Theory of the Fireball

G. We& Cool-ing Wave
In Stage C I1 tne cooling wave dominates the radiation (Sec. 5d) .
In Stage C I the cooling mme also exists, because the energy of the
radiztj-on must be provided. Hovever, the speed at wnich the trave proceeds
inward is nov governed by tne adiabatic expansion, (3 .LO) a In order to
obtain the correct flux of radiation J
1
at the radiating surface, we
must therefore use (5.18) in reverse: Tine temperature T at the inner
0
edge of Cne cooling 77ave (point B in Fig. 2) wil regulate itself in such
a vay that (5*18) is satisfied, with u given by (5.lJr5). Using (5.461,
we thus get the condition
or solving for To and inserting numbers:
13
y' - 0.9
P -3/2 Ti4 (5 059)
PlTeglecting Jo, we find that Ho increases rapidly as p decreases.
We may insert (5.31!-); then the right nand side varies as p
-5/2 - t3*
Thus the cooling wave starts very weak and then rapidly increases in
strengtn. Its "head" (point B in Fig.' 2) is at first close to its foot
(point C). As time goes on, it moves more deeply into t'ne hot material,
eating up region I1 of Fig. 2. The energy which is made available for
68