Nonlinear calculations for bump Cepheids

Abstract

Using the von Sengbusch-Stellingwerf relaxation method, hydrodynamic calculations have been made to find strictly periodic solutions for the fundamental mode pulsations of 7 M_⊙ models. These models have a helium enrichment in the surface convection zones up to Y = 0.78. From the linear theory period ratio π₂/π₀ and the Simon and Schmidt resonance hypothesis, the observed Hertzsprung progression of light and velocity curve bump phase with period should result. These surface helium enhanced models show the proper nonlinear bump phase behavior without resort to any mass loss before or during the blue loop phases of yellow giant evolution. At 6000 K and the luminosity of 4744 L_⊙ given by evolution theory for 7 M_⊙ (that is, at a fundamental mode period of 8.5 day), the velocity curve bump is well after the maximum expansion velocity. At 5400 K and the same luminosity (period of 12.5 day), the bump on the velocity curve occurs well before maximum expansion velocity time. The Christyechoes appear to be exhibited in the latter case but not in the former. The echo interpretation may not be appropriate for these masses which are larger than the anomalous masses used by Christy (1975); Stobie (1969a, 1969b); and Adams (1978). Resonance of the fundamental and second overtone modes should not necessarily show echoes of surface disturbances from the center. The conclusion is that helium enrichment in the surface convection zones can adequately explain observations of bump Cepheids at evolution theory masses.