Planetesimal Formation by Gravitational Instability of a Porous-Dust Disk

Recently it is proposed that porous icy dust aggregates are formed by pairwise accretion of dust aggregates beyond the snowline. We calculate the equilibrium random velocity of porous dust aggregates taking into account mutual gravitational scattering, collisions, gas drag, and turbulent stirring and scattering. We find that the disk of porous dust aggregates becomes gravitationally unstable as they evolve through gravitational compression in the minimum-mass solar nebula model for a reasonable range of turbulence strength, which leads to rapid formation of planetesimals.Comment: 14 pages, 5 figures, accepted for publication in ApJ Letter

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 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.Comment: 17 pages, 8 figures, accepted for publication in Ap

Dynamics of Porous Dust Aggregates and Gravitational Instability of Their Disk

We consider the dynamics of porous icy dust aggregates in a turbulent gas disk and investigate the stability of the disk. We evaluate the random velocity of porous dust aggregates by considering their self-gravity, collisions, aerodynamic drag, turbulent stirring and scattering due to gas. We extend our previous work by introducing the anisotropic velocity dispersion and the relaxation time of the random velocity. We find the minimum mass solar nebular model to be gravitationally unstable if the turbulent viscosity parameter $\alpha$ is less than about $4 \times 10^{-3}$. The upper limit of $\alpha$ for the onset of gravitational instability is derived as a function of the disk parameters. We discuss the implications of the gravitational instability for planetesimal formation.Comment: 38 pages, 14 figures, accepted for publication in Ap

Galactic Spiral Arms by Swing Amplification

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 Toomre's $Q$. As the epicycle frequency increases, the pitch angle and radial wavelength increases, while the azimuthal wavelength decreases. The pitch angle and radial wavelength increases with $Q$, while the azimuthal wavelength weakly depends on $Q$. The amplification factor decreases with $Q$ rapidly. In order to confirm the swing amplification model, we perform local $N$-body simulations. The wavelengths and pitch angle by the swing amplification model are in good agreement with those by $N$-body simulations. The dependence of the amplification factor on the epicycle frequency in $N$-body simulations is generally consistent with that in the swing amplification model. Using these results, we estimate the number of spiral arms as a function of the shear rate. The number of spiral arms increases with the shear rate if the disk to halo mass ratio is fixed.Comment: 23 pages, 10 figures, accepted for publication in Ap

Swing Amplification of Galactic Spiral Arms: Phase Synchronization of Stellar Epicycle Motion

We revisit the swing amplification model of galactic spiral arms proposed by Toomre (1981). We describe the derivation of the perturbation equation in detail and investigate the amplification process of stellar spirals. We find that the elementary process of the swing amplification is the phase synchronization of the stellar epicycle motion. Regardless of the initial epicycle phase, the epicycle phases of stars in a spiral are synchronized during the amplification. Based on the phase synchronization, we explain the dependence of the pitch angle of spirals on the epicycle frequency. We find the most amplified spiral mode and calculate its pitch angle, wavelengths, and amplification factor, which are consistent with those obtained by the more rigorous model based on the Boltzmann equation by Julian and Toomre (1966).Comment: 31 pages, 11 figures, accepted for publication in Ap

Global N-Body Simulation of Galactic Spiral Arms

The origin of galactic spiral arms is one of fundamental problems in astrophysics. Based on the local analysis Toomre (1981) proposed the swing amplification mechanism in which the self-gravity forms spiral arms as leading waves of stars rotate to trailing ones due to galactic shear. The structure of spiral arms is characterized by their number and pitch angle. We perform global $N$-body simulations of spiral galaxies to investigate the dependence of the spiral structure on disk parameters and compare the simulation results with the swing amplification model. We find that the spiral structure in the $N$-body simulations agrees well with that predicted by the swing amplification for the wide range of parameters. The pitch angle decreases with increasing the shear rate and is independent of the disk mass fraction. The number of spiral arms decreases with both increasing the shear rate and the disk mass fraction. If the disk mass fraction is fixed, the pitch angle increases with the number of spiral arms.Comment: 11 pages, 8 figures. Accepted for publication in MNRA

The two-fluid analysis of the Kelvin-Helmholtz instability in dusty layer of a protoplanetary disk: A possible path toward the planetesimal formation through the gravitational instability

We analyze the stability of dust layer in protoplanetary disk to understand the effect of the relative motion between gas and dust. The previous analyses not including the effect of relative motion between gas and dust show that the shear-induced turbulence may prevent the dust grains from settling sufficiently to be gravitationally unstable. We determine the growth rate of Kelvin-Helmholtz instability in wide range of parameter space, and propose a possible path toward the planetesimal formation through the gravitational instability. We expect the density of dust layer becomes $\rho_\mathrm{d}/\rho_\mathrm{g} \sim 200$ if the dust grains can grow up to 5m.Comment: 43 pages, 30 figure

Gravitational instability of a dust layer composed of porous silicate dust aggregates in a protoplanetary disk

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 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 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 $\alpha\lesssim10^{-5}$. If the dust-to-gas ratio is increased twice, the gravitational instability occurs for $\alpha\lesssim10^{-4}$. 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.Comment: 17 pages, 11 figures, accepted for publication in Ap

Coherent Stellar Motion in Galactic Spiral Arms by Swing Amplification

We perform local $N$-body simulations of disk galaxies and investigate the evolution of spiral arms. We calculate the time autocorrelation of the surface density of spiral arms and find that the typical evolution timescale is described by the epicycle period. We investigate the distribution of the orbital elements of stars and find that in spiral arms the epicycle motions of stars are in phase while the spatial distribution of the guiding center is nearly uniform. These facts clearly show that the phase synchronization of the epicycle motion takes place, which is theoretically predicted by the swing amplification.Comment: 13 pages, 10 figures, accepted for publication in Ap

Dynamics of Self-Gravity Wakes in Dense Planetary Rings I. Pitch Angle

We investigate the dynamics of self-gravity wakes in dense planetary rings. In particular, we examine how the pitch angle of self-gravity wakes depend on ring parameters using N-body simulations. We calculate the pitch angles using the two-dimensional autocorrelation function of the ring surface density. We obtain the pitch angles for the inner and outer parts of the autocorrelation function separately. We confirm that the pitch angles are 15 to 30 degrees for reasonable ring parameters, which are consistent with previous studies. We find that the inner pitch angle increases with the Saturnicentric distance, while it barely depends on the optical depth and the restitution coefficient of ring particles. The increase of the inner pitch angle with the Saturnicentric distance is consistent with the observations of the A ring. The outer pitch angle does not have the clear dependence on any ring parameters and is about 10 - 15 degrees. This value is consistent with the pitch angle of spiral arms in collisionless systems.Comment: 30 pages, 14 figures, accepted for publication in Ap