Astro 405/505, fall semester 2005
Homework, 2nd set, solutions
Problem 3: Radiation spectra under LTE
The supernova remnant subtends a solid angle element
d
Ω = 1
.
2
·
10

6
sr.
The intensity
therefore is
I
ν
=
F
ν
d
Ω
= 1
.
3
·
10

13
erg
/
cm
2
/
s
/
Hz
/
sr
which we need to compare with the Planckian, because that is the solution of the radiation
transport equation for LTE and large optical depth.
B
ν
(
T
) =
2
h ν
3
c
2
1
exp
hν
kT

1
⇒
B
100
(
T
) = (1
.
5
·
10

23
cgs)
1
exp
hν
kT

1
I
ν
=
B
100
(
T
)
requires
hν
kT
or, more precisely,
kT
= (8
.
7
·
10
9
)
hν
⇒
T
’
4
·
10
7
K
The radiation maximum occurs at about
hν
’
3
kT
or about
2
·
10
18
Hz.
The emission is not necessarily optically thick, in which case the radiating material can
only be hotter than calculated here.
Problem 4: Timedependent line profiles
The problem is similar to that discussed in class except that now we would wish to calculate
rates, i.e. also temporal probabilities. The ansatz would be
P
(
E
γ
, t
obs
)
dE
γ
dt
obs
=
P
(
v
)
dv P
(Ω)
dφ d
cos
θ P
(
t
)
dt
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 Fall '08
 RABE
 Physics, Radioactive Decay, Work, Radiation, Trigraph, tobs, Doppler Shift formula

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