Most of the Sun's mass lies in the central region called the radiative zone, which includes the core, in which thermonuclear fusion produces energy. It's called the radiative zone because this is how energy is transported toward the surface: via radiation...light. High energy photons are produced in the core, and these scatter continuously off matter particles in the dense inner regions, randomly wandering until they exit the radiative zone.

The intent of this exercise is to give you a feel for the way energy diffuses out of the Sun through this process. You'll experiment with radiative zones of various depths to see how depth affects the time required for diffusion of the photons.

Start up the CLEA Solar Energy lab by clicking on the Solar Energy icon.

Log in. You don't need an ID number, so don't enter anything, just hit OK. Click on Simulation. Go to Flow, and choose 1 Photon. Run it.

A single photon randomly rattles through the zone, and eventually happens upon the surface, where it escapes. If you Click on Parameters, go to trails, and choose yes, the photon will leave a trail where it's been.

Run this simulation 10 times, each time recording the number of interactions that occur before the photon escapes. This number is displayed on the screen. Find the average of these 10. The depth of the zone can be changed. Click Parameters, # of layers and type in 5. Run the simulation 10 more times with this smaller zone and record the number of interactions on each run. Find the average for the 10 runs.

Now do this experiment with radiative zones of 2 more depths and fill in the table.

Now make a graph, with number of layers on the horizontal axis, and average number of interactions on the vertical axis. Make this graph with Microsoft Excel. You can use the computers in the back of the lab room for this. Ask the instructor to show you how to do this if you don't know.

Does it appear to you from the graph that the time to escape is directly proportional to the depth?

Diffusion of the Photons

Now Click on Return to finish with this part. Then click on Simulation, go to Flow, and choose Diffusion. Run it. Now more photons are involved, each wandering on its own.

After all the photons have escaped, you can read on the display the average number of interactions per photon. After having run it with 100 photons, change the number of photons to 1000. Before running it, decide whether or not you think the average number of interactions will be very much different.

Now run it. Is the average number of interactions much different?

The increase in number allows you to run many experiments at once. Leave the number of photons on 1000, and let's repeat the earlier experiment, with just one run this time for each zone depth. We'll find the average number of interactions for each depth. Fill in the follow table. Important: For each zone depth, also time the run. That is, use a stopwatch to time how long the simulation takes for all the photons to leave the zone, and record the time in seconds in the "time" column.

Again, using Excel, graph this, Zone Depth on the x axis, # of interactions on the y axis. Is the dependence a direct proportionality?

If not, what kind of function does this look like?

To find out more difinitively what is the form of this graph, you'll use Excel to fit the data to a particular type of function. The instructor will show you how to do this. It turns out that the dependence of average interaction number on zone depth is a power law relationship. That is, of this type:

When the fit is made the equation of the fit can be displayed.

Write the equation here.

Now graph the amount of time for each run as a function of the average number of interactions (average number of interactions on the x axis, time on the y axis).

Does the graph appear to be a straight line?

Fit a straight line to this data, and have Excel give you the equation of this fit.

What's the slope of the fitted line?

This slope tells you the time in seconds per interaction that each photon must, on average, experience before leaving the zone. Call this S. Then, the time needed for all the photons to leave the zone is given by:

where I is the average number of interactions.

Now fill in the table below, using the equation that Excel fit to your data. Then, for the third column, compute how long it would take to do each of these runs in the lab if the software was designed to use zones of these greater depths.

How many seconds would the run take that uses a zone depth of 100,000,000?

How long is this in years?

This illustrates the time required for energy to move its way from the core of the Sun where it's produced, to the top of the radiative layer, a distance of 500,000 km.