Homework 2

Homework 2 - Physics 223 Stellar Astrophysics Homework#2...

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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 : High-energy 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 re-emitted 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 re-emitted 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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Homework 2 - Physics 223 Stellar Astrophysics Homework#2...

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