222 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1956 



below the solar surface. The turbulent layers may involve as much 

 as the outer 10 percent of the solar radius. 



We are now in a position to understand the darkness of the spot 

 relative to the surrounding photosphere. The answer is extremely 

 simple. In a region where magnetism has not inhibited convection, 

 the outer layers are hotter than they would be otherwise. They are, 

 consequently, more luminous than the spots, where convection does 

 not occur. In the region immediately surrounding the spots, the 

 convective layer must rise higher and indeed may even penetrate the 

 photosphere, since rising currents of hot gas must carry outward the 

 extra energy that the cooler spot cannot transport from the solar 

 interior by radiative transfer. 



One may speculate what the physical state of the sun would be if 

 a magnetic field strong enough to inhibit convection through the 

 entire solar atmosphere should suddenly come into existence. In the 

 absence of convection, energy transport would have to depend on 

 the less efficient radiative processes. The temperature of the photo- 

 spheric layer of the sun would cool by at least 2,000 degrees, to a 

 value approximating that of a sunspot. Indeed, under such condi- 

 tions, we could describe the solar surface as consisting of a single 

 spot. With the effective solar temperature reduced to about two- 

 thirds of its normal value, the total amount of energy radiated, which 

 varies as the fourth power of the temperature, would decline to about 

 20 percent of its present value. 



We have previously noted that radiation takes some 50,000,000 years 

 to leak out from the core. By the same argument, a change in the 

 sun's external layers could not have any immediate effect on the solar 

 interior, which would continue to generate energy at its present rate. 

 The accumulated radiation inside the sun would cause it to swell 

 gradually until, some tens of millions of years hence, the increased 

 surface area could compensate for the lowered radiation flux. Even 

 a small expansion, however, would cause marked changes in the rate 

 of energy production and we cannot foretell whether equilibrium will 

 occur or not. 



The greatest immediate effect would occur in the sun's outer layers, 

 especially those now in convective equilibrium. Since these layers 

 contain only a relatively small amount of heat we should expect their 

 configuration to change in tens of years rather than in millions. The 

 solar atmosphere would expand and alter the temperature distribution 

 simultaneously to values consistent with the sun's present total output 

 of energy. Although such a model is extreme for the sun, it might 

 apply with some changes to certain types of stars, notably the long- 

 period and Cepheid variables. Possibly no static state will exist and 

 the distended atmosphere will oscillate between maximum and mini- 



