306 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1963 



under its own gravity and has reached a stage where it fragments 

 into a number of smaller masses each of wliich then condenses further 

 into an indi^ddual star. The individual clouds, or proto-stars, will 

 go on contracting and in doing so they will convert their gravitational 

 potential energy into heat which then escapes as radiation. In the 

 last century this process was put forward by Helmholtz and Lord 

 Kelvin as the main source of stellar energy, but it is easily shown that 

 the Sun could not have lasted long enough on contraction alone to 

 satisfy geological evidence as to the age of the Earth, which is now 

 believed to be about 5,000 million years, and the discrepancy led to 

 long and sometimes acrimonious debates in the British Association 

 and elsewhere between Kelvin and the geologists, led by T. H. Huxley. 

 However, as the contraction of the proto-stars goes on, their internal 

 temperature and pressure will steadily increase until finally the con- 

 ditions at the center have become sufficiently extreme for the hydro- 

 gen to undergo a nuclear transmutation uito helium; the energy 

 produced by the reaction will be carried outward by processes of radi- 

 ative and convective transfer until it reaches the surface, from which 

 it will then bo radiated away into space. In order to reach a steady 

 state, the whole star must adjust itself until two conditions are ful- 

 filled: first, the energy radiated from the surface (or in other words 

 the star's total luminosity) must exactly balance the energy liberated 

 by nuclear reactions in the deep interior; and second, the pressure in 

 every layer of the star must exactly balance the weight of the layers 

 lying on top of it. When these conditions are worked out in detail, 

 it turns out that the whole structure of the star, and notably its bright- 

 ness and its size, are completely fixed by its mass. This is the basis 

 of the famous mass-luminosity relation, which says that the light 

 output of a star increases rapidly with the mass, about as the cube, so 

 that a star with twice the mass of the Sun should have about eight 

 times its intrinsic brightness. 



Unfortmiately we can only measure the masses of a few stars in 

 nearby double systems, and there is no general method of finding the 

 masses of stars in clusters. However, there is another relationship 

 that comes out of these considerations of a star's internal equilibrium : 

 the brightness is related to the surface temperature, varying as about 

 the 12th power of the latter, so that our star with twice the mass of the 

 Sun and eight times its brightness should have a surface temperature 

 of about 1.2 times that of the Sim or 7,000°, as compared with the 

 Sun's surface temperature of about 6,000°. 



Now we can estimate the surface temperatures of stars in two differ- 

 ent ways. Wlien you heat up a poker, then at fairly low temperatures 

 the radiation from it is concentrated in the infrared part of the spec- 

 trum. As the temperature is raised, the energy distribution shifts 

 its maximum from the red to the yellow and then to the blue and 



