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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?

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,