Shugo Michikoshi

N-Body Simulation of Planetesimal Formation through Gravitational Instability of a Dust Layer

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.

A TWO-FLUID ANALYSIS OF THE KELVIN-HELMHOLTZ INSTABILITY IN THE DUSTY LAYER OF A PROTOPLANETARY DISK: A POSSIBLE PATH TOWARD PLANETESIMAL FORMATION THROUGH GRAVITATIONAL INSTABILITY

Weanalyzethestabilityofthedustlayerinprotoplanetarydiskstounderstandtheeffectofrelativemotionbetween gas and dust. Previous analyses not including the effect of the relative motion between gas and dust show that shearinducedturbulencemaypreventthedustgrainsfromsettlingsufficientlytobegravitationallyunstable.Wedetermine the growth rate of the Kelvin-Helmholtz instability in a wide range of parameter space and propose a possible path toward planetesimal formation through gravitational instability. We expect the density of the dust layer to become � d/� g � 100 if the dust grains can grow up to 10 m. Subject headingg instabilities — planetary systems: formation — turbulence

Pitch angle of galactic spiral arms

One of the key parameters that characterize spiral arms in disk galaxies is a pitch angle that measures the inclination of a spiral arm to the direction of galactic rotation. The pitch angle differs from galaxy to galaxy, which suggests that the rotation law of galactic disks determines it. In order to investigate the relation between the pitch angle of spiral arms and the shear rate of galactic differential rotation, we perform local

N-BODY SIMULATION OF PLANETESIMAL FORMATION THROUGH GRAVITATIONAL INSTABILITY OF A DUST LAYER IN LAMINAR GAS DISK

N

Secular Gravitational Instability of a Dust Layer in Shear Turbulence

-body simulations of pure stellar disks. We find that the pitch angle increases with the epicycle frequency and decreases with the shear rate and obtain the fitting formula. This dependence is explained by the swing amplification mechanism.

N-Body Simulation of Planetesimal Formation through Gravitational Instability and Coagulation. II. Accretion Model

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 Toomres 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.

Formation of a Propeller Structure by a Moonlet in a Dense Planetary Ring

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.

GALACTIC SPIRAL ARMS BY SWING AMPLIFICATION

The gravitational instability of a dust layer is one of the scenarios for planetesimal formation. If the density of a dust layer becomes sufficiently high as a result of the sedimentation of dust grains toward the midplane of a protoplanetary disk, the layer becomes gravitationally unstable and spontaneously fragments into planetesimals. Using a shearing box method, we performed local N-body simulations of gravitational instability of a dust layer and subsequent coagulation without gas and investigated the basic formation process of planetesimals. In this paper, we adopted the accretion model as a collision model. A gravitationally bound pair of particles is replaced by a single particle with the total mass of the pair. This accretion model enables us to perform long-term and large-scale calculations. We confirmed that the formation process of planetesimals is the same as that in the previous paper with the rubble pile models. The formation process is divided into three stages: the formation of nonaxisymmetric structures; the creation of planetesimal seeds; and their collisional growth. We investigated the dependence of the planetesimal mass on the simulation domain size. We found that the mean mass of planetesimals formed in simulations is proportional to L 3/2 y , where Ly is the size of the computational domain in the direction of rotation. However, the mean mass of planetesimals is independent of Lx , where Lx is the size of the computational domain in the radial direction if Lx is sufficiently large. We presented the estimation formula of the planetesimal mass taking into account the simulation domain size.

DYNAMICS OF SELF-GRAVITY WAKES IN DENSE PLANETARY RINGS. I. PITCH ANGLE

The Cassini spacecraft discovered a propeller-shaped structure in Saturns A ring. This propeller structure is thought to be formed by gravitational scattering of ring particles by an unseen embedded moonlet. Self-gravity wakes are prevalent in dense rings due to gravitational instability. Strong gravitational wakes affect the propeller structure. Here, we derive the condition for the formation of a propeller structure by a moonlet embedded in a dense ring with gravitational wakes. We find that a propeller structure is formed when the wavelength of the gravitational wakes is smaller than the Hill radius of the moonlet. We confirm this formation condition by performing numerical simulations. This condition is consistent with observations of propeller structures in Saturns A ring.

Wave propagation in a weak gravitational field and the validity of the thin lens approximation

Based on the swing amplification model of Julian and Toomre (1966), we investigate the formation and structure of stellar spirals in disk galaxies. We calculate the pitch angle, wavelengths, and amplification factor of the most amplified mode. We also obtain the fitting formulae of these quantities as a function of the epicycle frequency and Toomres