Dynamics in dense stellar clusters:
Binary black holes
in galactic centers
M. Hemsendorf, R. Spurzem, D. Merritt
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Binary black holes in galaxies
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Point mass dynamics
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Parallelizing strategies
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The results
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Black holes in galactic centres
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- Larger
galaxies, like our own, harbor a supermassive black hole in their
centers. Their mass ranges approximately from solar masses and it is closely related to the
velocity dispersion in the hosting system.
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These central massive objects are made resposible for galactic
activity: e.g. The quasar phenomenon, or the jets streching out far
into the intergalactic medium.
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Their origin, however, is not clear to date. Supermassive black holes
might be direct descendants from the big bang, or might be the result
of the nonlinear collapse of a density fluctuation, or might have
evolved through stellar dynamical processes during galaxy formation.
Why binaries?
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- The
collapse of initial density fluctuations leads to the foam like
structures in our universe, as large -body
simulations show. The knots forming decouple from the universal
expansion and become protogalaxies. Galaxies and galaxy clusters form
by subsequent merging of protogalaxies. (Click here in order to see how a galaxy cluster
evolves Curtesy of B. Moore, T. Quinn, J. Stadel,
and G. Lake, Univ. of Washington. 6.0 Mbyte.)
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Many of these protogalaxies contain massive black holes. In the
merging processes these dark objects will roam between the stars and
sink to the center where they meet other black holes in order to form
binaries, triples, etc.
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The evoltion of these binaries until coalescence might be observable
by gravitational wave detectors.
What do you need for simulating such a system?
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The large differences in particle masses require large particle
numbers in the simulations (Ideally approx. ).
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Unlike cosmological simulations, collisional stellar dynamics require
high order direct force integrators.
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The direct force calculation takes up an arbitrarily large amount of the
CPU time: . However, it provides the most
accurate forces, so that steppers can give most accurate results.
How can you win against the scaling?
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Brute force: The GRAPE
project provides the astronomical community with special purpose
computers, which do the force calculation with more than 1.2 Teraflops
for a price of $40000,00. However, the rest of the calculation remains
at workstation speed.
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Intelligence: With neighbor schemes, or hybrid codes, which use
specialized routines for different physical regimes in the cluster,
the efficiency can be enhanced significantly. Still, practically all
parts of the program have to run efficiently in parallel. To
accomplish this can be an extremely tricky and difficult process.
The systolic algorithm
A method for circular contraction of a
distributed quantity is often called a systolic algorithm. The figure
below shows a communication pattern which makes use of nonblocking
communication. This pattern resembles a systolic algorithm: The data
is distributed evenly to all processing nodes, there are no redundant
data. While computing the forces on a set of positions, this set is
sent using nonblocking communication to the neighbouring
processor. The partial sum of the force calculation follows on the
next shift cycle. The load balance is perfect as long the
communication time is shorter than the computing time. In a direct
force computation this can always be accomplished by choosing a large
enough problem size.
Other routing mechanisms
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When one trades memory against communication speed, the time for the
communication can scale with . These methods are
called hypersystolic algorithm (Th. Lippert) or broadcasting method
(J. Makino)
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With a problem size of particles
these methods can make efficient use of thousands of T3E processors,
while the systolic code becomes ineffcient with more than 200.
However, a perfect load balancing is harder to accomplish in these
refined codes, while it is automatically perfect in systolic methods.
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- Depending on the available number
and speed of the processors, the communication bandwidth, and the
problem size and structure any of these methods might become optimal.
Finally results:
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We follow the motion of black hole particles in a merger scenario: Two
equal mass galaxies merge, each containing a black hole particle with
a mass of 1% of the galaxy mass. (Click
here in order to see a movie of this Curtesy of F. Cruz,
M. Milosavljevic, and D. Merritt. 39.7 MByte.)
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The stellar component quickly experiences violent relaxation and forms
a fairly spherical system. However, the black holes travel through the
system still with their cusps bound to each of them. In a second
merger process, these cusps get finally destroyed. (Also to be
observed in the movie above)
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The further evolution of the black holes is followed using a hybrid
method with a collisional and a collisionless field part: It shows the
binary hardens quickly, which promises a very likely detection of
gravitational radiation from these processes. (Click here to see a movie about the
hardening stage of the binary Please note, the binary shows a net
motion around the center, which is driven by three body interactions
with the stellar particles. 1.6 MByte.)
Summary:
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By using the 'intelligent' approach to parallelize complex integration
methods for collisional gravitational systems (e.g. pure scale free
Keplerian potentials) we can follow the evolution of a black hole
binary through a merger of two galaxies.
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Though special purpose computers exist, which can outperform 'big iron'
computers by an order of magnitude, Amdahl's law calls for fast
general purpose computers as well. With an increasing amount of
detail physics (e.g. interstellar matter, stellar evolution) in the
simulations general purpose computers become more important again.
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The ideal machine for these simulations would be an affordable or
accessible vector-parallel computer with a GRAPE attached to each
computing node.
Acknowledgements
This project is funded by
Deutsche Forschungsgemeinschaft (DFG) project Sp 345/9-1 and
SFB 439 at the University of Heidelberg and NSF grant AST 00-71099, NASA
grants NAG 5-7019, NAG 5-6037, and NAG 5-9046 at Rutgers, the State
University of New Jersey.
Technical help and computer resources are provided by
NIC in Jülich, HLRS in Stuttgart, EPCC in
Edinburgh, ZIB in Berlin, SSC in
Karlsruhe, the Pittsburgh Supercomputer Center, the
NASA Center for Computational Sciences (NCCS),
the San Diego Supercomputer Center (SDCS), and the National
Partnership for Advanced Computational Infrastructure (NPACI),
Rutgers University, University of Heidelberg, and University of Kiel.
Contact: marchems@physics.rutgers.edu
Marc Hemsendorf
Mon May 21 01:18:10 MEST 2001