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Degenerate Objects

The Evolution of X-Ray Binary Stars

A supernova explosion is the transforming event in the evolution of an x-ray binary. The implosion of a star's core to a neutron star causes a supernova that ejects most of the star's mass. The formation of a black hole within a star may also expel a similarly large quantity of mass in a supernova. This sudden mass loss can cause the binary system to become gravitationally unbound, with both stars flying away from each other at high velocity. For a binary star system with a circular orbit, unbinding occurs when the expelled mass is more than half of the system's mass. This suggests that in an x-ray binary, the star that is the mass donor to the compact object must have many times the mass of the compact object. Surprisingly, we find not only these systems, but also systems where the companion star is much less massive than the compact star.

X-ray binary stars fall into two classes: the high-mass systems, which have a donor star of more than 10 solar masses, and the low-mass systems, which have a donor star of less than 1 solar mass. This broad gap in mass reflects the different evolutionary paths that produce each system. The high mass systems follow our expectation for how a binary star survives a supernova. The low mass systems, on the other hand, need some mechanism that prevents the system from flying apart when it loses most of its mass.

High Mass Binaries

The star in a binary that is born larger is the star that exhausts its thermonuclear fuel first. If it is much larger than its companion, and if its mass does not change between its birth and its supernova, the binary system would generally not survive the supernova. For instance, if the stars in a binary system preserve their masses throughout their lives, and they were born with 30 and 20 solar masses, the 30 solar mass star would supernova, and the binary would be disrupted. In the absence of mass loss, the binary system could only survive if the stars were nearly identical in mass.

But stars lose mass over time. The mechanism for mass loss in a massive star is a wind driven by the pressure of light. The more massive the star, the more luminous it is, and the more effectively it drives a wind from its photosphere. A giant star may lose half of its mass in this way, evolving into a Wolf-Rayet star. This type of massive star has an atmosphere dominated by the products of thermonuclear fusion, such as helium, carbon, and oxygen, because the outer layer of hydrogen has been driven away. The Wolf-Rayet star would then be the progenitor of the supernova. The mass loss that drives this evolution also drives the progenitor star closer to the mass of its companion. If the companion star captures a significant fraction of this wind, it may even become more massive than the progenitor when the supernova occurs. In this way, a large number of binary stars protect themselves against a supernova explosion.

After a supernova, a surviving binary system contains either a neutron star or a black hole orbiting a very massive fusion-powered star. Because the fusion-powered star must at minimum be about the same mass as the supernova progenitor, and because the progenitor must be massive enough to enable its core to collapse to a neutron star rather than a degenerate dwarf, there must be a minimum mass for the fusion-powered star that reflects the minimum mass for a star to supernova. We see this limit in the observations; the fusion-powered star in an x-ray binary is more than 10 solar masses, which suggests that a supernova progenitor must be more than about 12 solar masses—taking into account the mass of the neutron star— at the time of the supernova. It also suggests that the binary system will experience a second supernova.

The tell tail signature that a high-mass x-ray binary has survived a supernova, beyond the fact that it contains a compact object, is that the binary orbit is very eccentric. The reason is principally that the sudden mass loss in a supernova raises the apastron of the companion star. For instance, if the binary orbit before the supernova is circular, the stars have a constant velocity that balance centrifugal force against the gravitational force. The supernova does not change the velocity of the progenitor's companion, but it does dramatically lower the gravitational force on that star, and it changes the position and velocity of the system's center of mass. From the standpoint of the companion, centrifugal force exceeds the gravitational force, so the star moves away from the supernova remnant star. An additional factor that makes add to the eccentricity is the kick that the remnant star receives during the supernova. The remnant star has a velocity that is different than the progenitor star's velocity. The change in velocity can be of order 100 km s-1, which is of order the orbital velocity of the progenitor. The binary orbit resulting from a supernova is therefore eccentric. This eccentricity is seen in the observations, where the apastron is often twice or more the periastron. We also see this eccentricity in a related class of binary system, radio pulsars orbiting massive main-sequence stars.

Low Mass Binaries

The existence of low-mass x-ray binaries would not be expected under the simple evolution that explains the high-mass binaries. The compact object in one of these systems is more massive than its donor star. A binary star must follow a much different evolutionary path if it is to survive a supernova and give us a low-mass system.

The most plausible theory for the creation of low-mass x-ray binary stars relies on the unstable transfer of mass when a star that is more massive than its companion is overflowing its Roche lobe. This mass transfer can occur if the distance between the stars is small. As gas flows from the larger star to the smaller star, the donor star swells, the distance between the stars decreases, and the flow becomes a flood until the whole binary system is engulfed in a common envelope of gas. The binary system evolves into a single massive star containing two cores. In this environment, the orbit of the cores should decay rapidly, so that in a short time most of the mass of this double-cored star lies outside of the orbit of the cores.

An interesting feature about gravity is that there is no gravitational force inside a uniform shell of matter. For instance, if the center of Earth were a hollow sphere, and we were able to place ourselves there, we would find ourselves floating. The orbiting cores of our star experience the same effect: the massive envelope of gas surrounding the orbit of the cores exerts no force on the cores, and has no effect on their orbits. This means that if the outer layers are suddenly removed, the orbit of the cores would be unaffected. So if one of the cores collapsed into a neutron star or a black hole candidate, it would release energy to drive ways the outer envelope of gas without disrupting its orbit with its companion core. Once the gas has cleared away, we would find a low-mass x-ray binary.

As with the high-mass systems, the low mass systems should reflect its evolution in the eccentricity of their orbits. The low-mass x-ray binaries have circular orbits, but because they are filling their Roche lobes, once could attribute this to the dissipation of orbital energy through tidal friction. Better evidence for our evolutionary theory is given by a related system, binary systems containing a radio pulsar orbited by a low-mass fusion-powered star. These systems also have circular orbits, and because the fusion-powered stars in these systems are not filling their Roche lobes, the effect of tidal friction on their orbits should be less. The orbital eccentricities of these systems are less than that of Earth's orbit around the Sun.

While this evolutionary theory is compelling , other possibilities have been suggested. One suggestion is to create the low-mass binaries from systems containing three stars. In this case, the third star carries away energy from the system after the supernova, keeping the remaining two stars gravitationally bound. Another very important theory pertains to low-mass x-ray binaries found in regions of high star density. If the density of stars is high enough, a low-mass x-ray binary can form when a main-sequence star captures a neutron star. The capture would require energy to be dissipated through tidal friction in the main-sequence star and through gravitational interactions with other nearby stars. This is the preferred explanation for the x-ray binaries we seen in globular clusters.

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