Modal selection in pulsating stars
Abstract
Initialvalue and periodic nonlinear pulsation integrations are carried out for a series of doublemode Cepheid models (P1/P0 equals about + 0.7) in the vicinity of the resonance omega (1) + omega (0) omega (3). None of the models tested shows persistent doublemode 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. The hydrodynamic results also agree at least partially with Stellingwerf's in that a region in the red where the models approach (though never reach) simultaneous instability of both limit cycles is found. Analysis of resonant effects on modal selection in the calculations leads to the conclusion that models lying between the resonances omega (1) + omega (0) = omega (3) and P2/P0 = 0.5 may yet be viable candidates for doublemode pulsation.
 Publication:

The Astrophysical Journal
 Pub Date:
 April 1980
 DOI:
 10.1086/157899
 Bibcode:
 1980ApJ...237..550S
 Keywords:

 Astrophysics;
 Cepheid Variables;
 Stellar Models;
 Periodic Variations;
 Time Dependence;
 Astrophysics