Age of Messier 3.

126, 326, 1957) studied the energy expenditure of stars in M3 using semiempirical evolutionary tracks. He found that if the absolute magnitude of the RR Lyrae stars is 0.0, for a cluster of 5.1 x 10~ years, stars emitted energy equivalent to conversion of their entire mass from hydrogen to helium. Woolf (Astrophys. J. 135, 644, 1962) pointed out the discrepancy between this result and estimated large ages using stellar models by Hoyle (Monthly Notices Roy. Astron. Soc. 119, 124, 1959). The study by semiempirical tracks has been repeated using Hoyle's stellar models as a basis. There are two modifying effects on the previous conclusion. The semiempirical study did not allow for evolved stars being slightly more massive than those at the turnoff point. The age for complete fuel consumption becomes 6.8 X 10~ years. Sandage's study used theoretical early evolution tracks giving a 0.94-mag. rise from main sequence to turnoff point, while Hoyle's tracks give a rise of 1.45 mag. This affects the result through the derivation of the initial luminosity function. The maximum permissible age rises from 6.8 X 10~ to 10.5 X 10~ years. For comparison, Hoyle's models give the age as 12.0x 10~ years using Mv RR Lyrae stars=0, m2= 15.67 and for the turnoff point mc + 18.79. This discrepancy is still serious because the age from semiempirical tracks is a maximum one, not allowing for incomplete combustion, rapid phases at high luminosity, or a possible 20% mass loss (Oort, J. H., and van Herk, G. Bull. Astron. Inst. Neth. 14, 299, 1959; Woolf, N. J. Publs. Astron. Soc. Pacific 73, 339, 1961). However, Hoyle's models still have uncertainties in the nuclear reactions and may give ages 30% too large (Hoyle, F. Report to IAU Commission 35). The age then, 8.4x 10~ years, would be consistent with the semiempirical tracks. Uncertainties in the absolute magnitude of the RR Lyrae stars are large. The latest value is +0.25 (Arp, H. C. Astrophys. J. to be published), and there are also uncertainties of helium abundance that may reduce these ages. There is no good evidence that M3 is more than 1010 years old.