216 ANlSrUAL REPORT SMITHSONIAN INSTITUTION, 1955 



tions it can be estimated that stars which have nearly exhausted their 

 central store of hydrogen yet remain dwarfs should be about 0.5 mag 

 (or by 60 percent) brighter than "normal" dwarfs of equal mass. 

 If we take this into account, it is estimated that the above-mentioned 

 "ultimate" dwarfs in globular clusters, about 10 times brighter than 

 our sun, should have a mass of 1.7 O. The total duration of the 

 dwarf stage at this mass would be around 4,000 million years. 



The numerical value of tliis estimate may be considerably in error; 

 yet, qualitatively there is little doubt about the soundness of the inter- 

 pretation which ascribes to the stellar population of the globular 

 clusters the same age as that of the galaxy itself. By essentially the 

 same method, but on the basis of more recent observational data, 

 Sandage (44) fuids an age of about 5,000 million years for the globular 

 clusters. We may take the average of the two estimates, 4.5 thousand 

 million years, as the probable age of the globular clusters, as well as 

 of our galaxy. 



Among the many data concordantly pointing to an age of the stellar 

 universe of a few thousand million years, there is one which seemingly 

 strikes a note of discord — some uneasiness may be felt about the high 

 frequency of white dwarfs. If tliey are remnants of supernovae, 

 which appear only once in a few hundred years, they would have 

 required perhaps 100,000 million years to accumulate. However, at 

 the beginnings of the galaxy, at the time when Population II was 

 formed, star formation must have proceeded at a faster rate than now. 

 The frequency of supernovae, directly related to the frequency of for- 

 mation of massive stars, may then have been much higher (26) . Fur- 

 ther, the possibility of white dwarfs being formed in another way 

 cannot be ruled out. Doubts as to the time scale cannot be maintained 

 on such slender evidence. 



Besides, a direct estimate of the age of individual white dwarfs can 

 also be made, and this turns out to be in agreement with the other 

 estimates. The energy source of white dwarfs can consist only in 

 the thermal agitation of atomic nuclei (45) or upon explicit heat — 

 like a kettle of hot water gradually cooling. The time of cooling, 

 until the present state is reached, or the age of a white dwarf can be 

 easily calculated when A, the mean atomic weight of this material, is 

 known. Considering that all hydrogen must previously have been 

 converted into helium, and that, before the "degenerate" stage of a 

 white dwarf is reached, triple collisions at temperatures of a few hun- 

 dred million degrees will convert all the helium into carbon, and then 

 into lighter metals such as magnesium, we find that J. =24 can be 

 assumed, and Mestel's highest values for the ages of white dwarfs 

 become equal to 4,000 million years. This may be near the age of 

 Population II and the galaxy, in thrilling agreement with other 

 estimates (27,28). 



