Dust Layer
The Astrophysical Journal, 2007Co-Authors: Shugo Michikoshi, Eiichiro Kokubo, Shuichiro Inutsuka, Izumi FuruyaAbstract:We performed N-body simulations of a Dust Layer without a gas component and examined the formation process of planetesimals. We found that the formation process of planetesimals can be divided into three stages: the formation of nonaxisymmetric wakelike structures, the creation of aggregates, and the collisional growth of the aggregates. Finally, a few large aggregates and many small aggregates are formed. The mass of the largest aggregate is larger than the mass predicted by the linear perturbation theory. We examined the dependence of system parameters on the planetesimal formation. We found that the mass of the largest aggregates increases as the size of the computational domain increases. However, the ratio of the aggregate mass to the total mass Maggr/Mtotal is almost constant, 0.8-0.9. The mass of the largest aggregate increases with the optical depth and the Hill radius of particles.
Shugo Michikoshi - One of the best experts on this subject based on the ideXlab platform.
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gravitational instability of a Dust Layer composed of porous silicate Dust aggregates in a protoplanetary disk
The Astrophysical Journal, 2018Co-Authors: Misako Tatsuuma, Shugo Michikoshi, Eiichiro KokuboAbstract: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. It has recently been proposed that they can grow as porous aggregates when their monomer radius is smaller than ~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 (GI) of this Dust Layer. To evaluate the disk stability, we calculate Toomre's 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 GI 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 α 10−5. If the Dust-to-gas ratio is increased twice, the GI occurs for α 10−4. 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.
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secular gravitational instability of a Dust Layer in shear turbulence
The Astrophysical Journal, 2012Co-Authors: Shugo Michikoshi, Eiichiro Kokubo, Shuichiro InutsukaAbstract:We perform a linear stability analysis of a Dust Layer in a turbulent gas disk. Youdin investigated the secular gravitational instability (GI) of a Dust Layer using hydrodynamic equations with a turbulent diffusion term. We obtain essentially the same result independently of Youdin. In the present analysis, we restrict the area of interest to small Dust particles, while investigating the secular GI in a more rigorous manner. We discuss the time evolution of the Dust surface density distribution using a stochastic model and derive the advection-diffusion equation. The validity of the analysis by Youdin is confirmed in the strong drag limit. We demonstrate quantitatively that the finite thickness of a Dust Layer weakens the secular GI and that the density-dependent diffusion coefficient changes the growth rate. We apply the results obtained to the turbulence driven by the shear instability and find that the secular GI is faster than the radial drift when the gas density is three times as large as that in the minimum-mass disk model. If the Dust particles are larger than chondrules, the secular GI grows within the lifetime of a protoplanetary disk.
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n body simulation of planetesimal formation through gravitational instability of a Dust Layer in laminar gas disk
The Astrophysical Journal, 2010Co-Authors: Shugo Michikoshi, Eiichiro Kokubo, Shuichiro InutsukaAbstract:We investigate the formation process of planetesimals from the Dust Layer by the gravitational instability in the gas disk using local N-body simulations. The gas is modeled as a background laminar flow. We study the formation process of planetesimals and its dependence on the strength of the gas drag. Our simulation results show that the formation process is divided into three stages qualitatively: the formation of wake-like density structures, the creation of planetesimal seeds, and their collisional growth. The linear analysis of the dissipative gravitational instability shows that the Dust Layer is secularly unstable although Toomre's Q value is larger than unity. However, in the initial stage, the growth time of the gravitational instability is longer than that of the Dust sedimentation and the decrease in the velocity dispersion. Thus, the velocity dispersion decreases and the disk shrinks vertically. As the velocity dispersion becomes sufficiently small, the gravitational instability finally becomes dominant. Then wake-like density structures are formed by the gravitational instability. These structures fragment into planetesimal seeds. The seeds grow rapidly owing to mutual collisions.
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N-Body Simulation of Planetesimal Formation through Gravitational Instability of a Dust Layer
The Astrophysical Journal, 2007Co-Authors: Shugo Michikoshi, Eiichiro Kokubo, Shuichiro Inutsuka, Izumi FuruyaAbstract:We performed N-body simulations of a Dust Layer without a gas component and examined the formation process of planetesimals. We found that the formation process of planetesimals can be divided into three stages: the formation of nonaxisymmetric wakelike structures, the creation of aggregates, and the collisional growth of the aggregates. Finally, a few large aggregates and many small aggregates are formed. The mass of the largest aggregate is larger than the mass predicted by the linear perturbation theory. We examined the dependence of system parameters on the planetesimal formation. We found that the mass of the largest aggregates increases as the size of the computational domain increases. However, the ratio of the aggregate mass to the total mass Maggr/Mtotal is almost constant, 0.8-0.9. The mass of the largest aggregate increases with the optical depth and the Hill radius of particles.
