Theory of the Fireball
Theory of the Fireball
Theory of the Fireball
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internal energy<br />
in that sFhere;<br />
in <strong>the</strong> iso<strong>the</strong>rmal sphere <strong>of</strong> temperature T and 7 ' = 1.15<br />
C<br />
<strong>the</strong>n (5.18) becomes<br />
Typically, p = 5, TI = 1, Tc = 3; <strong>the</strong>n u = 0.15 gm/cm sec. The expres-<br />
sion (3.33) includes all <strong>the</strong> black body radiation. If only <strong>the</strong> radiation<br />
actually emitted to large distances is to be included (which is reasonable<br />
at lower temperatures, Ti < 0.8) (3.37) should be used; <strong>the</strong>n u will be<br />
2<br />
smaller, 0.1 gm/cm sec or less.<br />
t I 2<br />
Before <strong>the</strong> cooling wave reacnes <strong>the</strong> iso<strong>the</strong>rmal sphere, Ho is smaller.<br />
This is partly compensated by <strong>the</strong> fact that Jo > 0. An interesting inter-<br />
mediate state is when <strong>the</strong> cooling wave has just reached <strong>the</strong> blocking<br />
layer. Tnen, using Tb<br />
t<br />
J1 - Jb,<br />
"b = 1% - H1<br />
= 1.8 and (5.14),<br />
Clearly this makes sense only if <strong>the</strong> subtracted term in <strong>the</strong> numerator is