2014ApJ...783L..15B

The waveform for Blazhko stars can be substantially different during the ascending and descending parts of the Blazhko cycle. A hybrid model, consisting of two component oscillators of the same frequency, is proposed as a means to fit the data over the entire cycle. One component exhibits a sawtooth-like velocity waveform while the other is nearly sinusoidal. One method of generating such a hybrid is presented: a nonlinear model is developed for the first overtone mode, which, if excited to large amplitude, is found to drop strongly in frequency and become highly non-sinusoidal. If the frequency drops sufficiently to become equal to the fundamental frequency, the two can become phase locked and form the desired hybrid. A relationship is assumed between the hybrid mode velocity and the observed light curve, which is approximated as a power series. An accurate fit of the hybrid model is made to actual Kepler data for RR Lyr. The sinusoidal component may tend to stabilize the period of the hybrid which is found in real Blazhko data to be extremely stable. It is proposed that the variations in amplitude and phase might result from a nonlinear interaction with a third mode, possibly a nonradial mode at 3/2 the fundamental frequency. The hybrid model also applies to non-Blazhko RRab stars and provides an explanation for the light curve bump. A method to estimate the surface gravity is also proposed.