Eiichiro Kokubo - One of the best experts on this subject based on the ideXlab platform.
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gravitational instability of a Dust Layer composed of porous silicate Dust aggregates in a protoplanetary disk
The Astrophysical Journal, 2018Co-Authors: Misako Tatsuuma, Shugo Michikoshi, Eiichiro KokuboAbstract: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. It has recently been proposed that they can grow as porous aggregates when their monomer radius is smaller than ~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 (GI) of this Dust Layer. To evaluate the disk stability, we calculate Toomre's 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 GI 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 α 10−5. If the Dust-to-gas ratio is increased twice, the GI occurs for α 10−4. 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.
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secular gravitational instability of a Dust Layer in shear turbulence
The Astrophysical Journal, 2012Co-Authors: Shugo Michikoshi, Eiichiro Kokubo, Shuichiro InutsukaAbstract:We perform a linear stability analysis of a Dust Layer in a turbulent gas disk. Youdin investigated the secular gravitational instability (GI) of a Dust Layer using hydrodynamic equations with a turbulent diffusion term. We obtain essentially the same result independently of Youdin. In the present analysis, we restrict the area of interest to small Dust particles, while investigating the secular GI in a more rigorous manner. We discuss the time evolution of the Dust surface density distribution using a stochastic model and derive the advection-diffusion equation. The validity of the analysis by Youdin is confirmed in the strong drag limit. We demonstrate quantitatively that the finite thickness of a Dust Layer weakens the secular GI and that the density-dependent diffusion coefficient changes the growth rate. We apply the results obtained to the turbulence driven by the shear instability and find that the secular GI is faster than the radial drift when the gas density is three times as large as that in the minimum-mass disk model. If the Dust particles are larger than chondrules, the secular GI grows within the lifetime of a protoplanetary disk.
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n body simulation of planetesimal formation through gravitational instability of a Dust Layer in laminar gas disk
The Astrophysical Journal, 2010Co-Authors: Shugo Michikoshi, Eiichiro Kokubo, Shuichiro InutsukaAbstract:We investigate the formation process of planetesimals from the Dust Layer by the gravitational instability in the gas disk using local N-body simulations. The gas is modeled as a background laminar flow. We study the formation process of planetesimals and its dependence on the strength of the gas drag. Our simulation results show that the formation process is divided into three stages qualitatively: the formation of wake-like density structures, the creation of planetesimal seeds, and their collisional growth. The linear analysis of the dissipative gravitational instability shows that the Dust Layer is secularly unstable although Toomre's Q value is larger than unity. However, in the initial stage, the growth time of the gravitational instability is longer than that of the Dust sedimentation and the decrease in the velocity dispersion. Thus, the velocity dispersion decreases and the disk shrinks vertically. As the velocity dispersion becomes sufficiently small, the gravitational instability finally becomes dominant. Then wake-like density structures are formed by the gravitational instability. These structures fragment into planetesimal seeds. The seeds grow rapidly owing to mutual collisions.
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N-Body Simulation of Planetesimal Formation through Gravitational Instability of a Dust Layer
The Astrophysical Journal, 2007Co-Authors: Shugo Michikoshi, Eiichiro Kokubo, Shuichiro Inutsuka, Izumi FuruyaAbstract:We performed N-body simulations of a Dust Layer without a gas component and examined the formation process of planetesimals. We found that the formation process of planetesimals can be divided into three stages: the formation of nonaxisymmetric wakelike structures, the creation of aggregates, and the collisional growth of the aggregates. Finally, a few large aggregates and many small aggregates are formed. The mass of the largest aggregate is larger than the mass predicted by the linear perturbation theory. We examined the dependence of system parameters on the planetesimal formation. We found that the mass of the largest aggregates increases as the size of the computational domain increases. However, the ratio of the aggregate mass to the total mass Maggr/Mtotal is almost constant, 0.8-0.9. The mass of the largest aggregate increases with the optical depth and the Hill radius of particles.
