Physics’ 223:’Stellar’ Astrophysics’
Homework’#2 ’
Due’Friday’February’24
th
’at’5pm’in’box’in’front’of’SERF’340’
’
Reading
: HKT Chapters 4 & 6
Exercises: [160 pts total]
(1)
Photon walk
: Highenergy thermal photons generated in the core of the
Sun by fusion traverse very short path lengths due to the high opacities of
the dense plasma.
We can describe this process as a random walk.
(a) [10 pt] Assume photons travel along a constant short pathlength
l
before
being absorbed, and then are instantly reemitted in a random direction.
Show that the photon, in order to reach a total displacement of R >>
l,
must
take on average N
≈
(R/
l
)
2
steps and therefore travels a total distance of R
2
/
l
.
(b) [10 pt] Verify this using a simple computer simulation.
Starting at an
origin point, follow the path of simulated photons which travel a unit length
in a random direction, are absorbed and reemitted and then travel unit
length in another random direction (i.e., randomly selecting spherical angles
θ
and
φ
at each integration step).
Follow the photon until it has reached a
radial distance of 50 units from the origin.
Repeat this for 10,000 trials, and
plot the distribution of the number of steps required for each photon to reach
the “surface”. What is the average of this distribution?
How does this
compare to (R/
l
)
2
?
What about the minimum and maximum number of
steps? Discuss how this distribution might be related to the lightcurve of an
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 Winter '08
 Fuller,G
 Electron, Energy, Work, Photon, Fundamental physics concepts, Plasma

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