Theory of the Fireball

or a radiating temperature of 10,800°. Tnis is a reasonable result,
thowh appreciably higher than the teqeratures usually observed. How-
ever, as we shall show in Secs. 5e md f, our calculation gives the max-
imum temperature reached, md is likely to be somewhat too high due to
OUT approxinmtions .
e. Bewinning of Strow Coolim Wave
2
Equation (5 -19) gives the inward speed of the cooling wave in @/a
sec. Precisely, this is the speed at which the point of teqerzhre T
1
(radiating temperature) moves relative to the material, once fne cooling
wave is fully established. But even if there is no cooling wave, i.e.,
if we have simply adiabatic expansion behind the shock, a point of given
temperature T1 will move intrzrd. This "adiabatic motion'' is the minimum
velocity vlnich the point T can nave. Therefore, if tne adiabatic speed
1
is greater than (5.19) , it will be tne correct velocity. Of course, there
will still be a. cooling wave because this is needed to supply the energy
for the radiation; tills 'be&< cooling wave" wil be described in Sec 5g.
But its inward motion, more accurately the velocity of its foot (point C
in Fig. 2), will not be determined by the requirement of sufficient energy
flow, (3.19) , but by the "adiabatic speed" which we shall derive from
(3.17) Region IV of Fig. 2 will nar be absent, Tnus, outside the
cooling wave, at point Cy region V wil begin Mediately, with the
temperature distribution given by (3.15).
It is therefore important to determine the time ta (and pressme p )
a
60