98 
RADIATIVE EQUILIBRIUM 
is no appreciable gain or loss of heat by conduction or radiation; it there 
fore expands without gain or loss of heat, i.e. adiabatically. For a perfect 
gas the relation between pressure and density in adiabatic expansion is 
P = Kp y (69-1), 
where y is the ratio of the specific heat at constant pressure to the specific 
heat at constant volume (§ 28). Since the different levels are continuously 
connected by ascending and descending currents the equilibrium condition 
must be such that (69-1) holds throughout the interior. The hypothesis 
that loss of heat by radiation is negligible must evidently break down near 
the surface, so that the equation could not be exact in the extreme outer 
layers. 
Since (69T) is the relation discussed in Chapter iv the solution for a 
perfect gas in convective equilibrium is given by the formulae and tables 
there explained. The value of y for the stellar material must be estimated 
or guessed; but the range of uncertainty from this cause is not very great. 
It is impossible for y to exceed the value § which corresponds to a mon 
atomic gas; and it can be shown that if y is less than f the distribution is 
unstable (see § 104). Hence the solution is limited to values of y between 
| and f or to values of n between 1-5 and 3. 
We shall not enter further into the historic problem of convective 
equilibrium since modern researches show that the hypothesis is untenable. 
In stellar conditions the main process of transfer of heat is by radiation 
and other modes of transfer may be neglected. 
We may remark that transfer by convection stands on a different 
footing from radiation and conduction. Radiation and conduction must 
always occur in a mass at non-uniform temperature, although their effects 
may be negligibly small. But convection need not occur at all. It will 
only be present if the conditions are such as to generate and maintain 
circulating currents. 70 
70. Since the density of radiation is proportional to T 4 its importance 
is enormously enhanced at the high temperatures in the stellar interior, 
and it is not surprising to find that it ousts the other vehicles of energy. 
But whilst great intensity of radiation strengthens its control over the 
temperature distribution, it is not essential. I think that an isolated mass 
of gas at quite low temperature* would take up radiative rather than 
convective equilibrium. 
Consider a gas stratified in radiative equilibrium. As explained in § 23 
radiation behaves as though it had a ratio of specific heats y = f and 
accordingly P and T are related by 
P oc T\ 
* But not so low that conduction becomes comparable with radiation.