Theory of the Fireball

smaller than the first term, i.e , when the pressure is sufficiently
high. As the pressure decreases below about 10 bars, the blocking layer
"opens up" and ceases to block t'ne flow of radiation.
In the very beginning, when t'ne cooling wave just starts, t'ne top
temperature of the cooling wave, is close to the radiating tempera-
TO'
ture T "hen (5.18) becomes
1'
"1 = - (EX 1
If we use (5.12) for J, assume d log T/d log R and R to be constant, wd
use (3.14), tinen
For further discussion, see Sec. 5f.
As T increases, u decreases from (5.23) via (5.21) to (5.19). Af'ter
the cooling wave has penetrated to the isothermal sphere, u is apt to
increase again because T in the denominator of (5.19) will decrease due
to adiabatic expansion of the isothermal sphere. Thus the velocity u is
apt to be a minimwn vhen the cooling wave has just reached the isothermal
sphere
C
The variation of u with time is not very great. Likewise, the shape
of the cooling wave changes only slowly with time. Tne shape is obtained
53