99 research outputs found

### 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

### Formation of Close-in Super-Earths by Giant Impacts: Effects of Initial Eccentricities and Inclinations of Protoplanets

Recent observations have revealed the eccentricity and inclination
distributions of close-in super-Earths. These distributions have the potential
to constrain their formation processes. In the in-situ formation scenario, the
eccentricities and inclinations of planets are determined by gravitational
scattering and collisions between protoplanets on the giant impact stage. We
investigate the effect of the initial eccentricities and inclinations of
protoplanets on the formation of close-in super-Earths. We perform $N$-body
simulations of protoplanets in gas-free disks, changing the initial
eccentricities and inclinations systematically. We find that while the
eccentricities of protoplanets are well relaxed through their evolution, the
inclinations are not. When the initial inclinations are small, they are not
generally pumped up since scattering is less effective and collisions occur
immediately after orbital crossing. On the other hand, when the initial
inclinations are large, they tend to be kept large since collisional damping is
less effective. Not only the resultant inclinations of planets, but also their
number, eccentricities, angular momentum deficit, and orbital separations are
affected by the initial inclinations of protoplanets.Comment: Accepted for publication in A

### 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 and Accretion of Planetesimals

We review the basic dynamics and accretion of planetesimals by showing N-body
simulations. The orbits of planetesimals evolve through two-body gravitational
relaxation: viscous stirring increases the random velocity and dynamical
friction realizes the equiparation of the random energy. In the early stage of
planetesimal accretion the growth mode of planetesimals is runaway growth where
larger planetesimals grow faster than smaller ones. When a protoplanet
(runaway-growing planetesimal) exceeds a critical mass the growth mode shifts
to oligarchic growth where similar-sized protoplanets grow keeping a certain
orbital separation. The final stage of terrestrial planet formation is
collision among protoplanets known as giant impacts. We also summarize the
dynamical effects of disk gas on planets and the core accretion model for
formation of gas giants and discuss the diversity of planetary systems

### Effect of Stellar Encounters on Comet Cloud Formation

We have investigated the effect of stellar encounters on the formation and
disruption of the Oort cloud using the classical impulse approximation. We
calculate the evolution of a planetesimal disk into a spherical Oort cloud due
to the perturbation from passing stars for 10 Gyr. We obtain the empirical fits
of the $e$-folding time for the number of Oort cloud comets using the standard
exponential and Kohlrausch formulae as functions of the stellar parameters and
the initial semimajor axes of planetesimals. The $e$-folding time and the
evolution timescales of the orbital elements are also analytically derived. In
some calculations, the effect of the Galactic tide is additionally considered.
We also show the radial variations of the $e$-folding times to the Oort cloud.
From these timescales, we show that if the initial planetesimal disk has the
semimajor axes distribution ${\rm d}n/{\rm d}a\propto a^{-2}$, which is
produced by planetary scattering (Higuchi et al. 2006), the $e$-folding time
for planetesimals in the Oort cloud is $\sim$10 Gyr at any heliocentric
distance $r$. This uniform $e$-folding time over the Oort cloud means that the
supply of comets from the inner Oort cloud to the outer Oort cloud is
sufficiently effective to keep the comet distribution as ${\rm d}n/{\rm
d}r\propto r^{-2}$. We also show that the final distribution of the semimajor
axes in the Oort cloud is approximately proportional to $a^{-2}$ for any
initial distribution.Comment: Accepted for publication in AJ, 15 figures, 3 table

### 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

### 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

### 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

### 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

### 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

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