Degenerate Matter: Neutron Stars

This post deals with neutron stars and their composition. For an introduction to degenerate matter and the quantum mechanical principles involved, see here. For a description of white dwarfs, the "first" state of degenerate matter, see here.

If only electron degeneracy is taken into account, one would predict that white dwarfs, after reaching a certain threshold, would contract to nothing, the electron degeneracy pressure not being enough to hold of the force of gravity, partly due to relativistic effects. However, this is not the case. For stars that leave stellar remnants in excess of 1.44 solar masses, the rapid shrinking of the core under the force of gravity that occurs after fusion ceases forms a new type of object: a neutron star.

In a neutron star, the nucleons (protons and neutrons) are pushed into such close proximity that the Pauli Exclusion Principle comes into play, forcing the particles involved to stay separate and not assume the same quantum state. Neutrons, being much more massive than electrons, produce less degeneracy pressure at the same density than electrons do, as it takes more energy to cause them to move at the same speeds. Therefore, a neutron star is much denser, and therefore smaller, than a white dwarf. These remarkable bodies are less than 10 miles in radius!

Neutron stars have many interesting properties, since they are among the densest forms of matter. First, they are in many ways similar to a giant atomic nucleus, but containing trillions and trillions instead of merely hundreds of nucleon; the two entities are quite comparable in density, however-each packs approximately 300,000,000,000,000,000 (3*10¹⁷) kilograms into each cubic meter. If the entire mass of the Earth were compressed to this density, it would occupy a volume roughly equivalent to that of the Great Pyramid of Giza! An object on the surface of a neutron star would have to achieve a velocity one-third of the speed of light to escape its gravity, and any matter that falls onto a neutron star impacts with such force that the atoms themselves are broken apart.

Another interesting phenomenon arising from the strong gravity of neutron stars is gravitational lensing. The light emitted from the surface of a neutron star, though having sufficient velocity to escape its gravitational pull, is distorted and curved back towards the surface. As a result, when looking at a neutron star from any given side, one can see more than half of the surface (illustrated below).

A diagram indicating the portion of the surface visible looking at a neutron star with the equator head-on. 

Each patch covers 30° by 30° of surface. The poles are visible as the points of convergence of the longitude lines. Note that, without distortion, one could only see up to the poles, but on a neutron star, one can see more than 40° beyond each pole and around the far side.

In addition, neutron stars rotate. The force of rotation of a parent star is conserved when it becomes a neutron star, but since a neutron star is many times smaller, the momentum causes it to spin extremely rapidly: usually completing each rotation in less than a second! This causes many neutron stars to have a "bulge" near the equatorial regions.

Another important property of a neutron star is its magnetic field. The magnetic field of a neutron star is on the order of a billion times stronger than Earth's, and in some cases it is over a trillion times stronger. Young neutron stars, at high temperatures, emit large amounts of electromagnetic radiation. The structure of the magnetic field causes these beams of energy to be released at the poles. Neutron stars with these electromagnetic beams are called pulsars. Pulsars can be easily detected when one of the poles faces Earth at some time during the neutron star's rotation.

A combined optical, and X-ray image of the Vela pulsar. A distinct beam of radiation in evident from its north pole.

The composition of neutron stars is not definitively known, and various types of matter appear between the outer crust and the center of a neutron star, as the density of the object increases significantly as one journeys inward.

A hypothetical cross-section of a neutron star, based on many simulations and models.

The densities are in terms of the constant ρ₀, the density at which isolated protons and neutrons actually touch one another.  The crust generally consists of atomic nuclei, whose valence electrons have been pushed out by the extreme pressures. The electrons themselves float freely, creating an "electron sea" around the nuclei. This makes the matter of the crust extremely conductive. A similar phenomenon actually occurs in regular metals, with free-flowing electrons surrounding ions. Metals are therefore by some definitions electron degenerate! However, they are not degenerate for the same reason as stellar remnants, as the metals obviously are not (usually) at extraordinarily high densities.

Proceeding inward, one reaches the outer core. Here, the high density causes electrons and protons to become neutrons through a reverse of beta decay, called electron capture. Therefore, the nuclei of the outer core are very neutron rich, to the extent that they would not be stable under normal conditions. Only the density of the neutron star keeps such neutron-rich nuclei together. As one penetrates farther into the outer core, however, neutrons begin to "drip" out of nuclei and become free-flowing, as even the tremendous pressure is not enough to hold together the neutron-rich nuclei.

Near the core, as the pressure exceeds ρ₀, neutrons come into physical contact. Being fermions, the Pauli Exclusion Principle (which states that no two fermions can have the same quantum state, that is, occupy the same location simultaneously) causes pressure counteracting the force of gravity. In a manner similar to the situation in white dwarfs, this counterpressure is known as neutron degeneracy pressure.

It is not known what type of matter exists at the very center of a neutron star, and the answer may vary with the neutron star's mass. However, matter consisting completely of neutrons by definition "should" compose the inner core of a neutron star (by its name), and if, as displayed above, other exotic types of matter exist there, the object would more appropriately be called a "quark star". Such hypothetical objects, their composition, and observational evidence for them, are discussed in the next post.

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Sources: http://en.wikipedia.org/wiki/Neutron_star, http://en.wikipedia.org/wiki/Degenerate_matter#Neutron_degeneracy, http://www.astro.umd.edu/~miller/nstar.html