Theory of the Fireball

inconsistency in our apyroximations .
In our one-diniensional tneoqy, tne end of Stage C I narks -the max-
Snrrm. of radiation, both in temperature and total emission. In Stage C I
because the material becomes more transparent. In Stage C I1 the reverse
is the case, (5.39), because the material which has gone through the
cooling wave becomes thicker with time, (5,.32). Tnis material provides
opacity for the visible light from the fireball; since it becomes more
opaque, the radiation must now come from a layer of smaller absorption
coefficient, (5.35), and therefore of lower temperature. As (5.36) sha~s,
the increase of thickness (t 2n the denominator) is more important than
the continued decrease of density (factor p 1/3 ). Tnese results will be
modified in the three-dimensional theory, Sec. 6.
1
The maximum temperature has been calculated as T = 0.92 or 1.08,
from om two calculations; it is clearly close to 1, i.e., ~O,OOO~.
This number is not too mucn out of line with observation considering
tnat we have calculated a maximum. In fact, tne transition from Stage
C I to C I1 cannot be sudden as we have assumed; the cooling wave must
begin gradually, and tnerefore the temperature peak which we have calcu-
lated will actually be cut off (Fig. 3). The observable maximum may
easily be 1000° lower than our calculation.
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