Week 5: Astrophysics in a Nutshell Ch3.1-3.4

This section of Astrophysics in a Nutshell covered the Virial theorem and radiative energy transport in stars. Something that I thought was interesting from this chapter was the idea of mean free path and random walk of photons within a star. The mean free path is the average distance that a photon can travel without getting absorbed and reemitted by a different particle. This distance is inversely dependent on the density of material through which the proton is traveling, so a photon traveling through something really dense, like the interior of a star, will have a smaller mean free path than a photon traveling through empty space.

When the photon gets reemitted, it gets reemitted in a direction independent of its original direction. As a result, the photon doesn't travel in a straight line. Instead, its movement is described as a random walk.

..not this kind of random walk. 

A random walk is essentially just a series of random steps. I knew a bit about random walks in a biology context, but it turns out that the concept is really useful in fields ranging from economics, physics, computer science, and even art. 

As the photon travels through the star's interior, it's constantly getting absorbed and reemitted such that its path looks less like a straight line and more like the path below: 

Obviously, moving at a constant speed, it takes longer to travel the random walk path than it would to just move from the green point to the red point. The density of the Sun is so great and the random walk is so pronounced that a photon produced in the center of the Sun--even moving at the speed of light--would take over 50,000 years to travel to the surface of the Sun. That's an average speed of about 1% of 1 mph! Once released from the Sun, over the next 50,000 years, that photon will have traveled across half of our galaxy--that is, unless it gets absorbed by something else in its path along the way. 

Sources: 
Astrophysics in a Nutshell, Dan Moaz 
http://stream1.gifsoup.com/webroot/animatedgifs7/2863395_o.gif
https://en.wikipedia.org/wiki/Random_walk
https://en.wikipedia.org/wiki/Quantum_Cloud
http://www2.ess.ucla.edu/~jewitt/images/random.gif
https://en.wikipedia.org/wiki/Milky_Way#Size_and_mass
https://en.wikipedia.org/wiki/Sun