Thermal pulses in helium shell-burning stars. II.

The shell-burning evolution of pure-helium stars in the mass range 0.5-1.0 . is studied, both including and neglecting neutrino energy losses due to the universal Fermi interaction. With neutrino energy losses included, stars of mass 0.5-0.8 undergo a single thermal pulse before becoming white dwarfs, while more massive stars have stable helium-burning shells. In the absence of neutrino energy losses, carbon burning occurs in the core for 0.8 . No thermal instability in the helium shell precedes the onset of carbon burning. At 0.7 carbon fails to ignite and a thermal pulse occurs in the helium shell, while at 0.5 neither carbon burning nor thermal instability is found. The significance of these results for the central stars of planetary nebulae is discussed, and a possible explanation is given for carbon features in the spectra of the nuclei of advanced planetary nebulae, and of some white dwarfs. A possible relationship with the hydrogendeficient carbon stars is also discussed. Subject headings: hydrogen-deficient stars - instabilities - interiors, stellar - planetary nebulae