How Nature Works by Per Bak

Author:Per Bak
Language: eng
Format: epub
Publisher: Springer-Verlag Wien 2012
Published: 2015-03-10T16:00:00+00:00

Black Holes and Solar Flares

Black holes are massive objects from which nothing can escape, not even light, so we know about their existence only from observation of the gravitational force of the black hole working on other cosmic objects. A black hole attracts massive particles from its environment, which are sucked into the interior of the hole, never to be heard from again.

Recently, Mineshigi, Takeuchi, and Nishimori, in Japan, suggested that this process works very much like a sandpile. The material is temporarily arranged in disks surrounding the black hole. Gas particles are randomly injected into these accretion disks from the environment. When the mass density of the disk exceeds some critical value, the accumulated material begins to drift inward as an avalanche, thereby emitting x-rays that can be observed from the earth. We might think of the process as an hourglass in which sand is falling through a hole in the botton, while new sand is supplied from the outside. The fluctuations of the intensity of the x-rays have a 1/f spectrum. On the basis of observations of x-rays from the black hole Cygnus X-1, and some simple computer modeling, the authors conclude that the formation of black holes is an SOC phenomenon.

However, we don’t have to travel so far out in the universe to find sources of x-rays with power law distribution. One of the finest and most spectacular applications of the idea involves solar flares. In contrast to pulsars and black holes, we can directly observe what is going on without too much guessing. The sun emits solar flares all the time. Most flares are relatively small. Some of them are very large, but much rarer, and cause disruptions of radio communication on earth.

Solar flares are observed to have a large dynamical range in both energy and duration. The solar flares emit x-rays, so the intensities of the solar flares can be measured as the intensity of these x-rays. Figure 25 shows the distribution of x-rays as measured by instruments on one of NASA’s spacecrafts, as presented by B. R. Dennis. The diagram shows the frequency of flares versus their intensity, as given by the measured “count rate.” Note the straight-line behavior over more than four orders of magnitude. The flattening of the curve for small flares might well be due to difficulties in measuring these small flares in the background of x-rays from other sources. The slope of the straight line, that is, the exponent τ for the corresponding power law distribution, is approximately 1.6. Figure 25. Histogram of x-ray intensity from solar flares, as measured by the NASA satellite ISEE 3/ICE (Dennis, 1985). The diagram shows the relative amount of flares with a given energy, as represented by the “counting rate.” The data fit a straight line over four orders of magnitude. The statistics is poor for the few large events.

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