Theory of the Fireball
Theory of the Fireball
Theory of the Fireball
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The fundamental statement <strong>of</strong> 2 is that <strong>the</strong> cooling wave keeps its<br />
shape, i.e., that <strong>the</strong> enthalpy (and o<strong>the</strong>r functions <strong>of</strong> <strong>the</strong> temperatme)<br />
is given by<br />
H = H(x +<br />
Here t is <strong>the</strong> time,<br />
Lagrangian velocity<br />
x is <strong>the</strong> Lagrangian coordinate, and u is <strong>the</strong><br />
<strong>of</strong> <strong>the</strong> cooling wave. We have written x + ut so that<br />
<strong>the</strong> cooling wave proceeds tmards smaller x, i. e. , inwards. H is, <strong>of</strong><br />
course, a decreasiw function <strong>of</strong> x + ut. The Lagrangian coordinate is<br />
2<br />
best measured in gm/cm and is defined by<br />
where X is <strong>the</strong> geometrical (Eulerian) coordinate. For given pressure p,<br />
<strong>the</strong> density p is a function <strong>of</strong> H so that X(x) can be calculated from<br />
(502) The Lagrangian velocity u, measured in gm/cm 2<br />
sec, is a' constant.<br />
For any given If, we know <strong>the</strong> temperature T, hence <strong>the</strong> opacity K and<br />
<strong>the</strong> radiation flow<br />
where a is <strong>the</strong> Stefan-Boltzmann constant,<br />
2 4<br />
a = 5.7 X lom5 erg/cm sec deg<br />
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