Author: Joseph Lazio <jlazio@patriot.net>

Neutron stars are the remnants of massive stars.  Sufficiently massive
stars form iron in their cores during the process of nuclear fusion.
Iron proves problematic for the star, though, as iron is among the
most tightly bound nuclei.  Nuclear fusion involving iron actually
requires energy to occur, as opposed to nuclear fusion involving
lighter nuclei in which the fusion produces energy.  At some point so
much iron accumulates in the core of the star that its nuclear
reactions do not produce enough heat (i.e., pressure) to
counter-balance the force of gravity due to the star's mass.  The star
implodes in a supernova, blowing off much of its outer layers and
leaving an NS as a remnant.  A star has to be (roughly) at least 8
times as massive as the Sun and not more than 25--50 times as massive
as the Sun to form an NS.  (The upper limit is quite uncertain.)

(There has been a second mechanism postulated as a way to form neutron
stars.  There is an upper limit to the mass of a white dwarf, 1.4
times the mass of the Sun, called the Chandrasekhar limit after
Subrahmanyan Chandrasekhar who first described it.  Above this mass
the force of gravity overwhelms the internal pressure provided by the
electrons in the WD.  If one had a WD that was quite close to the
Chandrasekhar limit and a small amount of mass was added to it, it
might collapse to form an NS.  This process is called
"accretion-induced collapse."  It is not clear if this mechanism
actually occurs, however.)

NSs can be divided into three broad classes, rotation-powered pulsars,
accretion-powered pulsars, and magnetars.

Rotation-powered pulsars are the kind of pulsars most commonly
described and were the first kind of NSs observed.  These NSs have
powerful magnetic fields and rotate.  If the axes of the star's
rotation and magnetic field are not aligned, this rotating magnetic
field produces an electric field; in the case of NSs, the electric
fields are strong enough to rip particles from the crust of the NS and
accelerate them.  The accelerated particles radiate.  The magnetic
field collimates the accelerated particles, so the radiation from the
NS is emitted in two narrow beams.  If one of the beams sweeps across
the Earth, we observe a pulsating source---a pulsar.  Most of the
known rotation-powered pulsars are observed in the radio (though the
radio emission itself is a usually just a tiny fraction of the
rotation energy of the NS).

Rotation-powered pulsars are often further sub-divided into
strong-field and recycled pulsars.  Strong-field pulsars have magnetic
fields of about 10^8 Tesla and observed pulse periods about 1 second.
As the pulsars lose energy, their rates of spin slow down.  At some
point, the rotating magnetic field is no longer produces electric
fields strong enough to power the pulsar mechanism, and the pulsar
"shuts off."  However, if the NS is a member of a binary system, its
companion star, during the course of its own evolution, increase in
size and start spilling matter onto the NS.  As the matter spills onto
the NS, if it hits the NS in the same direction that the NS is
rotating, it can increase the rate at which the NS is spinning or
"spin-up" the NS.  If this spin-up process goes on for a long enough
period of time, the NS may "turn on" as a pulsar again.  The process
of matter spilling onto the pulsar tends to suppress the magnetic
field, though.  With a weaker magnetic field, the spun-up pulsar
doesn't spin down as fast as before.  So, these recycled pulsars are
distinguished by having very slow spin-down rates.  As it turns out,
they also tend to have very short pulse periods, typically less than
0.1 seconds, with the shortest being 0.00156 seconds.

Accretion-powered pulsars are NSs onto which matter is spilling.  The
gravity well around an NS is so deep, it is actually fairly difficult
for matter to fall onto the NS.  Only matter that starts at rest with
respect to the NS can fall directly onto its surface.  If the matter
has any velocity relative to the NS, as it falls toward the NS, it
will begin to orbit the NS.  (This is the same principle that causes a
skater to spin faster as she pulls in her arms.)  If a lot of matter
is falling toward the NS, a disk is formed around the NS.  Due to
"frictional" forces within the disk, matter slowly works its way
closer to the NS until finally falling a short distance onto its
surface.  The process of the matter falling onto the NS' surface is
known as accretion, so the disk is called an accretion disk.  The
gravitational potential of a NS is so deep that a lot of energy can be
released as the matter forms an accretion disk and spills onto the NS'
surface.  Consequently, accretion-powered NSs are typically seen as
X-ray sources.

Magnetars are a recently recognized class of NSs.  It is thought that
rotation-powered pulsars only work if the magnetic field is not too
strong.  If the magnetic field is too strong, it can effectively shut
down the process by which the particles are produced.  The critical
field seems to be about 10^10 Tesla.  Only a few examples of magnetars
are known.  These generally appear as fairly constant X-ray sources,
though magnetars have also been suggested to be responsible for
sources known as soft-gamma ray repeaters.