Resonant excitation of nonradial modes in RR Lyr stars

We study a nonlinear development of radial pulsation instability to a reson ant excitation of nonradial modes. Our theory covers the cases of axisymmet ric (m = 0) modes as well as (m, -m) pairs. Adopting a simplified treatment of the radial and nonradial mode coupling we find that the asymptotic stat e is a pulsation with constant amplitudes and we evaluate the relative ampl itude of the nonradial component. Observable consequence of the m = 0 mode excitation is a small period chang e and a more significant amplitude change, especially in the case of a dipo le mode (l = 1). Such a mode has a fairly large excitation probability. Significant amplitude and phase modulation is predicted in the case of exci tation of a m = +/-1 pair. We suggest that this may explain Blazhko-type mo dulation in RR Lyr stars. If this model is correct, the modulation period i s determined by the rotation rate and the Brunt-Vaisala frequency in the de epest part of the radiative interior.