Theory of the Fireball

varying (increasing) function of T and the variation of H - H is less
0
important; therefore, T(x) becomes steeper as T increases; but when H
gets very close to II the most rapidly varying function- in (5.8) is
0'
Ho - H, and H approaches Ho exponentially as ea for small X. The qual-
itative behavior of T(x) is sham in Fig. 1, in accord with Z. To obtain
this shape it is essential that K(T) increase much faster than T 3 .
*O
Fig. 1. Temperature distribution in' Cooling wave.
On the outside, we finally come to a point xlwhere only one optical
mean free path is outside xlo From this point we get black body emission,
4
J(xl) 3 J1 = aTl '
Using this in (5.7) we find
47
(5.9)