Golden Ratio Defines New Class Of Variable Star
Using data from the Kepler Space Telescope (KST), and specially devised ‘model-independent nonlinear analysis’ techniques, a team from the University of Hawaii have discovered a new class of variable star that has unique fractal (strange) behaviour never-before-seen outside a laboratory environment.
Typically, variable stars (Cepheid/RR Lyrae) pulsate at a single frequency. However, light curves of the new class have been found to exhibit fluctuations at multiple frequencies approximate to the golden ratio, φ (where φ ≈ 1.62): ‘As the most irrational number, the golden ratio can have significant dynamical consequences,’ describe the team; ‘for example, by the KAM theorem dynamics with two frequencies in the golden ratio maximally resist perturbations. Furthermore, nonlinear systems driven by two incommensurate frequencies, forming an irrational ratio, and especially the golden ratio, exhibit distinctive dynamics that exist between order and chaos.’
‘A nonlinear dynamical system driven by an irrational ratio of frequencies generically exhibits a strange but nonchaotic attractor’, which has been found to exist in the RRc Lyrae star KIC 5520878, making it a model proto-type of the new class.
The team further expanded their non-linear technique to an additional five RR Lyrae KST objects: three exhibiting irrational, near golden ratio, pulsations and two with a rational ratio of 3/2; by comparing the two different classes, researchers found that only ‘golden stars’ displayed strange nonchaotic behaviour.
The team predict that the new discovery will help refine the classification of variable stars. A host of potential ‘golden’ objects have been isolated by the OGLE and ASAS sky surveys, which should help realise this prediction as well as updating current interior models: ‘The strange nonchaotic signatures of variable stars like KIC 5520878 may elucidate phenomena like the Eddington valve mechanism thought to underlie their pulsations: variations in the opacity of the star might quasiperiodically modulate the normal hydrostatic balance between pressure outward and gravity inward, thereby generating light curves somewhere between order and chaos that the best models will need to reproduce’, conclude researchers. ‘The pulsating star KIC 5520878 may be the first strange nonchaotic dynamical system observed in the wild.’
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