Astro 405/505, fall semester 2004
Homework, 6th set, solutions.
Problem 1: Eddington limit
We cannot assume that the mean free path of photons is very small. Instead we explicitely
calculate the force density on a population of electrons with density
n
e
exerted by radially
streaming photons with flux
F
=
n
ph
c
=
L
4
π R
2
hν
The momentum transfer per scattering depends on the scattering angle as
δp
=
hν
c
(1

cos
θ
)
and thus we calculate the force density as
F
=
d
Ω
hν
c
(1

cos
θ
)
F n
e
dσ
d
Ω
=
n
e
L σ
T
4
π R
2
c
Gravitation pulls the gas (hydrogen for simplicity) inward with a force density
F
g
=

G M n
e
m
p
R
2
Dominance of gravity then requires
F
g
+
F
<
0
⇒
M >
L σ
T
4
π G m
p
c
= (1
M
)
L
1
.
3
·
10
38
erg
/
s
For pair plasma we have to replace the proton mass in the gravitational force density by two
times the electron mass. The required mass is therefore around a factor 1.000 higher than for
ordinary gas, or for a given mass the maximum luminosity is correspondingly less.
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 Fall '08
 RABE
 Physics, Force, Work, Photon, jssc, force density, νs

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