Nonlinear Cepheid Pulsation Calculations and Comparison with Linear Theory

Abstract

Linear and nonlinear pulsation calculations have been carried out on a number of purely radiative classical Cepheid models, using identical input physics and models as nearly identical as is feasible. The models chosen for the comparison all had the composition X = 0.602, Z = 0.044, but some of the linearized calculations were performed using different compositions. Two main mass-luminosity relations have been assumed, one based on evolution calculations with conventional masses, the other with masses reduced by a factor of about 2 for given luminosity. The linear blue instability edges are discussed, and it is concluded that uncertainties in both theory and observation preclude a clear distinction between the above two mass-luminosity relations on the basis of the blue edges alone, although the larger ("evolutionary") masses are very weakly favored. Comparison of the two sets of calculations show that, overall, the nonlinear results are consistent with the linear results. In particular, no well-established cases of "hard" self-excited oscillations have been found. The nonlinear calculations suggest that some models which according to the linear theory are simultaneously unstable in both F and 1 H modes, can attain an apparently stable, finite limiting amplitude in either mode, depending on initial conditions (e.g., direction of evolution). The portion of the instability strip where this kind of behavior is expected to be most likely, is found to correspond, for the adopted composition, to periods around 6-11 days (including both F and 1 H periods) if Cepheids have the "evolutionary" masses, and around 2-4 days if their masses are half as large. Stars lying well above (below) these period ranges in the instability strip are expected to be predominantly F(1H) pulsators. It is likely that these period ranges would occur at shorter periods with a smaller helium abundance. For example, for Y = 0.20 it is estimated that the above period range would be around 2.5-5 days for the "evolutionary" masses. Finally, it is concluded that the large-amplitude mode behavior is predictable from linear theory in certain cases, but not in all. Subject headings: Cepheids and W Virginis stars - interiors, stellar - pulsation