Wojciech A. Dziembowski

arXiv2003

Nonlinearity of nonradial modes in evolved stars

We show that in evolved stars, even at relatively low surface amplitudes, nonradial modes become strongly nonlinear in the hydrogen shell source, where the Brunt-Vaisala frequency has its absolute maximum. The measure of nonlinearity is the product of horizontal displacement times the radial wavenumber. It becomes large already in evolved delta-Scuti stars. This nonlinearity presents a major problem for interpretations of amplitude modulation in RR Lyrae stars in terms of nonradial mode excitation.

astro-ph↗

arXiv2001

Resonant Excitation of Nonradial Modes in RR Lyr Stars

We study a nonlinear development of radial pulsation instability to a resonant excitation of nonradial modes. Our theory covers the cases of axisymmetric (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 state is a pulsation with constant amplitudes and we evaluate the relative amplitude of the nonradial component. Observable consequence of the m=0 mode excitation is a small period change and a more significant amplitude change, especially in the case of a dipole mode (l=1). Such a mode has a fairly large excitation probability. Significant amplitude and phase modulation is predicted in the case of excitation of a m=1,-1 pair. We suggest that this may explain Blazhko-type modulation in RR Lyr stars. If this model is correct, the modulation period is determined by the rotation rate and the Brunt-Vaisala frequency in the deepest part of the radiative interior.

astro-ph↗