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The Question
(Submitted June 09, 1997)
I'm curious as to the recent need for teraflop and
petaflop computers for the sole purpose of calculating the
evolution of clusters (gravitational pulls, twin star
formations, and other collisions).
When we finish calculating many of these virtual
clusters of galaxies, will we be able to understand if our
cluster is really the center of the Universe and if it is
truly an average cluster? Has this already been explored?
The Answer
Thank you for your question about evolution of galaxy
clusters, and the need for fast (or special purpose) computers
for this work.
The basic reason why the investigation of the dynamical
evolution of galaxy clusters (as well as the evolution of single
galaxies, or even globular clusters) is so computer intensive
actually is due to a fundamental mathematical property of the
equations that determine this evolution. The gravitational
attraction between all objects is described by Newton's Laws,
which you are probably familiar with. One law states that the
gravitational force between two objects is a constant multiplied
by the product of the two masses, divided by the distance separating
the objects squared. In most of the solar system examples
we are presented with on a 'day to day' level, the system can
be described as two bodies. For each of the planets, we can
treat their orbital evolution largely as if they were a single
object in orbit about the Sun (the other planets produce only
minor perturbations to this simple two-body orbit). Likewise,
the Moon's orbit about the Earth can be treated largely as a
two-body problem, since the distance between the Earth and
Moon is much smaller than that between the Earth-Moon system
and the Sun. Mathematically, the two-body problem is one that
we refer to as 'integrable'. What this means is that it is
possible to write down the solution to the equations of motion
in closed form. Then for any set of initial conditions, we can
use this closed form solution to determine the positions and
velocities of the two bodies for all time.
When even one more body is added to the mix, the problem
becomes 'non-integrable'. This has two important consequences. The
first is the equations that determine the evolution are no longer
in closed form. The second is that the system can now have parameter
ranges for which the evolution is extremely sensitive to the initial
conditions of the system. Very small changes in the initial conditions
(positions and velocities) can lead to drastically different evolutions.
Putting these two consequences together, you can probably see now why
one needs a lot of computer power: galaxy clusters are comprised of
numerous objects (galaxies) which are themselves made up of individual
stars, interacting with each other. There are clever ways to make the
calculation of the cluster evolution less computationally intensive,
such as concentrating only on the interactions of nearest neighbor stars,
and treating the contribution from the numerous more distant stars as
a smooth gravitational potential. You still need to have a lot of
computer power to do this. The sensitivity to initial conditions means
that researchers often try a very large number of initial conditions
so they can get an idea of the statistical behavior of the interactions.
To answer your specific questions: the need for teraflop or faster
computers to do these calculations is not recent. However, the development
of special purpose computers (that are hard wired to do nothing but the
cluster evolution calculation) and novel ways of networking computers
to achieve greater speeds, are currently very active areas of computational
astrophysics research. The sophistication of the cluster evolution
models is constantly growing. None of these calculations are aimed
at trying to determine if our cluster is the center of the Universe.
One of the fundamental assumptions of modern cosmology is that no
single location in the Universe is special, and that there is no
meaning to the concept 'the center of the Universe.' However, the
average observer in any location in the Universe would observe galaxies
to be receding from her position, and so might erroneously suppose
herself to be at the center of the Universe. In any case, the dynamical
evolution of the cluster is a local phenomenon, not connected to the
overall expansion of the Universe.
Sorry if this is long-winded, but your questions touch on topics
which are not easy to answer without going into the details.
Cheers,
Padi Boyd
for the Ask an Astrophysicists Team
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