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IBM scientist uses fractal theory to explain stellar mystery
Nobody really knows how many stars actually glitter our skies, but have you ever wondered how they were formed and ultimately found their home in the Universe?
Bruce Elmegreen, a researcher at IBM's T.J. Watson Research Center, has been investigating this phenomena for several years. He believes that understanding the birth of stars in a cluster is far too complicated for conventional methods, which are based on solving the equations of gas flow and gravitational collapse in interstellar clouds.
How are stars born?
Gas, pulled in by gravity and tossed around by turbulence, becomes denser by 20 orders of magnitude (1 followed by 20 zeros) before it makes a new star. Computers are not yet powerful enough to simulate all of the steps during this process, and simply analyzing the equations does not help either.
"Stars form when turbulent gas collapses on itself because gravity overcomes all the irregular motions," Elmegreen says. "But these motions are so chaotic and unpredictable that understanding or simulating them is as impossible for us now as forecasting a detailed weather report several months in advance."
Fortunately there are some aspects of star formation that may be understood now, including one of the oldest problems in this field: explaining the relative proportion of high- to low-mass stars. Low mass stars are much more common than high mass stars, but no one really understands why. The Sun, for example, is a medium-sized, common type of star, but bright, massive stars like Sirius (the Dog Star near Orion) are relatively rare.
"This problem is essentially statistical," says Elmegreen. "To solve it, we don't have to say how any particular star formed, which is very difficult, but only find how many of one type formed relative to another." A remarkable observation is that the relative proportion of high- to low-mass stars is the same for all clusters.
Fractal key
Elmegreen believes that the key to this problem is the fractal nature of interstellar gas. Fractal distributions are hierarchical, like smoke trails or billowy clouds in the sky. Fractal mathematics is a way of quantifying and working with these structures.
"Turbulence shapes both the clouds in the sky and the clouds in space, giving them an irregular but repetitive pattern that would be impossible to describe without the help of fractal geometry," says Elmegreen.
A cloud in the Earth's atmosphere has structure on a wide range of scales. There are generally a few large clumps, and each of these contains several smaller clumps, which, in turn, contain even smaller clumps down to the limit of what can be seen from the ground. Click on the buttons to see it zoom in to smaller and smaller scales, all the while preserving the overall "cloudy" appearance.
An important element of all turbulence is the appearance of randomness. So, Elmegreen (with the aid of an IBM RS6000 SP) samples random pieces of a hierarchical cloud to select stars in a physically realistic way.
The result of this random sampling is a mass distribution for "computer" stars that is identical to that for real stars, with essentially no dependence on any cloud property. This is the first explanation for the stellar mass distribution that is universally applicable to all star-forming clouds.
"The ultimate goal of this work," Elmegreen points out, "is to explain how the Earth and solar system formed from tenuous, cosmic gas."
Fractal Science
Fractal geometry makes it possible to describe mathematically the kinds of irregularities existing in nature. In 1967, a scientist at IBM Research, Benoit B. Mandelbrot, published a paper in Science introducing this concept -- seeming irregular natural shapes, such as the branching of trees, have the same form when viewed from close up or from far away. "The Mandelbrot Set," a fractal object discovered in 1980, has been described as the most complex, and possibly most beautiful, object ever seen in mathematics. In the thirty years since they were first identified, the study of fractals has brought new insight to a wide variety of fields, including mathematics, physics, earth sciences, economics, and computer graphics and animation.
Other links
IBM CyberDigest technical papers 1987-1998
Extensive Bibliography of Fractal Compression Links
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