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Degenerate Objects

Compact Binary Stars

Main sequence stars are not the only stars one finds in binary systems. White dwarfs, neutron stars, and black hole candidates can also be found in orbit with fusion-powered stars. What makes these systems particularly interesting is that they can release massive amounts of energy when the stars are close together. Such compact binary systems give rise to many of the brilliant x-ray sources we see in the sky, as well as to many bright and variable optical sources. In all cases, the source of energy is the same: gas from one star is pulled onto the other star, releasing gravitational potential energy. The donor star can be a main-sequence star, a giant star, or a degenerate dwarf star. If the accreting star in the system is a white dwarf, the system is a cataclysmic variable, but if the accreting star is a neutron star or a black hole candidate, the system is an x-ray binary.

For mass transfer to occur between stars in compact binaries, these systems must be of order the size of a star. This means that the stars in these systems orbit very rapidly. Cataclysmic variables have orbital periods ranging from several hours down to a minimum of 80 minutes. The periods of x-ray binaries extend over a wider range, extending from over 100 days down to just over 10 minutes. By way of comparison, the orbital period of Mercury is 88 days, and the orbital period of an object skimming the Sun's photosphere in a circular orbit is 2.8 hours.

It may seem unlikely that stars would be born so close to each other that they nearly touch, but there is more to this than an accident of birth. The orbit of a binary star can decay, bringing the two stars closer together. Two mechanism can carry energy and angular momentum away from the system: a magnetized stellar wind, and gravitational waves. For most of the history of a binary system, orbital decay is driven by the stellar wind. Gravitational waves drive orbital decay only when the stars are very close together.

In a binary system, the star that is larger at birth is the star that evolves first into a compact object. If this star is less than about 8 solar masses, it becomes a degenerate dwarf, and the system can evolve into a cataclysmic variable. If this star is between about 8 and 40 solar masses, it becomes a neutron star, while if it is above 40 solar masses, it becomes a black hole candidate. Binary systems with either a neutron star or a black hole candidate can evolve into an x-ray binary.

An accretion disk is a common feature of all of these systems. An accretion disk is a disk of hot gas that orbits the compact object. Gas captured by a compact object cannot flow onto the object until it gives up angular momentum. The accretion disk is the mechanism that removes angular momentum from gas flowing to the surface of the compact object. In some systems, the disk extends down to the surface of the compact object, but in others, the inner region of the disk is disrupted by the magnetic field of the compact object. These details determine the appearance of a compact binary system.

Cataclysmic variables were first seen with ground-based telescopes. They stand out because they are bright, blue, and very variable at visual wavelength. Their accretion disks glow predominately at ultraviolet wavelengths, but the degenerate dwarf in the system also radiates x-rays.

In a cataclysmic variable, the companion star to the degenerate dwarf is undergoing something called Roche lobe overflow. The Roche lobe is a bulge on the side of the companion star facing the degenerate dwarf. This bulge is caused by the degenerate dwarf's tidal force. A point of unstable equilibrium lies on a line between the companion star and the degenerate dwarf; this point exists for every binary star, regardless of separation. Place an object just to the side of this point, and the object will fall into orbit around one or the other of the stars. As the orbit of a binary system shrinks, the atmosphere of the companion star can extend out to this unstable equilibrium point. When this happens, the atmosphere of that star start flowing onto the degenerate dwarf. If the star experiencing Roche lobe overflow is more massive than its companion, it becomes unstable, and it swells until it completely engulfs the degenerate dwarf. If the companion star is less massive than the degenerate dwarf, the transfer of mass is stable, being set by the decay rate of the orbit.

We see x-ray binaries in the way you would expect: with x-ray telescopes. These systems fall into two broad categories: the low-mass x-ray binaries, which have fusion-powered stars of 1 solar mass or less, and the high-mass x-ray binaries, which have fusion-powered stars of 10 or more solar masses.

The physics governing the low-mass x-ray binaries is similar to that of the cataclysmic variable. The fusion-powered star is experiencing Roche lobe overflow, and because it is always less massive than the accreting object, the flow of gas to the compact star is stable. The one difference from the cataclysmic variables is that a wider variety of stars can be the mass donor in a low mass x-ray binary. If the donor star is a helium burning star or a degenerate dwarf, the flow of gas from it to the compact object occurs for a much smaller separation than for a hydrogen-burning star. This accounts for the lower orbital periods found for x-ray binaries compared to the cataclysmic variables.

The mechanism causing mass flow within the high-mass x-ray binary is generally not Roche lobe overflow. The reason is that the donor star in the high-mass system is usually more massive than the accreting object. When the accreting object is a neutron star, the donor star is always more massive. Roche lobe overflow for such a system is unstable, and if it occurred, the whole system would soon be covered by a thick atmosphere. Such a system would appear to be a single star. The systems we see are either in the earliest stages of Roche lobe overflow, or they are expelling a wind that is being captured by the compact object.

The most interest aspect of the x-ray binaries is their existence. When a star undergoes a supernova, leaving behind a neutron star, it expels most of its mass almost instantaneously. This can unbind the binary system if the expelled mass is more than half of the mass of the binary system. Because the more massive star is the star that undergoes a supernova, one expects the binary system to become unbound unless the companion star is nearly the same mass as the star experiencing the supernova.

This picture of a binary system that survives a supernova explosion is certainly consistent with the high-mass x-ray binaries, especially if the star experiencing the supernova can shed some mass before the supernova, either expelling mass as a wind or transferring mass to its companion. With enough mass loss, the supernova progenitor can be less massive than its companion star, which would ensure the survival of the binary system. One characteristic of this theory that fits the observations very nicely is that the sudden loss of mass in the supernova creates a very eccentric binary orbit.

How a low-mass x-ray binary can survive a supernova is more puzzling. The theories for the creation of low-mass x-ray binaries have some of the feel of “just-so” stories. Of the several theories for these systems, the most plausible explanation is that the stars in a binary system merge into a single star before the supernova occurs. The merged star would have a single envelope but two cores. The cores would continue to orbit each other, but this orbit would decay rapidly. Eventually, most of the mass of the merged star would be outside of the orbit of the two cores; this mass has no effect on the orbit of the cores, and its loss would not change the orbit of the cores. Before merging into a single core, the larger core implodes, creating a supernova that drives away the common envelope. The core that implodes would become either a neutron star or a black hole candidate, and the remaining core would be the donor star. The creation of low-mass x-ray binaries under this theory is a rare event.

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