Pulsational study of BL Herculis models. I - Radial velocities

The linear and nonlinear pulsational behavior of nine sequences of BL Herculis models is studied, and their radial velocity curves are discussed in detail. The pulsations of these stars, in analogy to the classical Cepheids, are strongly affected by internal resonances, most importantly the 2:1 resonance with the second overtone. This latter coupling causes a characteristic systematic progression of the Fourier phases and amplitude ratios as the period ratio P2/P0 is varied. In contrast to Cepheids, the strength of the resonance depends very sensitively on the stellar mass and luminosity, and the morphology of the Fourier progression changes significantly when M or L are varied. In most of the model sequences, narrow windows are found in which the pulsations exhibit periodic alternations of deep and shallow minima in the radial velocity and light curves. This behavior occurs for periods somewhere in the range from 2.0 to 2.6 d, depending on the sequence. It is caused by the 3:2 resonance between the fundamental mode and the first overtone. In the two most nonadiabatic sequences the same resonance causes windows of chaotic oscillations.