On the Blazhko Effect in RR Lyrae Stars

TL;DR

This paper investigates the Blazhko effect in RR Lyrae stars, demonstrating through amplitude equations that nonlinear resonant interactions can produce irregular, chaotic amplitude modulations similar to observations.

Contribution

It introduces a nonlinear amplitude equation model showing how resonant mode interactions lead to chaotic amplitude modulations in RR Lyrae stars.

Findings

Resonant interactions cause amplitude modulation and chaos.

Modulations can be irregular and chaotic, matching observations.

The model explains the physical origin of the Blazhko effect.

Abstract

The Blazhko effect is a long term, generally irregular modulation of the light curves that occurs in a sizeable number of RR Lyrae stars. The physical origin of the effect has been a puzzle ever since its discovery over a hundred years ago. We build here upon the recent observational and theoretical work of Szabo et al. on RRab stars who found with hydrodynamical simulations that the fundamental pulsation mode can get destabilized by a 9:2 resonant interaction with the 9th overtone. Alternating pulsation cycles arise, although these remain periodic, i.e. not modulated as in the observations. Here we use the amplitude equation formalism to study this nonlinear, resonant interaction between the two modes. We show that not only does the fundamental pulsation mode break up into a period two cycle through the nonlinear, resonant interaction with the overtone, but that the amplitudes are modulated, and that in a broad range of parameters the modulations are irregular as in the observations. This irregular behavior is in fact chaotic and arises from a strange attractor in the dynamics.