17 research outputs found
Instability of the Gravitational N-Body Problem in the Large-N Limit
We use a systolic N-body algorithm to evaluate the linear stability of the
gravitational N-body problem for N up to 1.3 x 10^5, two orders of magnitude
greater than in previous experiments. For the first time, a clear ~ln
N-dependence of the perturbation growth rate is seen. The e-folding time for N
= 10^5 is roughly 1/20 of a crossing time.Comment: Accepted for publication in The Astrophysical Journa
Collisional dynamics around binary black holes in galactic centers
We follow the sinking of two massive black holes in a spherical stellar
system where the black holes become bound under the influence of dynamical
friction. Once bound, the binary hardens by three-body encounters with
surrounding stars. We find that the binary wanders inside the core, providing
an enhanced supply of reaction partners for the hardening. The binary evolves
into a highly eccentric orbit leading to coalescence well beyond a Hubble time.
These are the first results from a hybrid ``self consistent field'' (SCF) and
direct Aarseth N-body integrator (NBODY6), which combines the advantages of the
direct force calculation with the efficiency of the field method. The code is
designed for use on parallel architectures and is therefore applicable to
collisional N-body integrations with extraordinarily large particle numbers (>
10^5). This creates the possibility of simulating the dynamics of both globular
clusters with realistic collisional relaxation and stellar systems surrounding
supermassive black holes in galactic nuclei.Comment: 38 pages, 13 figures, submitted to ApJ, accepted, revised text and
added figure
Core Formation by a Population of Massive Remnants
Core radii of globular clusters in the Large and Small Magellanic Clouds show
an increasing trend with age. We propose that this trend is a dynamical effect
resulting from the accumulation of massive stars and stellar-mass black holes
at the cluster centers. The black holes are remnants of stars with initial
masses exceeding 20-25 solar masses; as their orbits decay by dynamical
friction, they heat the stellar background and create a core. Using analytical
estimates and N-body experiments, we show that the sizes of the cores so
produced and their growth rates are consistent with what is observed. We
propose that this mechanism is responsible for the formation of cores in all
globular clusters and possibly in other systems as well.Comment: 5 page
Systolic and Hyper-Systolic Algorithms for the Gravitational N-Body Problem, with an Application to Brownian Motion
A systolic algorithm rhythmically computes and passes data through a network
of processors. We investigate the performance of systolic algorithms for
implementing the gravitational N-body problem on distributed-memory computers.
Systolic algorithms minimize memory requirements by distributing the particles
between processors. We show that the performance of systolic routines can be
greatly enhanced by the use of non-blocking communication, which allows
particle coordinates to be communicated at the same time that force
calculations are being carried out. Hyper-systolic algorithms reduce the
communication complexity at the expense of increased memory demands. As an
example of an application requiring large N, we use the systolic algorithm to
carry out direct-summation simulations using 10^6 particles of the Brownian
motion of the supermassive black hole at the center of the Milky Way galaxy. We
predict a 3D random velocity of 0.4 km/s for the black hole.Comment: 33 pages, 10 postscript figure
Double Black Holes in Galactic Nuclei – Do they Merge or not?
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