Dynamical systems – such as pendulums, the weather and variable stars – tend to fall into circumscribed patterns of behavior that are a subset of all the ways they could possibly behave.
In 1912, Henrietta Leavitt discovered that the frequency at which variable stars pulsate corresponds to their intrinsic brightness, a feature that later allowed them to be used as “Standard candles” for gauging cosmic distances.
The conventional explanation for the stars’ behavior comes from Sir Arthur Eddington, who proposed in the 1930s that variable stars grow and shrink in a continual cycle: First, a star shines brightly, but as it gradually shrinks and heats up, its outer layer turns opaque, dimming the starlight.
In more than 100 of these variable stars – including those, like KIC 5520878, belonging to a subclass called “RRc” – the ratios defining the duration of one frequency relative to the other inexplicably fell between 1.58 and 1.64.
Upon seeing the number last summer, Ditto instantly suspected that KIC 5520878 and stars like it might be exhibiting strange nonchaotic dynamics.
The discovery, reported in February in Physical Review Letters, has some astronomers turning to arcane mathematics papers for new clues about the inner workings of variable stars.
Adding to the mystery are the hundreds of other variable stars that are also driven through their attractor by two frequencies whose ratio is near the golden mean, though not always near enough to give rise to such special dynamical behavior.