The evolution of an isolated carbon-oxygen degenerate dwarf which has a surface layer initially containing hydrogen and helium and is of mass 0.6 M_sun; is followed from the planetary nebula nucleus stage at a luminosity of 5×10³L_sun; until luminosity drops to 10⁻⁵L_sun;. Wind mass loss and accretion from the interstellar medium are neglected. Shortly after the model reaches a maximum surface temperature of about 1.5×10⁵K, CN cycle reactions cease abruptly to contribute dominantly to surface luminosity, which drops to below 100 L_sun;. However, hydrogen-burning reactions continue to take place. The effect of diffusion induced by gravity forces and by composition gradients on the contribution of hydrogen burning to surface luminosity is studied. The total amount of hydrogen left in surface layers after 10¹⁰yr of cooling is about 1.4×10⁻⁴M_sun;, compared with a value of about 2.1×10⁻⁴M_sun; obtaining at the point of maximum surface temperature. Thus, diffusion and nuclear burning cannot reduce the mass of hydrogen in surface layers to below 10⁻⁷M_sun;, as demanded by a current interpretation of the light variations of ZZ Ceti stars.
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I. et al. (1985) studied this question.