The Theory of the Horizontal Branch and the Cosmic Abundance of Helium.

Stellar models deriving their luminosities from helium burning in the core and hydrogen burning in a shell are investigated for helium core masses of 0.425, 0.450, and 0.475 M/sub sub solar /, and for total masses ranging from 1.35 M/sub sub solar / down to the respective core masses. The investigated helium and heavy-element abundances lie within the ranges (0.25, 0.45) and (0.0001, 0.06) respectively. The readjustment of the hydrogen bunning shell on the horizontal branch is studied. The effect of a changing core mass as a function of the width of this hydrogen profile is used to extend the validity of previous zero-age-horlzontal-branch computations with steep profiles into the regime of broadened, typical horizontal-branch profiles. The color dispersion of stars along the horizontal branch is found to be about twice as sensitive to a core-mass spread than to an equal spread in total mass. Preliminary evidence for the existence of a core-mass spread along the blue horizontal branches of globular clusters is presented. A new method for determining the helium abundances of horizontal-branch stars is presented. The method is shown to be independent of the heavy-element abundance, of the mixing length, of small changes in the hydrogen composition profile,more » and independent of the main effects of evolution during the core-helium burning phase. Comparisons with available observations indicate that the helium abundance of the halo population of the Galaxy is greater than 0.30 plus or minus 0.04 by mass fraction. The helium abundances of seven open clusters average to 0.23, with an uncertainty of 0.10 to 0.20. This inverse correlation between the helium abundance and angular momentum of the populations in our Galaxy is supported by a preliminary study of helium abundances obtained from other methods. The cosmological implications of this inverse'' helium composition gradient suggest that either some helium enriching mechanism acted during the protogalactic collapse in regions of high density and low metal abundance or (and) the chemical inhomogeneities were created in the primeval fireball. (auth)« less