Blazhko RR Lyrae light curves as modulated signals

Abstract

We present an analytical formalism for the description of Blazhko RR Lyrae light curves. In this formalism the amplitude and frequency modulations are treated in a manner similar to the theory of electronic signal transmission. We consider monoperiodic RR Lyrae light curves to be carrier waves, and modulate their amplitude (AM), frequency (FM) and phase (PM); as a general case we discuss simultaneous AM and FM. The main advantages of this method are the following: (i) the mathematical formalism naturally explains numerous light-curve characteristics found in the Blazhko RR Lyrae stars such as mean brightness variations, complicated envelope curves and non-sinusoidal frequency variations; (ii) our elucidation also explains the properties of the Fourier spectra such as apparent higher order multiplets, amplitude distribution of the sidepeaks, the appearance of the modulation frequency itself and its harmonics. In addition, compared to the traditional methods, our light-curve solutions reduce the number of necessary parameters. This formalism can be applied to any type of modulated light curves, not just to Blazhko RR Lyrae star light curves.