Lone neutron stars appear as bright radio sources that are powered their spin. Called radio pulsars, or more spin-powered pulsars, to distinguish them from the accretion-driven x-ray pulsars, these stars generate power in the same way that dynamos at power plants generate power: the variation in time of a magnetic field generates an electric field. In the case of a dynamo, if a magnet is spun rapidly, and if a conductor at rest is held near the magnetic, the spinning magnet induces an electric field in the conductor that drives an electric current. If a neutron star with a magnetic field is spun at a sufficiently-high rate, a massive electric field is created that drives a current from the surface of the neutron star. The current created at the neutron star travels along the magnetic field lines of the star, emitting electromagnetic radiation as it curves along the field lines. Much of this radiation is seen at radio wavelengths.
Neutron stars are very peculiar objects. They are the remnants of massive stars. As a massive star burns it central elements to iron, the core of the star becomes incapable of supporting itself against gravitational collapse. The core collapses until nuclear densities are reached, and the pressure of protons and neutrons counteracts the gravitational force. The energy released in this collapse creates the supernova, driving the outer layers of the star way from the core. At birth a neutron star is extremely hot, around 1011° K, because the collapse that formed it releases a large fraction of the rest mass energy of the original core, but this energy is rapidly lost as neutrino radiation. The surface of the star rapidly falls to several million degrees Kelvin, which places the surface radiation predominantly in the x-ray band.
The mass of a neutron star can be found for stars in binary systems. A typical value is 1.4 times the mass of the Sun. The radius of a neutron star is expected to be around 10 km. With such values, the density of a neutron star is over 1014 g cm-3, which is the density of the nuclei of atoms.
The whole game in neutron stars is to understand the internal composition. Not surprisingly, the densities and temperatures of matter in neutron stars cannot be replicated in the laboratory. A nucleus, a collection of less than 300 nucleons held together by the strong force, is worlds apart from a star of 1057 nucleons supporting itself against gravity through degeneracy pressure. Are neutron stars just giant atoms, composed only of protons and neutrons, or do they contain other fundamental particles, such as muons or K mesons, or are they composed solely of quarks, the constituents of protons and neutrons? Theorists suggests a variety of compositions; how do we distinguish the theories?
The strongest test of the composition of neutron stars is provided by the relationship between their radius and mass. This relationship tells us how the material composing the star behaves under compression. One possibility is that the material is stiff, so that a small change in density produces a large change in pressure; a composition of neutrons and protons should be stiff. Another possibility is that the material is soft, so that the density must change by a large factor to produce a small increase in pressure; material that undergoes a phase transition when squeezed—for instance, freeing quarks that are bound within protons and neutrons—is soft. Whether a material is stiff or soft shows up in the relationship of mass to radius. The radius of a star composed of a stiff material increases more rapidly with mass than does the radius of a star of soft material. A second difference between these two types of material is that the maximum mass of a stiff star, the mass above which a star collapses to form a black hole, is greater than for a soft star. The maximum mass of a stiff star is around 2 to 2.5 times the mass of the Sun, while the maximum mass of a soft star is around 1.5 times the mass of the Sun.
A second test of composition is provided by the rate at which a neutron star cools. Neutron stars initially cool by emitting neutrinos. Neutrinos, which interacts weakly with other types of matter, can easily pass through the dense layers of the neutron star. In the Sun, neutrinos account for a small fraction of the lost energy, but in neutron stars, virtually all of the energy trapped in the star at birth is releases as neutrinos. But the processes that create the neutrinos depend on the composition of the star, so measuring the rate at which a young neutron star cools is a diagnostic of the star's composition.
X-ray astronomy provides the primary tool for applying these diagnostics. By measuring both the radius and mass of a star of known distance, we can derive through x-ray observations a temperature, a brightness, and a redshift. Assuming a black-body spectrum (not too bad a model), a measured temperature gives the surface brightness of the star. When this value is combined with the flux measured at Earth, we have a value for the radius of the star as a weak function of the gravitational redshift. The redshift comes in because gravity redshifts all of the photons emitted from the surface, which has the effect of redshifting the observed temperature, and because the gravitational bending of light allows us to see more than half of the star's surface. If we can measure the redshift of atomic lines at the surface of the neutron star, we can remove the effects of redshift to have a pure measure of radius. A measured redshift is also a direct measure of surface gravity, which when combined with the known radius gives us a measure of stellar mass. The only question is whether this can be done.
The first part of the process, the measurement of a temperature and a flux, has been carried out for a number of spin-powered pulsars of known distance. Some of these stars have spectra that are close to black body; others that deviate from a black body can be matched to theoretical models of the radiation from a neutron star's atmosphere, which gets us to the same place: a measure of radius and redshift. Where the project has stumbled is in the measurement of a redshift. Most isolated neutron stars have featureless spectra, and in the one neutron star that appears to have lines, the identification of the lines (which element produced the lines) is not possible. So far, the only neutron stars with identifiable surface lines are binary neutrons stars undergoing a thermonuclear runaways at their surfaces, but the radiation from these objects is confused by the accretion of material from companion stars, so there is no measure of radius. Obtaining a relationship between neutron star radius and mass is therefore still out of reach.
The relationship between age and temperature of a star can be measured combining radio and x-ray observations. As before, observations in the x-ray provide a temperature for the star's surface. The theoretical models for neutron star structure can relate this surface temperature to the temperature in the star's interior. Age is estimated from the rate at which the pulsar is spinning down, which is done using radio telescopes. These measurements have been carried out for a number of spin-powered pulsars, and the results can be compared to theory. But again, the results are less than satisfying: a single theory of cooling cannot explain the observations. As often happens in astrophysics, the physical world is more complex than suits the theorist.