Author: Michael Richmond <richmond@a188-l009.rit.edu>,
	Peter R. Newman

Disks are common in astronomical objects: The rings around the giant
planets, most notably Saturn; the disks surrounding young stars; and
the disks thought to surround neutron stars and black holes.  Why are
they so common?  First a simple explanation, then a more detailed one.

Consider a lot of little rocks orbiting around a central point, with
orbits tilted with respect to each other.  If two rocks collide, their
vertical motions will tend to cancel out (one was moving downwards,
one upwards when they hit), but, since they were both orbiting around
the central point in roughly the same direction, they typically are
moving in the same direction "horizontally" when they collide.

Over a long enough period of time, there will be so many collisions
between rocks that rocks will lose their "vertical" motions---the
average vertical motion will approach zero.  But the "horizontal"
motion around the central point, i.e., a disk, will remain.

A more detailed explanation starts with the following scenario:
Consider a "gas" of rubber balls (molecules) organized into a huge
cylindrical shape rotating about the axis of the cylinder.  Make some
astrophysically-reasonable assumptions:

- The laws of conservation of angular momentum and conservation of
linear momentum hold (this is basic, well-tested Newtonian mechanics).

- The cylinder is held together by gravity, so the gas doesn't just
dissipate into empty space.

- The main motion of each ball is in rotation about the cylinder's
axis, but each ball has some random motion too, so the balls all run
into each other occasionally.  The sum of the angular momentum of the
whole system is thus not zero, but the sum of the linear momentum is
zero (relative to the centre of mass of the entire cylinder).

- The balls are not perfectly bouncy, so that collisions between balls
results in some of the energy of collision going to heating each ball.

Now, consider the motion of the balls in two directions: perpendicular
to the cylinder axis, and parallel to the axis.

First, perpendicular to the axis: conservation of the non-zero angular
momentum will tend to keep the diameter of the cylinder stay
relatively constant.  When the balls bounce off each other, some are
thrown towards the axis and some away.  In a more realistic model,
some balls are, indeed, ejected from the system entirely, and others
(to conserve angular momentum) will fall into the center (i.e., the
central object).

Parallel to the axis, however, the net linear momentum is zero, and
this, too, is conserved.  Balls falling from the top and bottom (due
to the gravity of all the other balls) will again hit each other and
get heated.  They don't bounce back as far as they fall, so the length
of the axis is continuously (if slowly) shortened.

Continue with both sets of changes for long enough, and the cylinder
collapses to a disk (i.e., a cylinder with small height).  A similar
explanation works for a rotating gas organized into any initial shape
such as a sphere.  The subsequent evolution of the initial disk starts
to get complicated in the astrophysical setting, because of things
like magnetic fields, stellar wind, and so on.

So, in short, what makes the disk is the rotation.  If an initial
spherical cloud were not rotating, it would simple collapse as a
sphere and no disk would form.