Astron. Astrophys. 336, 553-564 (1998)

6. Conclusions

Purely radiative Cepheid models cannot satisfactorily account for all observational data, and this has forced us to include turbulence and convection in our Cepheid models. We have adopted a simple 1D model diffusion equation for turbulent convection (TC) that can easily be incorporated into a radial stellar pulsation code. Although there is no guarantee that such a single 1D equation can satisfactorily approximate the effects of turbulence and convection it is worth exploring to what extent we can obtain agreement with observation. The model TC equations contain several dimensionless, order unity parameters that are directly related to the physical quantities of the model that need to be calibrated with the help of observational astronomical constraints.

Instead of performing CPU intensive fully nonlinear hydrodynamic computations of the pulsations, we have developed a code to perform an efficient linear nonadiabatic stability analysis of the models. This has allowed us to make an exploration of the sensitivity to the free parameters of the TC equation, both of the structure of the equilibrium Cepheid models and of their linear properties.

In agreement with other studies we find that the static Cepheid models exhibit convection primarily in their H and He partial ionization regions (PIRs), although in some parameter range a convective zone also appears in the Fe PIR. For strongly convective models the separate convective zones merge into a large one that penetrates up to 320,000 K.

The coupling of pulsation and convection modifies the linear properties of the pulsational modes, as expected. It also creates a new branch of turbulent diffusion modes that our linear stability analysis establishes to be extremely damped, fortunately for our 1D TC recipe. These additional modes thus cannot create havoc numerically or physically. This large damping is consistent with the convective timescales being very short compared to the periods of the vibrational of the excited modes which themselves are short compared to the growth-times.

Our survey shows that the stability of the fundamental and first overtone modes depends on all the TC parameters, but that it is dominated by the strengths of (1) the convective flux and (2) the eddy viscosity, and (3) on the value of the mixing length. Generally, the effects of eddy viscosity and mixing length are greater in the higher overtones.

In agreement with other much less detailed TC studies we find that reasonable parameter values exist for which IS's of the galactic Cepheid F and O1 have an acceptable range of temperatures. In this paper we have made no effort to narrow down the acceptable range of TC parameters by using the large amount of observational information. An application of the TC code to a broader sample of Cepheid models and its comparison to the large data base of Galactic, and Magellanic Cloud Cepheids is in progress, as is an extension to RR Lyrae stars.

As a final remark we note that while purely radiative models have totally failed in the modelling of beat Cepheid pulsations, the inclusion of TC quite naturally produces such behavior (Kolláth et al. 1998).

© European Southern Observatory (ESO) 1998

Online publication: July 20, 1998
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