451 research outputs found
Time-Symmetrized Kustaanheimo-Stiefel Regularization
In this paper we describe a new algorithm for the long-term numerical
integration of the two-body problem, in which two particles interact under a
Newtonian gravitational potential. Although analytical solutions exist in the
unperturbed and weakly perturbed cases, numerical integration is necessary in
situations where the perturbation is relatively strong. Kustaanheimo--Stiefel
(KS) regularization is widely used to remove the singularity in the equations
of motion, making it possible to integrate orbits having very high
eccentricity. However, even with KS regularization, long-term integration is
difficult, simply because the required accuracy is usually very high. We
present a new time-integration algorithm which has no secular error in either
the binding energy or the eccentricity, while allowing variable stepsize. The
basic approach is to take a time-symmetric algorithm, then apply an implicit
criterion for the stepsize to ensure strict time reversibility. We describe the
algorithm in detail and present the results of numerical tests involving
long-term integration of binaries and hierarchical triples. In all cases
studied, we found no systematic error in either the energy or the angular
momentum. We also found that its calculation cost does not become higher than
those of existing algorithms. By contrast, the stabilization technique, which
has been widely used in the field of collisional stellar dynamics, conserves
energy very well but does not conserve angular momentum.Comment: figures are available at http://grape.c.u-tokyo.ac.jp/~funato/; To
appear in Astronomical Journal (July, 1996
Evolution of Massive Black Hole Binaries
We present the result of large-scale N-body simulations of the
stellar-dynamical evolution of a massive black-hole binary at the center of a
spherical galaxy. We focus on the dependence of the hardening rate on the
relaxation timescale of the parent galaxy. A simple theoretical argument
predicts that a binary black hole creates the ``loss cone'' around it. Once the
loss cone is formed, the hardening rate is determined by the rate at which
field stars diffuse into the loss cone. Therefore the hardening timescale
becomes proportional to the relaxation timescale. Recent N-body simulations,
however, have failed to confirm this theory and various explanations have been
proposed. By performing simulations with sufficiently large N (up to )
for sufficiently long time, we found that the hardening rate does depend on N.
Our result is consistent with the simple theoretical prediction that the
hardening timescale is proportional to the relaxation timescale. This
dependence implies that most massive black hole binaries are unlikely to merge
within the Hubble time through interaction with field stars and gravitational
wave radiation alone.Comment: Reviced version accepted for publication in ApJ. Scheduled to appear
in the February 10, 2004 issu
Multimedia based E-learning tools for dynamic modeling of dc-dc converters
Author name used in this publication: C. K. TseRefereed conference paper2005-2006 > Academic research: refereed > Refereed conference paperVersion of RecordPublishe
The Orbit, Mass, and Albedo of Transneptunian Binary 1999 RZ253
We have observed 1999 RZ253 with the Hubble Space Telescope at seven separate
epochs and have fit an orbit to the observed relative positions of this binary.
Two orbital solutions have been identified that differ primarily in the
inclination of the orbit plane. The best fit corresponds to an orbital period,
P=46.263 +0.006/-0.074 days, semimajor axis a=4,660 +/-170 km and orbital
eccentricity e=0.460 +/-0.013 corresponding to a system mass m=3.7 +/-0.4
x10^18 kg. For a density of rho = 1000 kg m^-3 the albedo at 477 nm is p = 0.12
+/-0.01, significantly higher than has been commonly assumed for objects in the
Kuiper Belt. Multicolor, multiepoch photometry shows this pair to have colors
typical for the Kuiper belt with a spectral gradient of 0.35 per 100 nm in the
range between 475 and 775 nm. Photometric variations at the four epochs we
observed were as large as 12 +/-3% but the sampling is insufficient to confirm
the existence of a lightcurve
On relaxation processes in collisionless mergers
We analyze N-body simulations of halo mergers to investigate the mechanisms
responsible for driving mixing in phase-space and the evolution to dynamical
equilibrium. We focus on mixing in energy and angular momentum and show that
mixing occurs in step-like fashion following pericenter passages of the halos.
This makes mixing during a merger unlike other well known mixing processes such
as phase mixing and chaotic mixing whose rates scale with local dynamical time.
We conclude that the mixing process that drives the system to equilibrium is
primarily a response to energy and angular momentum redistribution that occurs
due to impulsive tidal shocking and dynamical friction rather than a result of
chaotic mixing in a continuously changing potential. We also analyze the merger
remnants to determine the degree of mixing at various radii by monitoring
changes in radius, energy and angular momentum of particles. We confirm
previous findings that show that the majority of particles retain strong memory
of their original kinetic energies and angular momenta but do experience
changes in their potential energies owing to the tidal shocks they experience
during pericenter passages. Finally, we show that a significant fraction of
mass (~ 40%) in the merger remnant lies outside its formal virial radius and
that this matter is ejected roughly uniformly from all radii outside the inner
regions. This highlights the fact that mass, in its standard virial definition,
is not additive in mergers. We discuss the implications of these results for
our understanding of relaxation in collisionless dynamical systems.Comment: Version accepted for Publication in Astrophysical Journal, March 20,
2007, v685. Minor changes, latex, 14 figure
Evolution of Massive Blackhole Triples I -- Equal-mass binary-single systems
We present the result of -body simulations of dynamical evolution of
triple massive blackhole (BH) systems in galactic nuclei. We found that in most
cases two of the three BHs merge through gravitational wave (GW) radiation in
the timescale much shorter than the Hubble time, before ejecting one BH through
a slingshot. In order for a binary BH to merge before ejecting out the third
one, it has to become highly eccentric since the gravitational wave timescale
would be much longer than the Hubble time unless the eccentricity is very high.
We found that two mechanisms drive the increase of the eccentricity of the
binary. One is the strong binary-single BH interaction resulting in the
thermalization of the eccentricity. The second is the Kozai mechanism which
drives the cyclic change of the inclination and eccentricity of the inner
binary of a stable hierarchical triple system. Our result implies that many of
supermassive blackholes are binaries.Comment: 20 pages, 12 figure
The Origin of the Brightest Cluster Galaxies
Most clusters and groups of galaxies contain a giant elliptical galaxy in
their centres which far outshines and outweighs normal ellipticals. The origin
of these brightest cluster galaxies is intimately related to the collapse and
formation of the cluster. Using an N-body simulation of a cluster of galaxies
in a hierarchical cosmological model, we show that galaxy merging naturally
produces a massive, central galaxy with surface brightness and velocity
dispersion profiles similar to observed BCG's. To enhance the resolution of the
simulation, 100 dark halos at are replaced with self-consistent
disk+bulge+halo galaxy models following a Tully-Fisher relation using 100000
particles for the 20 largest galaxies and 10000 particles for the remaining
ones. This technique allows us to analyze the stellar and dark matter
components independently. The central galaxy forms through the merger of
several massive galaxies along a filament early in the cluster's history.
Galactic cannibalism of smaller galaxies through dynamical friction over a
Hubble time only accounts for a small fraction of the accreted mass. The galaxy
is a flattened, triaxial object whose long axis aligns with the primordial
filament and the long axis of the cluster galaxy distribution agreeing with
observed trends for galaxy-cluster alignment.Comment: Revised and accepted in ApJ, 25 pages, 10 figures, online version
available at http://www.cita.utoronto.ca/~dubinski/bcg
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