7,823 research outputs found
Long-term evolution of a planetesimal swarm in the vicinity of a protoplanet
Many models of planet formation involve scenarios in which one or a few large protoplanets interact with a swarm of much smaller planetesimals. In such scenarios, three-body perturbations by the protoplanet as well as mutual collisions and gravitational interactions between the swarm bodies are important in determining the velocity distribution of the swarm. We are developing a model to examine the effects of these processes on the evolution of a planetesimal swarm. The model consists of a combination of numerical integrations of the gravitational influence of one (or a few) massive protoplanets on swarm bodies together with a statistical treatment of the interactions between the planetesimals. Integrating the planetesimal orbits allows us to take into account effects that are difficult to model analytically or statistically, such as three-body collision cross-sections and resonant perturbations by the protoplanet, while using a statistical treatment for the particle-particle interactions allows us to use a large enough sample to obtain meaningful results
Formation of Kuiper Belt Binaries by Gravitational Collapse
A large fraction of 100-km-class low-inclination objects in the classical
Kuiper Belt (KB) are binaries with comparable mass and wide separation of
components. A favored model for their formation was capture during the
coagulation growth of bodies in the early KB. Instead, recent studies suggested
that large objects can rapidly form in the protoplanetary disks when swarms of
locally concentrated solids collapse under their own gravity. Here we examine
the possibility that KB binaries formed during gravitational collapse when the
excess of angular momentum prevented the agglomeration of available mass into a
solitary object. We find that this new mechanism provides a robust path toward
the formation of KB binaries with observed properties, and can explain wide
systems such as 2001 QW322 and multiples such as (47171) 1999 TC36. Notably,
the gravitational collapse is capable of producing 100% binary fraction for a
wide range of the swarm's initial angular momentum values. The binary
components have similar masses (80% have the secondary-over-primary radius
ratio >0.7) and their separation ranges from ~1,000 to ~100,000 km. The binary
orbits have eccentricities from e=0 to ~1, with the majority having e<0.6. The
binary orbit inclinations with respect to the initial angular momentum of the
swarm range from i=0 to ~90 deg, with most cases having i<50 deg. Our binary
formation mechanism implies that the primary and secondary components in each
binary pair should have identical bulk composition, which is consistent with
the current photometric data. We discuss the applicability of our results to
the Pluto-Charon, Orcus-Vanth, (617) Patroclus-Menoetius and (90) Antiope
binary systems.Comment: Astronomical Journal, in pres
A coherent method for the detection and estimation of continuous gravitational wave signals using a pulsar timing array
The use of a high precision pulsar timing array is a promising approach to
detecting gravitational waves in the very low frequency regime ( Hz) that is complementary to the ground-based efforts (e.g., LIGO,
Virgo) at high frequencies ( Hz) and space-based ones (e.g.,
LISA) at low frequencies ( Hz). One of the target sources for
pulsar timing arrays are individual supermassive black hole binaries that are
expected to form in galactic mergers. In this paper, a likelihood based method
for detection and estimation is presented for a monochromatic continuous
gravitational wave signal emitted by such a source. The so-called pulsar terms
in the signal that arise due to the breakdown of the long-wavelength
approximation are explicitly taken into account in this method. In addition,
the method accounts for equality and inequality constraints involved in the
semi-analytical maximization of the likelihood over a subset of the parameters.
The remaining parameters are maximized over numerically using Particle Swarm
Optimization. Thus, the method presented here solves the monochromatic
continuous wave detection and estimation problem without invoking some of the
approximations that have been used in earlier studies.Comment: 33 pages, 10 figures, submitted to Ap
A primer of swarm equilibria
We study equilibrium configurations of swarming biological organisms subject
to exogenous and pairwise endogenous forces. Beginning with a discrete
dynamical model, we derive a variational description of the corresponding
continuum population density. Equilibrium solutions are extrema of an energy
functional, and satisfy a Fredholm integral equation. We find conditions for
the extrema to be local minimizers, global minimizers, and minimizers with
respect to infinitesimal Lagrangian displacements of mass. In one spatial
dimension, for a variety of exogenous forces, endogenous forces, and domain
configurations, we find exact analytical expressions for the equilibria. These
agree closely with numerical simulations of the underlying discrete model.The
exact solutions provide a sampling of the wide variety of equilibrium
configurations possible within our general swarm modeling framework. The
equilibria typically are compactly supported and may contain
-concentrations or jump discontinuities at the edge of the support. We
apply our methods to a model of locust swarms, which are observed in nature to
consist of a concentrated population on the ground separated from an airborne
group. Our model can reproduce this configuration; quasi-two-dimensionality of
the model plays a critical role.Comment: 38 pages, submitted to SIAM J. Appl. Dyn. Sy
Binary-induced collapse of a compact, collisionless cluster
We improve and extend Shapiro's model of a relativistic, compact object which
is stable in isolation but is driven dynamically unstable by the tidal field of
a binary companion. Our compact object consists of a dense swarm of test
particles moving in randomly-oriented, initially circular, relativistic orbits
about a nonrotating black hole. The binary companion is a distant, slowly
inspiraling point mass. The tidal field of the companion is treated as a small
perturbation on the background Schwarzschild geometry near the hole; the
resulting metric is determined by solving the perturbation equations of Regge
and Wheeler and Zerilli in the quasi-static limit. The perturbed spacetime
supports Bekenstein's conjecture that the horizon area of a near-equilibrium
black hole is an adiabatic invariant. We follow the evolution of the system and
confirm that gravitational collapse can be induced in a compact collisionless
cluster by the tidal field of a binary companion.Comment: 9 Latex pages, 14 postscript figure
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