Modal Selection In Pulsating Stars

Initial-value and periodic nonlinear pulsation integrations are carried out for a series of doublemode Cepheid models (PdPo 0.7) in the vicinity of the resonance WI + Wo = W3. None of the models tested shows persistent double-mode behavior. A new, semiquantitative description of modal selection, based upon the iterative theory of Simon, is introduced to analyze the nonlinear results. In the simplest version of this description, modal section categories emerge which are identical to those of Stellingwerf. Our hydrodynamic results also agree at least partially with Stellingwerf's in that we find a region in the red where the models approach (though never reach) simultaneous instability of both limit cycles. Analysis of resonant effects on modal selection in our calculations leads to the conclusion that models lying between the resonances WI + Wo = W3 and P2/Po = 0.5 may yet be viable candidates for double-mode pulsation. Subject headings: stars: Cepheids stars: pulsations