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Degenerate Objects

Binary Pulsars and Millisecond Pulsars

Nature gives us two types of of x-ray binary system: high-mass binaries, where a fusion-powered star of 10 solar masses or more orbits a neutron star, and low-mass binaries, where a fusion-powered star of a solar mass or less orbits a neutron star. Eventually thermonuclear fusion within the fusion-powered star ends, and the binary system reaches one of three destinies: it becomes a binary system containing a neutron star and a degenerate (white) dwarf, it becomes a binary system containing two neutron stars, or it is disrupted by a supernova explosion, liberating two neutron stars into the Galaxy. The systems that remain bound appear to us as binary pulsars; the disrupted systems appear to us as the millisecond pulsars.

Binary Pulsars

Few pulsars are found in binary systems. In those that have been found, the companion to the pulsar is usually a degenerate dwarf. In several instances, the companion is a neutron star. Binary pulsars have two uses: they give us ancient neutron stars to study, and they provide a natural experimental apparatus for testing general relativity.

The pulsar in a binary pulsar is quite different from the common isolated radio pulsar. The former often spins with a period of several milliseconds, while the latter normally spins with a period near 1 second. Despite its dramatically shorter rotational period, a binary pulsar loses rotational energy at a much slower rate than does a common radio pulsar. This difference suggests that the magnetic field of a pulsar in a binary system is much less than that of an isolated pulsar, as the timescale for losing rotational energy is proportional to P2B−2, where P is the rotational period and B is the characteristic magnetic field strength at the pulsar's surface. A common radio pulsar loses its rotational energy on the timescale of 10 million years, which implies a magnetic field of 1012 Gauss, but a pulsar in binary systems loses energy on a timescale of 1 billion years, 100 times longer than a common pulsar, which suggests a magnetic field of 109 Gauss.

The low magnetic field strength implies that pulsars in binary systems are much older than the isolated radio pulsars. The reason is that astronomers believe neutron stars are born with high magnetic fields that gradually decay away, so the pulsars with relatively weak magnetic fields must be many times older than the pulsars with strong magnetic fields.

But we need not rely on such conjecture about age, because we can derive an age for the binary pulsars that contain a degenerate dwarf. A degenerate dwarf is a natural timer. Because energy is not generated within this star, its temperature is directly related to its age. In practice, one sees both hot and cool degenerate dwarfs in binary pulsars. The ages derived from the degenerate dwarfs is consistent with the pulsars in binary pulsars being about 1 billion years old.

Only 8 of the observed binary pulsars have neutron star companions. These systems are remarkably compact. The first of these systems to be found, PSR B1913+16, happens to be the first binary pulsar of any type to be found; it is therefore The Binary Pulsar. This system has a highly elliptical orbit of only 7 hours 45 minutes duration and a semimajor axis no smaller than 7×105 km. The orbit is therefore about the size of the Sun. What makes the two-neutron-star binary systems so interesting is that they exhibit the effects of general relativity. Because a pulsar is a very accurate clock, these binary pulsar systems are ideal for testing general relativity.

Millisecond Pulsars

A handful of isolated pulsars are called millisecond pulsars. These stars resemble the binary pulsars in combining a rapid spin with a slow rate of change in the spin period. As in binary pulsars, the millisecond pulsars lose energy at a rate that suggests a magnetic field of 109 G or less, which means these stars are ancient. At one time they were members of compact binary systems, but were expelled when their companion stars exploded in supernovae.

One point to make is that the name for the millisecond pulsar is misleading, because not all pulsars with millisecond periods are millisecond pulsars. Very young pulsars such as the Crab Pulsar spin with a millisecond period, but are not grouped with the millisecond pulsars because of their rapid loss of angular momentum suggests a strong magnetic field and a recent birth.


The origin of binary pulsars with degenerate dwarf companions is easy to understand. The rapid spin of the pulsar, the nearly circular orbit of the binary, and the presence of a degenerate dwarf all point to these systems evolving from low-mass x-ray binaries. During this phase, the neutron star is not a pulsar, but an x-ray and gamma-ray source, as it pulls material onto itself from its companion. As mass is transferred from one star to the other, angular momentum is also transferred, causing the neutron star to spin more rapidly. Eventually thermonuclear fusion in the companion star ceases, and the companion becomes a degenerate dwarf. If mass transfer ceases at this point, the system becomes a detached binary system containing a rapidly spinning neutron star and a degenerate dwarf. If the neutron star is spinning rapidly enough to generate a current and emit radio waves, it becomes a pulsar, and we would see the system as a binary pulsar.

The binary pulsars containing two neutron stars must follow a much different evolutionary path than the binary pulsars containing a degenerate dwarf. The problem in creating the two-neutron-star systems is the same encountered in creating high-mass x-ray binaries: the system must survive a supernova explosion. If the supernova expels more that half the mass in the binary system, the binary is disrupted.

If the massive star in a high-mass x-ray binary explodes, the system should be disrupted. The neutron star in the system is less than 2 solar masses, while the companion star is generally over 10 solar masses. When the companion explodes, it expels most of this mass, leaving behind a neutron star of less than 2 solar masses. The explosion has expelled more than half of the system's mass. This disruption of a high-mass x-ray binary explains the origin of the millisecond pulsars, but not the origin of the two-neutron-star binary pulsars.

For a high-mass x-ray binary to evolve into a binary pulsar, likely it must first collapse to a single star, with the neutron star orbiting the core of its companion deep beneath the companion star's photosphere. In this way, the neutron star can remain bound to its companion when the companion star's core collapses to a neutron star and drives away the star's outer layers. This type of evolution would explain the characteristics of binary pulsars containing two neutrons stars. The pulsar has a high rate of spin from accretion, and the binary orbit is highly eccentric because of the sudden mass loss in the supernova. This theory applies to the binary pulsars within our Galactic Plane; an alternate theory involving he interactions between stars when stellar densities are high may apply to the one double-neutron-star binary pulsar found in a globular cluster.

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