1,000 Shares of Magnetar at 12-1/2!

December 07, 1999

Quakes on pulsars follow the same power law as the stock market, traffic jams Dec. 8, 1999 - Here's a hot stock tip: the market, earthquakes, traffic jams, and magnetars follow the same power law. This oddity of the universe won't make you rich; it certainly can't be used to predict where the market is headed. But it follows a recent theory called self-organizing criticality.

As often happens in nature, statistics can yield intriguing answers after months of individual observations, like those made by Ersin Gogus, a doctoral candidate at the University of Alabama in Huntsville, and several colleagues. Gogus earned his bachelor's degree at Middle East Technical University in Ankara, Turkey. "Subsystems self-organize to a critical state in which a slight disturbance can cause a chain reaction, such as an avalanche, an earthquake, or a magnetar outburst," Gogus explained. While this self-organization - a theory developed in 1988 by Per Bak - cannot predict the strength or time of the next event, "It does let us expect that the strongest events at high energies tend to occur less frequently than other events." In the case of earthquakes or starquakes, the distribution of strength will follow a pattern called a power law.

"It's a good test to see how the energy distribution forms," Gogus said. He and his colleagues analyzed the statistical properties of SGR 1900+14, one of four known soft gamma repeaters. These are neutron stars that repeatedly emit bursts of low-energy gamma rays at random intervals. The SGRs have well known locations and are within or near our galaxy (unlike true gamma-ray bursters which are once-only events that occur deep in the universe). SGR 1900+14 and other SGRs have been identified as magnetars, neutron stars with magnetic fields intense enough to drag on the star's rotation and to pump massive amounts of energy into space. Gogus looked at SGR 1900+14 during an extremely active period between May 1998 and January 1999. This followed an extended period with virtually no activity. For nine months, though, it let loose with more than a thousand events. This activity was measured with the Burst and Transient Source Experiment (BATSE) aboard the Compton Gamma Ray Observatory and with the Rossi X-ray Timing Explorer. Two interesting phenomena emerged from their data.

"When you get a large sample set," Gogus said, "the distribution of the logarithm of recurrence times of events forms a bell curve." In other words, an ordinary graph produces a graph that few people would recognize. But putting time on a logarithmic scale, which compresses large quantities into scales that can be fit onto a sheet of paper, produces the familiar bell curve. Gogus found that the waiting time between successive bursts ranged from 0.25 to 1,421 seconds (almost 24 minutes), with a peak at 49 seconds in the middle of the bell curve formed by the burst waiting times. This does not translate into a way of predicting when a burst will occur, but implies some underlying mechanism within the magnetar is driving events and that they are not totally random. In addition, it doesn't seem to store up energy for "the big one" since there was no correlation between the waiting time and the intensity of the next burst. The other interesting effect is called a power law energy distribution. That is, plotting discrete event energies against the number of events within discrete energy ranges produces a straight line. #The outbursts from SGR 1900+14 followed a power law of 1.66. Other researchers have measured similar distributions for SGR 1806-20 and 1627-41. Power law distributions have been found for earthquakes (with power laws ranging from 1.4 to 1.8) and for solar flares (1.53 to 1.73). Looking at similar behavior in earthquakes and even in how much sand will pile up before sliding led Bak, with C. Tang and K. Wiesenfeld, to propose self-organized criticality theory. Bak is at the Neils Bohr Institute in Copenhagen, Denmark. He proposed that large, dynamic systems will behave according to some variation of a power law.
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NASA/Marshall Space Flight Center--Space Sciences Laboratory

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