On the Interactive-Beating-Modes Model: Generation of Asymmetric Multiplet Structures and Explanation of the Blazhko Effect

Abstract

This paper considers a nonlinear coupling between a radial and a nonradial mode of nearly the same frequency. The results may be of general interest, but in particular have application to the "beating-modes model" of the Blazhko effect which was recently shown to accurately reproduce the light curve of RR Lyr. For weak coupling, the two modes do not phase-lock and they retain separate frequencies, but the coupling nevertheless has important consequences. Upon increasing the coupling strength from zero, an additional side-peak emerges in the spectrum forming an asymmetric triplet centered on the fundamental. As the coupling is further increased, the amplitude of this side-peak increases and the three peaks are also pulled towards each other, decreasing the Blazhko frequency. Beyond a critical coupling strength, phase-locking occurs between the modes. With appropriate choice of coupling strength, this "interactive beating-modes model" can match the side-peak amplitude ratio of any star. The effects of nonlinear damping are also explored and found to generate additional side-peaks of odd order. Consistent with this, the odd side-peaks are found to be favored in V808 Cyg. It is also shown that the Blazhko effect generates a fluctuating "environment" that can have a modulatory effect on other excited modes of the star. An example is found in V808 Cyg where the modulation is at double the Blazhko frequency. An explanation is found for this mysterious doubling, providing additional evidence in favor of the model.