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Observational Astronomy

X-rays from Compact Binary Stars

Compact binary systems are among the brightest x-ray sources in the sky. These systems are compact in two senses: one of the stars in the binary is either a compact star, such as a degenerate dwarf or a neutron star,or a black-hole candidate, and the distance between the stars is so small that the gravitational pull of the compact object is stripping the companion star of its atmosphere. The consequence of this compactness is that matter from the companion star flows to the surface of the compact star, usually through an accretion disk, converting gravitational potential energy into thermal energy, and then into electromagnetic radiation. For many of these systems, the electromagnetic radiation appears predominately in the x-ray band, although it can also appear in the ultraviolet and gamma-ray bands.

Compact binary systems are subdivided into two groups: the cataclysmic variables, which contain a degenerate dwarf, and the x-ray binaries, which contain a neutron star or a black-hole candidate.

Cataclysmic Variables

A degenerate dwarf, which is also called a white dwarf, has roughly the mass of the Sun confined to a sphere with roughly the radius of Earth. These stars are the remains of small stars that have burned their hydrogen and helium to exhaustion, and are of insufficient density to burn the remaining fusible elements. These stars are held up by the degeneracy pressure of their electrons. While they are very bright when young, degenerate dwarfs eventually cool to invisibility. When a degenerate dwarf is in a compact binary with a main-sequence or giant star, the system is called a cataclysmic variable.

The free-fall velocity at the surface of a white dwarf is less than 2% of the speed of light. This means that an object falling to the surface of a white dwarf releases gravitational potential energy that is less than 0.02% of its rest-mass energy. This is tiny compared to the energy released in hydrogen fusion, not to speak of the energy released in a free-fall to the surface of a neutron star. But even this small amount of energy translates to an absolute upper limit on temperature of about 120 keV, where I assume that 100% of the free-fall energy goes to thermal energy; this value is well in gamma-ray range of temperatures.

What we see is much tamer than implied by the absolute upper limit on temperature. When we observe the hottest cataclysmic variables, we see temperatures of several tens of keV, dramatically lower than the absolute maximum temperature. Why is this happening? The reason is that the electrons of the material falling into the degenerate dwarf's atmosphere are always much cooler than the ions. For instance, in some cataclysmic variables, the free-falling gas passes through a standing shock in the star's atmosphere. This shock is caused by the supersonic gas flowing onto the star striking the subsonic atmosphere. The shock that develops maintains a fixed position altitude in the atmosphere, and the gas flowing through the shock slows down and converts its free-fall energy into thermal energy. Behind this shock, the electrons and ions come to different temperatures, with the electron temperature lower than the ion temperature. The electrons come to an equilibrium temperature, where the energy flow from ions to electrons is offset by the radiative cooling of the electrons. So while the ions have a temperature not much lower than the maximum possible temperature, the electrons have a much lower temperature that balances heating though collisions with hot ions against cooling through various radiative processes. This cooler radiation appears as x-rays rather than gamma-rays.

X-Ray Binaries

X-ray binaries encompass a large class of objects involving neutron stars or black-hole candidates. Neutron stars are created in supernovae, and they are generally more massive than the Sun, with maximum masses around 2.5 solar masses—the precise mass depends on the physics of the interior, which is highly uncertain. Above this upper limit, the compact object under the theory of general relativity must be a black-hole because the pressure at the center of such a massive star cannot counteract the force of gravity.

The free-fall velocity at the surface of a neutron star is about half of the speed of light. The gravitational potential energy released when matter free-falls to the surface of a neutron star is therefore about 15% of the rest mass energy, which is much more than the 0.8% that is released in converting hydrogen into iron. The gravitational potentials of neutron stars and black-hole candidates provide the most effective mechanism of releasing energy from matter. But while the maximum possible temperature that can be achieved through this mechanism is a substantial fraction of the rest-mass energy of the matter, which for hydrogen places the maximum temperature at several hundred MeV, the characteristic temperatures seen in the radiation is in the tens to hundreds of keV range, so that the energy appears as x-rays and gamma-rays.

For neutron stars, about half of the gravitational potential energy is released as matter flows through the accretion disk, and the remainder is released when the matter falls from the accretion disk into the neutron star's atmosphere. If the black-hole candidates are in fact black holes, the gravitational potential energy is released only through the accretion disk, because black holes do not have a surface that matter can strike, but an event horizon towards which matter, from the standpoint of an observer far from the system, slowly settles.

In an accretion disk, the matter orbits the compact object many times as it slowly drifts to the compact objects. The viscosity in the accretion disk slowly converts gravitational energy into thermal energy. This slow heating of the matter is counteracted by the release of electromagnetic radiation; the temperature of the disk adjusts itself to balance the cooling against the heating. The accretion disk pages describe how the power released by an accretion disk is related to its minimum temperature. For a minimum temperature in the 1 keV range, the mass flow rate onto a solar-mass neutron star must be above 1038 ergs s-1, which makes these systems 104 time more luminous than the Sun.

For a black hole, the inner edge of the accretion disk does not extend to the event horizon. Black holes have a peculiar property: circular orbits around black holes only exits outside a certain critical radius beyond the event horizon. This critical radius is called the point of last stable orbit. For an object to orbit in a circle at this radius, it must travel at the speed of light. Inside this point, every orbit that starts parallel to the event horizon bends and meets the event horizon. This means that as matter in an accretion disk flows beyond the last stable orbit, it fall towards the event horizon, reaching the event horizon before it can complete a full orbit. Once on this path, the viscosity that had converted gravitational potential energy into radiation ceases to work, so that the gravitational potential energy remains with the matter as it falls to the event horizon.

The accretion of material into the atmosphere of a neutron star produces at least as much energy as is released in the accretion disk. If the neutron star has a weak magnetic field, the accretion disk extends to the neutron star's atmosphere, where the problem becomes very difficult from a theoretical standpoint. The interaction is between supersonic (half the speed of light) centrifugally-supported fluid and a pressure-supported subsonic atmosphere. What can be said from the temperatures seen in these systems is that the temperature characterizing the radiation is much lower than the temperatures encountered in a shock.

If the magnetic field on the neutron star is strong enough, it disrupts the inner-edge of the accretion disk before it reaches the star's atmosphere, and the material in the disk flows along magnetic field lines to the magnetic poles of the star, making the magnetic poles x-ray hot-spots on the neutron star. As the neutron star rotates, these hot spots change orientation or pass behind the star, making the x-ray luminity of such a star oscillate at the star's rotation period. These systems are called x-ray pulsars.

As stated above, most of the energy released from a neutron-star binary is gravitational potential energy. But nuclear fusion still plays a role in these systems. Normally the neutron star is accreting a mixture of hydrogen and helium onto its surface from its companion. This means that the atmosphere of an accreting neutron star is composed of hydrogen and helium under extreme pressures. This leads to the nuclear fusion of hydrogen and helium into heavier elements. In some systems, nuclear fusion burns hydrogen and helium as fast as it is added to the star, so that the energy of nuclear fusion is a small addition to the continuous release of gravitational potential energy, but in other systems, fusion cannot keep pace, and hydrogen and helium build up on the star until the star's atmosphere is unstable to a nuclear runaway. In a runaway, the lower part of the atmosphere of the star detonates, and this immediate release of nuclear energy exceeds the release of gravitational potential energy for a short time. This energy diffuses through the neutron star's upper atmosphere and is released as x-rays. These systems, which detonate regularly, are called x-ray bursters.

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