Helium Content of M 92 deduced from the Subgiant Luminosity Function

Abstract

HARTWICK¹ has used the method of semi-empirical evolution due to Sandage², together with homologously transformed stellar models of Iben and Faulkner³, to deduce that the helium content of M 92 is probably close to Y=0.35. This result was obtained by plotting the fuel consumed (expressed in terms of mass-fraction) against the bolometric magnitude, and comparing this theoretical quantity with the equivalent quantity deduced by the semi-empirical method. Good agreement was obtained for Y=0.35, but not for Y=0.10 or 0.01. The disagreement in the last two cases was particularly striking in the regions just above the turn-off point. As Hartwick noted, this was in part a reflexion of the fact, first pointed out by Simoda and Kimura⁴, that the slope of the luminosity function ϕ in this region is extremely sensitive to the helium content. Indeed, this sensitivity was dramatically exhibited when Hartwick, on “unevolving” the M 92 data, found that the initial luminosity function would be required to decrease quite sharply to fainter magnitudes for Y=0.10 and 0.01, whereas it increased slightly for Y=0.35. The former behaviour is most unpalatable, but the latter is what one might expect on other statistical grounds⁵.