Is There an Edge to the Sun?
The visible edge of the Sun is called
the photosphere. It is a difficult concept for students to
grasp. It might be thought that this edge is very solid—it
is not.
Some teachers use the analogy of how light comes off of a
cloud. The light bounces around a cloud. We see the last bounce
which is the light that bounces off of particles close to
edge and then out. The edge doesn’t have to be dense
or even denser than the rest of the cloud. It is just the
surface of last scattering.
For the Sun, a photon is generated at the center and makes
its way to the surface. It may take up to several million
years to get to the surface, and the form of the energy may
change from Xray to visible wavelengths. When the photon
leaves the Sun, it takes eight minutes to get to us at the
speed of light.
What Is a Random Walk?
Most electromagnetic energy gets
out of the Sun in a very round about way which depends on
random motion. The path a photon takes is unpredictable but
we can gain an understanding through models of how it works.
The photons that we see as sunlight actually took a long time
to leave the interior of the Sun. They did what physicists
call a random walk. It's kind of like trying to make your
way through a crowded subway station. You head off in one
direction, get bounced in another direction, then still another,
and so on. The problem is that, unlike the person in a subway
station, the photons (particles of light) don't know which
way they want to go. They are jostled about in scattering
collisions with particles (mostly electrons). It's like being
blindfolded in a crowded subway station. Eventually you will
work your way to the door by chance and leave. But how many
steps will it take you to go a certain distance?
A demonstration that can be used in class illustrates that
one can predict quite a bit about a random or unpredictable
path.
 Pick a point in the middle
of a room where you can move 10 steps in any direction.
Place a marker at that center starting point. With a piece
of string, or if you can, mark with chalk on the floor a
circle that is 10 steps away from the center. The radius
of the circle should be ten studentsized steps.
 One student acts as the
photon and we see how many steps it takes to travel ten
paces, if the person is moving in a random direction on
each step. After the instructor has defined a circle around
the student ten paces in radius he or she should now entertain
predictions from the class. Write the predictions on the
board.
 The question is, how many
steps will it take for the student to get outside the circle
if they move one step in a random direction each time? At
best it will take a minimum of ten steps, if they moved
the same way each time, which is unlikely. We will use a
little compass wheel or spinner to tell him/her which direction
to take each step. If that is not available, drop a pencil
with the eraser down (or a cheap pen) on the ground and
notice which way the tip is pointed. Use the orientation
like a compass.
 Don’t have the student
move in the direction the tip points but rather at the angle
(relative to north, or better yet to the front of the room).
To do this, have students determine the angle relative to
the front of the room and specify a number (e.g. 137 degrees).
Then have the student in the middle of the room rotate to
exactly that angle (as verified by the class) and then take
one step forward. Again verify that the step is exactly
onetenth of the distance to the circle.
It turns out that to go outside the circle that
is ten paces in radius will require (10)^{2} or about
a hundred different paces, if each pace is in a random direction.
Stated differently, a random walk of N steps, on the average,
will move you a distance of N^{1/2} steps away. So,
it should take about 100 steps to get across a circle ten
steps in radius.
For the Sun, radiation leaves the center, where it was generated,
by a random walk process. A photon moves about 1 cm before
it has a collision and is randomly redirected. Since the radius
of the Sun is 10^{11} (100 billion) cm, a photon must
travel about 10^{22} cm before it will make its way
to the surface. Since the photon travels at the speed of light
(3 X 10^{10} cm/sec), it will take a minimum of 10^{4}
(a thousand) years for a photon to emerge. A much more detailed
calculations give a time range of a few hundred thousand to
10^{7} (ten million) years, since the mean free path
of a photon is not always one centimeter throughout the Sun.
This exercise implies that changes deep in the Sun will take
a considerable amount of time to be reflected in the light
that we see. This is true. Neutrinos, which are not scattered
in the same way as photons (neutrinos go right through matter
without interacting), pass directly out of the Sun at the
speed of light. They reflect very rapidly any changes in the
interior of the Sun. They are also very hard to detect, since
nothing absorbs them well. A great many neutrinos pass through
our body every second without any interaction or effect.
To conclude, ask the students to identify other random processes
that have some element of predictability. A common example
is traffic lights—we don’t know how many traffic
signals there'll be, but we can approximate how many red lights
we'll hit in going from one place to another (about half).
