Theory of the Fireball

Since p - C,
-1 02
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entirely due to tihe "opening up" of the shock, i.e., the decrease in
absorption with decreasing density (pressure) .
For given pressure, the radiating temperature (5.54) is slightly
higher for smaller yield, an effect which has been observed. A factor
of 1000 in yield corresponds to a factor 1.6 in temperature, hence a
factor 7 in radiation per unit area. The total radiated' power (assuming
black body) at given p is proportional to
The relatively law power of the yield is remarkable in this formula,
vnich describes Stage C I. Since the total energy radiated should be
approximately proportional to Y, the duration of Stage C I is then pro-
portional to Yo*6o. The observed time to the second radiation maximum
0.7 1
is abotrt proportional to Y . Our theoretical dependence of T on yield
is therefore sornewnat too strone;. The time dependence of (3.56) is quite
strong, about as t 2
As ve nave snam in Sec. 5e, Stage C I ends when the pressure reaches
5 bars. For this value of p, and for Y = 1, (7 .S&) gives T = 0.92.
Tnis is slizhtly less than the T' = 1.08 deduced in Sec. 5d for the same
p md Y from the cooling ??me. The discrepancy must be due to a small
1