1,141 research outputs found
Yet another fast multipole method without multipoles --- Pseudo-particle multipole method
In this paper we describe a new approach to implement the O(N) fast multipole
method and tree method, which uses pseudoparticles to express the
potential field. The new method is similar to Anderson's method, which uses the
values of potential at discrete points to represent the potential field.
However, for the same expansion order the new method is more accurate and
computationally efficient.Comment: 14 pages, 2 figure
Post-Collapse evolution of globular clusters
A number of globular clusters appear to have undergone core collapse, in the
sense that their predicted collapse time is much shorter than their current
age. Simulations using gas models and Fokker-Planck approximation have shown
that the central density of a globular cluster after the collapse undergoes
nonlinear oscillation with large amplitude (gravothermal oscillation). However,
whether such an oscillation actually takes place in a real -body system has
remained unsolved, because an -body simulation with a sufficiently high
resolution would have required the computing resource of the order of several
Gflopsyears. In the present paper, we report the result of such a
simulation, performed on a dedicated special-purpose computer GRAPE-4. We
simulated the evolution of isolated point-mass systems with up to 32,768
particles. The largest number of particles reported previously is 10,000. We
confirmed that gravothermal oscillation takes place in an -body system. The
expansion phase shows all signatures that are considered as the evidences of
the gravothermal nature of the oscillation. At the maximum expansion, the core
radius is \% of the half-mass radius for the run with 32,768 particles.
The maximum core size depends on , as .Comment: To appear in Apj, Vol 470, Oct 20, 11 pages, 7 figures, Postscript
(or GIF) version available at
http://grape.c.u-tokyo.ac.jp/pub/people/makino/papers/osclong.ps or
http://grape.c.u-tokyo.ac.jp/pub/people/makino/papers/osclong.htm
Direct Simulation of Dense Stellar Systems with GRAPE-6
In this paper we describe the current status of the GRAPE-6 project to
develop a special-purpose computer with a peak speed exceeding 100 Tflops for
the simulation of astrophysical N-body problems. One of the main targets of the
GRAPE-6 project is the simulation of dense stellar systems. In this paper,
therefore, we overview the basic algorithms we use for the simulation of dense
stellar systems and their characteristics. We then describe how we designed
GRAPE hardwares to meet the requirements of these algorithms. GRAPE-6 will be
completed by the year 2001. As an example of what science can be done on
GRAPE-6, we describe our work on the galactic center with massive black holes
performed on GRAPE-4, the predecessor of GRAPE-6.Comment: 12 pages, to appear in Dynamics of Star Clusters and the Milky Way,
eds. R. Spurzem et al. (ASP Conference Series
On the Origin of Density Cusps in Elliptical Galaxies
We investigated the dynamical reaction of the central region of galaxies to a
falling massive black hole by N-body simulations. As the initial galaxy model,
we used an isothermal King model and placed a massive black hole at around the
half-mass radius of the galaxy. We found that the central core of the galaxy is
destroyed by the heating due to the black hole and that a very weak density
cusp (, with ) is formed around the
black hole. This result is consistent with recent observations of large
elliptical galaxies with Hubble Space Telescope. The velocity of the stars
becomes tangentially anisotropic in the inner region, while in the outer region
the stars have radially anisotropic velocity dispersion. The radius of the weak
cusp region is larger for larger black hole mass. Our result naturally explains
the formation of the weak cusp found in the previous simulations of galaxy
merging, and implies that the weak cusp observed in large elliptical galaxies
may be formed by the heating process by sinking black holes during merging
events.Comment: 14 pages with 29 EPS figures; LaTeX; new results added; accepted for
publication in Ap
Exponential Growth of Distance between Nearby Rays due to Multiple Gravitational Scatterings
We give an estimate of the relative error in the angular measurement of
observations for high redshift objects induced by gravitational scatterings
(lensing). Gunn (1967) concluded that the gravitational scatterings by galaxies
induce the relative error of a few percent in the observations for objects at
. This estimate has been considered as a fundamental limitation of
accuracy of the angular measurements in the observational cosmology. In
multiple graviational scatterings, bending angle of single ray grows through
the random work process. Gunn (1967) assumed that the difference of nearby rays
also grows through the random walk process. However, distance between nearby
photons grows exponentially because the two rays suffer coherent scatterings by
the same scattering object. This exponential growth continues as long as the
scattering is coherent. In the case of scattering by individual galaxies, the
exponential growth continues until the angular distance reaches an arcminute or
so. The relative error of the angular measurements under an arcminute due to
the exponential growth is at and exceeds at , in
the case that the density parameter of galaxies is 0.2. The effects of clusters
of galaxies or superclusters are more difficult to estimate accurately, but
might be significant. In the case of supercluster the angular measurements up
to a few degrees could be affected.Comment: compressed uuencoded postscript, 8 pages including 5 figures, APJL
accepte
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