The Pulses of a Distant Star Hide the Golden Ratio

Time itself can be fractal. As some shapes in nature resist the elegant closure of rational number representation, the natural frequencies of some stars do too.

This is according to new work from a team of astronomers and chaos theorists at the University of Hawaii. In a recent paper, they offer an unexpected analysis of data collected by the Kepler space telescope describing the white-blue star KIC 5520878. In plotting the star's periodic brightness fluctuations at half-hour intervals over the course of four years, they were able to hone in on some mysterious patterns.

Stars often don't shine at a constant rate. Ours does, yes, but that's hardly the rule. As giant nuclear furnaces they're subject to all sorts of different influences, some known and others not so much. Some pulsars spin around every few milliseconds, like cosmic strobo-lighthouses, while asymmetric binary star systems often have their own characteristic wobble. Even relatively "normal" stars might expand and contract like molten hydrogen hearts as outward bursts of radiation seek balance with inward gravitational attraction. So: in this way, a star can have a characteristic frequency.

KIC 5520878 actually has two characteristic frequencies (for reasons so-far unknown), and it's in the relationship between the two that we find our fractals. It's simple really: "two of KIC 5520878's characteristic frequencies—with a 4.05- and a 6.41-hour cycle, respectively—had a ratio of 1.58, close to the golden mean, an irrational number," the researchers, led by systems theorist William L. Ditto, write.

So what? Well … patterns are interesting, particularly the difficult anti-patterns of irrational numbers, which are just real numbers that can't be reduced to a fraction of two whole numbers (integers). (The intuition is like this: take a pizza, probably a square pizza, and there exists a first slice dividing the pizza into two parts such that it's no longer possible to divide the pizza evenly, no matter how small you make the slices.) It's weird.

But, anyhow: patterns tend to mean things. As the authors note, "this observation of fractal pulsing may carry information about aspects of the star's surface, like its changing opacity." Or we might look back to a December study from the same group describing an odd recurrence of prime numbers in the same KIC 5520878 data. While they noted then that the pattern was probably artificial ("SETI null"), it may be possible for cleverer extraterrestrial civilizations to use stars as communications beacons by "boosting" them with neutrino beams, offering the needed kick to get the star oscillating.

It was the discovery of the prime numbers emanating from KIC 5520878 that got Ditto and his team thinking deeply about the two frequencies in the first place, he told me.

"Nature connects intimately prime numbers, golden ratio and vibonacci sequences," Ditto explained. "To see all this in a star 16,000 light years away struck me as truly a profound glimpse into how the universe is structured, with so many repeating themes, like notes and chord, always repeating but in an infinite number of ways and manifestations."

As for the aliens, well, it's a nice thought. But stars are capable of producing irrational numbers and fractal patterns on their own, thanks. "While I do believe that this is natural," Ditto said, "I fundamentally believe that if one were going to try to communicate by flashing variable stars with a recognizable signal I would use the golden mean as it is so fundamental to our universe and unmistakable—except maybe to a bunch of scientists looking for something else and missing it right in front of their faces."

The pattern discovered by Ditto and co. seems to be reasonably common even, but the reason why is less clear. "The fractal behavior is probably much more rare," he said, "but it seems some universal mechanism is at work bringing a significant number of stars to have pulsations near the golden mean ratio. Once we figure out that mechanism—I think we are close—we will know something significant about how these stars work and again reveal another secret of the cosmos."