On the Age and Initial Helium Abandance of Extreme Population II Stars

We determine the following characteristics of metal-poor clusters as a function of assigned cluster age and initial composition: MRG = mass of a star along the giant branch, Mcore = mass in the hydrogen- exhausted core of a star at the red-giant tip, and L~0 = luminosity of a star near cluster turnoff. Using the observational fact that log LRR log L~0 + 1.4, we then determine, for every assumed initial com- position and cluster age, the additional cluster characteristics: = luminosity of a cluster RR Lyrae star, MHB = mass of a horizontal-branch star, and M~ = initial mass in the helium core of a star just reaching the horizontal branch. On further insisting that M~ = Mcore, we find that, for every choice of values for Z = heavy-element abundance and for Y = initial helium abundance, there corresponds a unique set of values for MRG, MHB, log L10, log LRR, and for cluster age I~. Choosing Z `-S-' 2 X 1O-~, as is consistent with spectroscopic results for extremely metal-poor clusters, we find that cluster characteristics must lie within the follow- ing limits: 0.0 «= V «= 0.33, 20 »= t, »= 9, 0.46 «= (MEG - MHB) «= 0.0, 0.71 «= MHB «= 0.84, 1.17 »= MRG »= 0.84, and 1.77 «= log LRR ~ 1 99, where t~ is in billions of years and M and L are in solar units. In each case, the left-hand limit follows from the requirement that Y »= 0.0. The right-hand limit is a consequence of demanding that MRG »= MHB. It is apparent that we achieve consistency with the results of recent "Big Bang" calculations (V 0.3) and with the simplest interpretation of the Hubble time (t~ < 2/3tg `--` 9 X 10° yr) by supposing that horizontal-branch stars and red-giant stars (in any given cluster) are of essentially the same mass. We feel that this consistency is not entirely fortuitous but, on the contrary, provides strong evidence for a high initial galactic helium abundance, formed during the early stages of a hot, expanding universe described by the simplest of cosmologies