Astronomers have discovered variable stars that periodically dim and brighten at frequencies close to the famed golden mean
The connection between the golden ratio and these variable stars could be meaningful or it could just be a fluke. “Many claims about natural phenomena and the golden ratio are exaggerated,” says mathematician and computer scientist George Markowsky of the University of Maine, Orono. “I refuse to accept anything off by 2 percent or more as evidence of the golden ratio. After all, around any real number there are infinitely many other real numbers. People don’t seem to write papers about the mystic properties of .6 (which is very close to .618….).” Astronomer Szabó, who leads the working group studying Kepler data on RR Lyrae stars, says he is not yet convinced that the golden ratio in this case is more than a coincidence, but that characterizing the stars’ oscillation frequencies is important. “This paper is a significant contribution to the topic,” he says.
Although the sample of stars in this study was very small, the researchers noticed an intriguing pattern among the four stars with pulsation frequencies close to the golden ratio. These stars all exhibited fractal behavior—never-ending patterns that repeat on continuously smaller scales—whereas the two non–golden ratio stars did not. “That suggests there might be a pattern,” Linder says. “What we need is more data.” An example of a fractal is a jagged coastline, which reveals more and more wiggles in its outline as you zoom in from any vantage point. “It’s the same with the frequencies in these stars,” Linder says. “As we lower the threshold we see more and more frequencies.”
The golden stars are actually the first examples outside of a laboratory of what’s called “strange nonchaotic dynamics.” The “strange” here refers to a fractal pattern, and nonchaotic means the pattern is orderly, rather than random. Most fractal patterns in nature, such as weather, are chaotic, so this aspect of the variable stars came as a surprise. “If you look in the literature, you see lots of examples of strange chaotic behavior,” Linder says. “I think our paper is going to bring this overlooked type of dynamics to the foreground.” If the same pattern is seen in more stars with golden ratio frequencies, it might help astronomers better understand and predict the detailed physics of stellar pulsations. “From a dynamics perspective,” Livio says, “it is quite intriguing to understand why systems would be attracted to this ratio.”
Article from Scientific American