1,074 research outputs found

### Resonant capture by inward migrating planets

We investigate resonant capture of small bodies by planets that migrate
inwards, using analytic arguments and three-body integrations. If the orbits of
the planet and the small body are initially circular and coplanar, the small
body is captured when it crosses the 2:1 resonance with the planet. As the
orbit shrinks it becomes more eccentric, until by the time its semimajor axis
has shrunk by a factor of four, its eccentricity reaches nearly unity
(1-e<<10^{-4}). In typical planetary systems, bodies in this high-eccentricity
phase are likely to be consumed by the central star. If they can avoid this
fate, as migration continues the inclination flips from 0 to i=180 degrees;
thereafter the eccentricity declines until the semimajor axis is a factor of
nine smaller than at capture, at which point the small body is released from
the 2:1 resonance on a nearly circular retrograde orbit. Small bodies captured
into resonance from initially inclined or eccentric orbits can also be ejected
from the system, or released from the resonance on highly eccentric polar
orbits (i\simeq 90 degrees) that are stabilized by a secular resonance. We
conclude that migration can drive much of the inner planetesimal disk into the
star, and that post-migration multi-planet systems may not be coplanar.Comment: 12 pages, 5 figures, submitted to Astronomical Journa

### Gravitational Collapse in One Dimension

We simulate the evolution of one-dimensional gravitating collisionless
systems from non- equilibrium initial conditions, similar to the conditions
that lead to the formation of dark- matter halos in three dimensions. As in the
case of 3D halo formation we find that initially cold, nearly homogeneous
particle distributions collapse to approach a final equilibrium state with a
universal density profile. At small radii, this attractor exhibits a power-law
behavior in density, {\rho}(x) \propto |x|^(-{\gamma}_crit), {\gamma}_crit
\simeq 0.47, slightly but significantly shallower than the value {\gamma} = 1/2
suggested previously. This state develops from the initial conditions through a
process of phase mixing and violent relaxation. This process preserves the
energy ranks of particles. By warming the initial conditions, we illustrate a
cross-over from this power-law final state to a final state containing a
homogeneous core. We further show that inhomogeneous but cold power-law initial
conditions, with initial exponent {\gamma}_i > {\gamma}_crit, do not evolve
toward the attractor but reach a final state that retains their original
power-law behavior in the interior of the profile, indicating a bifurcation in
the final state as a function of the initial exponent. Our results rely on a
high-fidelity event-driven simulation technique.Comment: 14 Pages, 13 Figures. Submitted to MNRA

### Comparison of simple mass estimators for slowly rotating elliptical galaxies

We compare the performance of mass estimators for elliptical galaxies that
rely on the directly observable surface brightness and velocity dispersion
profiles, without invoking computationally expensive detailed modeling. These
methods recover the mass at a specific radius where the mass estimate is
expected to be least sensitive to the anisotropy of stellar orbits. One method
(Wolf et al. 2010) uses the total luminosity-weighted velocity dispersion and
evaluates the mass at a 3D half-light radius $r_{1/2}$, i.e., it depends on the
GLOBAL galaxy properties. Another approach (Churazov et al. 2010) estimates the
mass from the velocity dispersion at a radius $R_2$ where the surface
brightness declines as $R^{-2}$, i.e., it depends on the LOCAL properties. We
evaluate the accuracy of the two methods for analytical models, simulated
galaxies and real elliptical galaxies that have already been modeled by the
Schwarzschild's orbit-superposition technique. Both estimators recover an
almost unbiased circular speed estimate with a modest RMS scatter ($\lesssim 10
\%$). Tests on analytical models and simulated galaxies indicate that the local
estimator has a smaller RMS scatter than the global one. We show by examination
of simulated galaxies that the projected velocity dispersion at $R_2$ could
serve as a good proxy for the virial galaxy mass. For simulated galaxies the
total halo mass scales with $\sigma_p(R_2)$ as $M_{vir}
\left[M_{\odot}h^{-1}\right] \approx 6\cdot 10^{12} \left(
\frac{\sigma_p(R_2)}{200\, \rm km\, s^{-1}} \right)^{4}$ with RMS scatter
$\approx 40 \%$.Comment: 19 pages, 14 figures, 4 tables, accepted for publication in MNRA

### Lattice Stellar Dynamics

We describe a technique for solving the combined collisionless Boltzmann and
Poisson equations in a discretised, or lattice, phase space. The time and the
positions and velocities of `particles' take on integer values, and the forces
are rounded to the nearest integer. The equations of motion are symplectic. In
the limit of high resolution, the lattice equations become the usual
integro-differential equations of stellar dynamics. The technique complements
other tools for solving those equations approximately, such as $N$-body
simulation, or techniques based on phase-space grids. Equilibria are found in a
variety of shapes and sizes. They are true equilibria in the sense that they do
not evolve with time, even slowly, unlike existing $N$-body approximations to
stellar systems, which are subject to two-body relaxation. They can also be
`tailor-made' in the sense that the mass distribution is constrained to be
close to some pre-specified function. Their principal limitation is the amount
of memory required to store the lattice, which in practice restricts the
technique to modeling systems with a high degree of symmetry. We also develop a
method for analysing the linear stability of collisionless systems, based on
lattice equilibria as an unperturbed model.Comment: Accepted for publication in Monthly Notices. 18 pages, compressed
PostScript, also available from http://www.cita.utoronto.ca/~syer/papers

### Slow m=1 instabilities of softened gravity Keplerian discs

We present the simplest model that permits a largely analytical exploration
of the m=1 counter-rotating instability in a "hot" nearly Keplerian disc of
collisionless self-gravitating matter. The model consists of a two-component
softened gravity disc, whose linear modes are analysed using WKB. The modes are
slow in the sense that their (complex) frequency is smaller than the Keplerian
orbital frequency by a factor which is of order the ratio of the disc mass to
the mass of the central object. Very simple analytical expressions are derived
for the precession frequencies and growth rates of local modes; it is shown
that a nearly Keplerian disc must be unrealistically hot to avoid an
overstability. Global modes are constructed for the case of zero net rotation.Comment: 6 pages, four figure

- …