Theory of the Fireball

6. EFFECT OF THREE DDENSIOUS
a. Initial Conditions and Assumptions
The fact tnat the fireball is spherical causes some deviations from
the one-dimensional tiieory of Sec. 5. In this section we shall discuss
Stage C 11, tine penetration of the cooling wave into the isothermal
sphere, in three dimensions. Initially, we assume tnat the cooling wme
has just reached the isotnermal sphere; we call the corresponding tine
t = ta, and the pressure is the criticd pressure p a = 5 bars derived in
Sec. 5do Subsequently, the mass of tne isothermal sphere decreases due
to tine cooling wave.
We assume that the material, tfnich is at temperature T > Tm = !+OCOo
at the initial time t will stay in this temperature range t'hroughout
a'
Stage C 11. Tnis is reasonable because this material will be heated by
the ultraviolet radiation coming from the inside, because of tne strong
absorption of air of medium temperature (3000 to 6000~) for W (Sec. 4c)
The W heating is expected to compensate approximately the cooling due
to adiabatic expansion of this material; tnis is confirmed by rough
estimates of the heating and cooling. We do not know how tine temperature
is distributed in the '%arm layer" between the radiating temperature T 1
and Yne temperature Tm = 4000'; tnis could only be determined by a detailed
calculation of the UV radiation flow in this region. We assume that the
distribution is smooth, as it is in Stage C 1, and that therefore the
2
thickness of the 'harm layer" in gm/cm is directly proportional to the
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