Variable turbulent convection as the cause of the Blazhko effect - testing the Stothers model

The amplitude and phase modulation observed in a significant fraction of the RR Lyrae variables - the Blazhko effect - represents a longstanding enigma in stellar pulsation theory. No satisfactory explanation for the Blazhko effect has been proposed so far. In this paper we focus on the Stothers idea, in which modulation is caused by changes in the structure of the outer convective zone, caused by a quasi-periodically changing magnetic field. However, up to this date no quantitative estimates were made to investigate whether such a mechanism can be operational and whether it is capable of reproducing the light variation we observe in Blazhko variables. We address the latter problem. We use a simplified model, in which the variation of turbulent convection is introduced into the non-linear hydrodynamic models in an ad hoc way, neglecting interaction with the magnetic field. We study the light-curve variation through the modulation cycle and properties of the resulting frequency spectra. Our results are compared with Kepler observations of RR Lyr. We find that reproducing the light-curve variation, as is observed in RR Lyr, requires a huge modulation of the mixing length, of the order of +/- 50 per cent, on a relatively short time-scale of less than 40 d. Even then, we are not able to reproduce all the observed relations between modulation components present in the frequency spectrum and the relations between Fourier parameters describing the shape of the instantaneous light curves.