An Observational Test for Helium Diffusion in Red Giant Stars: Theoretical Considerations.

Mathematics – Logic

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Long slit spectra of the Galactic planetary nebulae (PNs) NGC 6210, 6543, 6720, 6826, 6891, and IC 4593 and Abell 78, are obtained to examine the helium abundances in the PN halos. The halos are believed to be the outer envelopes of the PN central star precursors, which are expelled during ascent of the AGB. As the PN phase represents a late stage of stellar evolution for stars 1 < M/Msun < 8, the determination of the halo He/H ratio, and therefore evidence of He diffusion, is subject to several uncertainties. Stellar evolution models incorporating He diffusion during the main sequence phase are limited to initial masses M < 0.8\Ms\ and metallicities Z ~ 0.001. The effect of He diffusion during the main sequence is almost completely removed during the first dredge-up episode on the first giant branch. However, the amount of mixing is mainly dependent upon the mixing length parameter and stellar rotation. No models with He diffusion have been evolved from the main sequence to beyond the first giant branch where subsequent dredge-up episodes occur. PN halo abundances have been examined for NGC 6543 and NGC 6826 by Middlemass, Clegg, & Walsh (1989, MNRAS, 239, 1) and Balick et al. (1994, ApJ, in press). The first group find the halos to be deficient in He by ~ 50% with respect to the core. The second group claim there is no variation in He abundance along the slit in their long slit spectra. The presence of He diffusion in stars means that halo globular clusters will be younger by 20--25% than the ~ 16--17 Gyr currently accepted. At present, the halo globular clusters are older than the cosmological age of the Universe T < 13 Gyr derived from values of the Hubble constant > 75 km s(-1) Mpc(-1) .

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