Theory of the Fireball

The fundamental statement of 2 is that the cooling wave keeps its
shape, i.e., that the enthalpy (and other functions of the temperatme)
is given by
H = H(x +
Here t is the time,
Lagrangian velocity
x is the Lagrangian coordinate, and u is the
of the cooling wave. We have written x + ut so that
the cooling wave proceeds tmards smaller x, i. e. , inwards. H is, of
course, a decreasiw function of x + ut. The Lagrangian coordinate is
2
best measured in gm/cm and is defined by
where X is the geometrical (Eulerian) coordinate. For given pressure p,
the density p is a function of H so that X(x) can be calculated from
(502) The Lagrangian velocity u, measured in gm/cm 2
sec, is a' constant.
For any given If, we know the temperature T, hence the opacity K and
the radiation flow
where a is the Stefan-Boltzmann constant,
2 4
a = 5.7 X lom5 erg/cm sec deg
45