Theory of the Fireball

y integrating (5.8); it depends on time because K is a (rather slowly
variable) function of the pressure, and H is a (slow) function of time.
0
This justifies approximately the basic assumption (3 .l) of 2: While the
cooling wave does not preserve its shape exactly, it does so approximately.
The picture is then that at any given time t there are up to five
regions behind the shock. In Fig. 2 the temperature is plotted schemat-
ically against the Lerange coordinate r. Starting from the center,
there is first the isothermal sphere (I in Fig. 2) .
Fig. 2. Schematic temperature distribution. I, isothermal
sphere; 111, cooling wave; VI, undisturbed 'air; E,
shock front 11, IY, and V are expanding adiabat -
ically.
This may be followed by a region I1 in which the temperature distribu-
tion is essentially that established by adiabatic expansion behind the