Surprising behavior of stars

Astronomers have found a fractal behavior, in terms of time, in a pulsating white-blue star. The study, conducted by the group of John Lindner from University of Hawaii, suggests that the object, called KIC 5520878, could be the first example of what chaos theorists call “strange attractor but not chaotic.” The results are published in Physical Review Letters.

False color image of the RR Lyrae variable KIC 5520878.


Credit: Michael Hippke et al.

Thanks to a series of observations made with the Kepler satellite, a group of researchers at the University of Hawaii found that the oscillations of a star are consistent with the golden ratio, an irrational number (1.6180339887 …), and follow a pattern fractal. The protagonist of this work, published in Physical Review Letters, is a variable RR Lyrae, i.e. a pulsating star, named with the initials KIC 5520878, which has been observed for several years and which according to the authors, it is a very interesting object to take under the eye.
Astronomers have monitored the pulse emitted from KIC 5520878 over a period of time that lasted four years, and the data were recorded with 30-minute intervals. The results indicate that two frequencies of pulsation occurs on cycles of 4.05 and 6.41 hours whose ratio (1.58) is close to 1,618, which is the famous golden ratio, also known as the golden ratio or constant that Fidia indicates the relationship between two unequal lengths, typical of the visual arts and mathematics.
Intrigued, scientists have gone further and found that the frequencies of pulsation follow a trend of fractal type: in other words, separating the oscillations in the individual components you notice additional frequencies, the weakest, whose graph appears similar to the pictures – so as described by the authors – that show the steep coastal lines, regardless if you show up close or from a distance: they are a classic example of the British coast.


Credit: John F. Lindner et al. 2015

Then performing an analysis of the peaks that are greater than a certain threshold, the researchers have derived a power law which is a characteristic signal of fractal behavior. The discovery of this fractal behavior of the pulsations might contain important information about some aspects of the stellar surface, such as the change of opacity.
Of course, the difference is that while the behavior of the traditional fractals systems is visually observed in spatial terms, but here is seen as a time factor. In their article, the researchers claim, however, that their results constitute the first example of “strange attractor but not chaotic” observed in nature, that is a physical system that shows a fractal structure but does not possess those properties to other known chaotic systems, such as the weather.
Finally, the scientists analyzed five other stars buttons to see if there was a similar pattern instead finding anything: three cases have close relations to the golden number and fractal properties while in the other two cases are not noticed particular characteristics. What is not yet clear, at this point, is whether the behavior of the stars showing a fractal structure is something that happens for a reason, and that could perhaps offer new clues about stellar physics, or if it is otherwise of pure coincidence.

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