Astrophysical Simulation Basics

Over the past couple of months, we've examined several of the current areas of interest in the field of astronomical simulation. We've seen studies involving phenomena from colliding galaxies to the spontaneous emission of high-speed particle jets near a black hole, and we've looked at the computer codes being used to study them. What's interesting is that a common thread can be found underlying each of these scenarios: the reliance on hydrodynamic methods to conduct the research. It is instructive, then, to take a step back and spend some time learning the basics of such a ubiquitous description of heavenly activities.

The governing principle of the behavior of matter in space is how tightly bunched it is. Besides determining a system's properties, this measure also dictates which methods to use in a numerical study. Hydrodynamics comes into play when the space between particles is very small compared to the size scale of the overall system. In this case, collisions between constituents of the whole happen frequently, and the matter is dubbed "collisional," or "fluid."

On the other hand, if the matter in a system is more spread out, then the distance each particle can travel without collision with another represents a more significant percentage of the total length scale of interest. Under these conditions, matter tends to flow in its gravitational and/or electrical fields, developing a much more uniform and consistent velocity. As a result, the particles can form stream-like structures, the mixing of which may cause interesting physical effects. This type of substance is called "collisionless" matter, examples of which include the gas responsible for cooling flows in galaxy clusters and the dark matter in galaxies.

Studying either of these types of systems numerically involves solving the Boltzmann equation, either directly or indirectly. In brief, the Boltzmann equation describes the spatial and temporal evolution of the probability distribution function (pdf) of a system's particles. (The pdf, f(x,p), gives the probability of finding a particle at position x with momentum p. For a more detailed discussion of statistical mechanics, follow some of the links at http://tigger.uic.edu/~mansoori/Thermody...

Next week, we'll look at some of the methods used for examining these types of systems.

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