The matter at the surface of a neutron star is composed of ordinary nuclei as well as ionized electrons. Proceeding inward, one encounters nuclei with ever increasing numbers of neutrons; such nuclei would quickly decay on Earth, but are kept stable by tremendous pressures. Proceeding deeper, one comes to a point called neutron drip where free neutrons leak out of nuclei. In this region we have nuclei, free electrons, and free neutrons. The nuclei become smaller and smaller until the core is reached, by definition the point where they disappear altogether. The exact nature of the superdense matter in the core is still not well understood. Some researchers refer to this theoretical substance as neutronium. It could be a superfluid mixture of neutrons with a few protons and electrons, other high energy particles like pions and kaons may be present, and even sub-atomic quark matter is possible. However so far observations have not indicated nor ruled out such exotic states of matter.
Some neutron stars that can be observed are:
Neutron stars rotate extremely rapidly after their creation due to the conservation of angular momentum; like an ice skater pulling in his arms, the slow rotation of the original star's core speeds up as it shrinks. A newborn neutron star can rotate several times a second; sometimes, when they orbit a companion star and are able to accrete matter from it, they can increase this to several thousand times per second, distorting into an oblate spheroid shape despite its own immense gravity. Over time, however, neutron stars slow down because their rotating magnetic fields radiate energy; older neutron stars may take several seconds or minutes for each revolution.
The rate at which a neutron star slows down its rotation is usually constant and very small: the observed rates are between 10-12 and 10-19 seconds for each century. In other words, a neutron star now rotating in 1 second will rotate in 1.000000000001 seconds after a century.
Sometimes a neutron star will undergo a glitch: a rapid and unexpected increase of its rotation speed (of the same, extremely small scale as the constant slowing down). Glitches are thought to be the effect of internal re-organizations of the matter composing the neutron star, something similar to starquakes. Such a starquake would register as grade 20 or 25 on the Richter scale.
Neutron stars also have very intense magnetic fields - about 1012 times stronger than Earth's. Neutron stars may "pulse" due to electrons accelerated near the magnetic poles, which are not aligned with the rotation axis of the star. These electrons travel outward from the neutron star, until they reach the point at which they would be forced to travel faster than the speed of light in order to still co-rotate with the star. At this radius, the electrons must stop, and they release some of their kinetic energy in the form of X-rays and gamma-rays. External viewers see these pulses of radiation whenever the magnetic pole is visible. The pulses come at the same rate as the rotation of the neutron star, and thus, appear periodic. Neutron stars which emit such pulses are called pulsars.
When pulsars were first discovered, they were believed by some to be evidence of extra-terrestrial intelligences. Because of their highly regular pattern of emmisions, they were initially thought to be beacons of some type.
Another class of neutron star, known as the magnetar, exists. These have a magnetic field of above 1014 gauss, strong enough to wipe your credit card from the distance of the Sun away, strong enough to be fatal from the distance of the moon away. By comparison, Earth's natural magnetic field is .5 gauss. The processes in a magnetar involve the rotation of the neutron star tangling field lines until they become exceptionally dense, giving rise to a resonant magnetic field.
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