Theory of the Fireball

adiation is essentially the difference H : Tne material drops
suddenly in temperature from T to T as the cooling wave sweeps over
0 1
0 -
it, and the energy difference is set free for radiation.
The term J depends on H on p, and on the temperature gradient
0 0'
in the region inside the cooling wave (region 11). If this region is
adiabatic, the temperature gradient can be calculated from (3.15). Since
J1 is also related to the temperature gradient in the adiabatic region
IV, the ratio J /J tends to unity as Ho -.)
0 1
H1.
Thus the left hand side
of (7.39) will have a certain minimwn value. Tnis seems to indicate
that there is no cooling wave at all until the pressure has fallen below
a certain critical value. We have not investigated thi's point in detail.
It is possible that it is simply related to tne break-away of the lumi-
nous front from the shock wave, i. e., the beginning of Stage C .
Equation (5.99) describes the weak cooling wave in Stage C I no
matter what the distribution of tempe,rature in region 11. me stage
comes to an end when H reaches the maximum possible value, Hc . There-
0
after, the wave described by (5.39) becomes inadequate to supply the
radiation energy: Since the enthalpy cm no longer increase, the speed
of the cdoling wave has to increase. Tnis speed is tnen given by (5 .l9),
and Stage C I1 has begun.