Theory of the Fireball

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6. Sinrinkage of Isotnemal Sphere We denote the 'tmass'' of the isothermal sphere, as defined by (6.1)~ by 5, Then this mass will decrease, due to the progress of tne coding wave inward, according to d"l dt= - PO Rf Note the po 5n the denominator and the absence of the factor &fly both due to the definition (6.1) The density of the isothermal sphere is nearly uniform and vi11 be denoted by p is Initial values at time tar will be denoted by a subscript a. The isothermal sphere expands adia- bat ically, hence and therefore at any time t The speed of the cooling wave is given by (5 .LO), thus u= 5 - Hl (6.4) where J has been set equal to zero because there is no appreciable flow 0
of radiation inside the sphere. H is the enthalpy inside tne sphere, 0 which decreases adiabatically H is the enthalpy at the radiating surface. It will be shown in See. 6c 1 that the temperature T is nearly constant with tlme, so tnat in good 1 approximation 5 and J in (6.5) are constant. We shall also make the 1 poorer approximation that 3 Ho. Then (6.5) and (6.6) give We define t x=Ea 73 J . ..
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, - Ip.L ,. : CIC-14 REPORT COLLECT
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LA-3064 UC-34, PHYSICS TID-4500 (30
Page 6 and 7:
i.e., the part which has not yet be
Page 9:
1. INTRODUCTION 2. PHASES IN DETELO
Page 12 and 13:
6 radiation .(Stage A of Sec. 2) is
Page 14 and 15:
frequency, the opacity, which is su
Page 16 and 17:
elations as (3.2) between shock rad
Page 18 and 19:
in this case there is no Stage D 11
Page 20 and 21:
highest possible density of about l
Page 22 and 23:
\ and the average of y' is taken ov
Page 24 and 25: The radius R is given R3 = I"- P P
Page 26 and 27: T-R -10 (3.16) 8 The numerical calc
Page 28 and 29: Since the interesting values of R a
Page 30 and 31: Most of the radiation comes from a
Page 32 and 33: higher frequency (above, and Sec. L
Page 34 and 35: 4. ABSORPTION coEFF1c1ms a. Infrare
Page 36 and 37: (3.21), it is small compared to the
Page 38 and 39: hv (ev) P/Po = 1 ff N2 0- Table N.
Page 40 and 41: w Q P/Po 1 0.1 0.01 T 4,000 6,000 8
Page 42 and 43: Table VI. Average Mean Free Paths (
Page 44 and 45: The fraction of the Planck spectm b
Page 46 and 47: The W beyond 3.5 ev will be strongl
Page 48 and 49: The equation of continuity is aH aJ
Page 50 and 51: U" J, A Ho - H(T1) To determine u w
Page 52 and 53: temperature is aromd Tb, and in whi
Page 54 and 55: internal energy in that sFhere; in
Page 56 and 57: y integrating (5.8); it depends on
Page 58 and 59: a log I1 - y' - 1 a log p at - y' a
Page 60 and 61: 2 vitn A = 0.1G q/cm and n = 6.3. T
Page 62 and 63: or a radiating temperature of 10,80
Page 64 and 65: assuming the strong shock relation
Page 66 and 67: pressure is larger than pa, (5.50)
Page 68 and 69: inconsistency in our apyroximations
Page 70 and 71: G. We& Cool-ing Wave In Stage C I1
Page 72 and 73: 6. EFFECT OF THREE DDENSIOUS a. Ini
Page 76 and 77: Pa f(x) = - P and obtain the simple
Page 78 and 79: From y = 1.18, y=l-A Y= -1 2.2 - 0*
Page 80 and 81: where Re is the outer edge of the l
Page 82 and 83: esult of the three-dimensional cons
Page 84 and 85: 4 dF: = - 4KaT at where a is the St
Page 86 and 87: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10 . REF
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Theory of the Fireball

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