X-ray binaries are powered by mass accretion. The current concept of the mass accretion process, which determines the X-ray properties of XBs, is summarized later. In HMXBs, the stellar wind of a massive early-type companion feeds mass to the compact object. The mass accretion mechanism in LMXBs is different. LMXBs are contact binary systems in which the companion fills its own Roche equipotential lobe. As the binary separation tends to become smaller (hence the Roche lobe tends to shrink), matter from the companion overflows through the inner Lagrangian point L1 into the gravitational potential well of the compact object. This is called Roche-lobe overflow.
Matter from the companion star has angular momentum and cannot fall directly onto the compact object. It forms a disk-like structure circulating around the compact object. This is called an accretion disk. The gas rotates in the Keplerian orbit with velocity (GMx/r)1/2 at a distance r from the compact object. Since the inner layer moves faster than the outer layer, the gas is in differential rotation. In such a disk, viscosity acts to transport angular momentum outward, allowing gas to fall gradually inward. At the same time, viscous energy is dissipated for heating the gas. Thus, the gravitational potential energy is converted to rotational energy and thermal energy, as the gas falls into the deep potential well. Half of the gravitational energy released goes to rotational energy and the other half to thermal energy. The accretion process and the accretion disk structure have been studied extensively over the past decades. Shakura and Sunyaev  gave the most comprehensive description, which is often referred to as the standard accretion disk model.
In the case of a nonspinning black hole (Schwarzschild hole), the accretion disk extends to 3Rs, which is the radius of the innermost stable circular orbit (Rin). Inside the innermost disk, matter falls freely into the black hole. If the black hole is spinning (Kerr hole) in the same direction as the disk rotation, the disk can extend further inward. For an extreme Kerr hole, the innermost disk radius equals Rg. When the mass accretion rate is M, the amount of gravitational energy transformed to thermal energy is GMM/2Rin, which is the source of radiation. Eventually —6% of the rest mass energy of the accreting matter, Mc2, is radiated for a Schwarzschild hole, and —40% for an extreme Kerr hole.
According to the standard disk model, the accretion disk is geometrically thin and optically thick when the accretion rate M is sufficiently high (quantitative discussion follows). In such a disk, the thermal energy is radiated away in the form of blackbody radiation. The inner disk becomes as hot as 107 K, and the radiation is predominantly in the X-ray band. Depending on M, the X-ray luminosity Lx of black-hole XBs can be as high as 1038 erg s-1or may even go up to the Eddington limit, LEdd = 1.5 x 1038(M/M0) erg s"1.
In the case of neutron-star binaries, the accretion depends on the magnetic fields of the neutron stars. For strongly magnetized neutron stars, typically —1012 Gauss, the accretion disk stops at the magnetospheric boundary where the accretion pressure and the magnetic pressure are balanced, inside of which matter is funneled onto the magnetic poles. They manifest themselves as X-ray pulsars, an unambiguous signature of neutron stars.
On the other hand, most of neutron stars in LMXBs have much weaker magnetic fields of the order of 108 Gauss. Such weak magnetic fields do not disturb the accretion flow unless the accretion rate is extremely low, and the disk extends close to the neutron star surface. Since the radius of a canonical 1.4 M0 neutron star is considered to be comparable with 3Rs (—12 km), this situation is not much different from a Schwarzschild black hole. Hence, the structure of the accretion disk is expected to be similar in both cases.
However, there is a fundamental difference between a neutron star and a black hole. It is the presence or the absence of a solid surface. If the compact object is a neutron star, accreting matter eventually hits the neutron star surface and releases the rest kinetic energy in the dense neutron star atmosphere. This energy will be emitted as additional blackbody radiation. On the other hand, for a black hole, matter simply disappears across the event horizon. This difference provides an important clue to distinguish between a black hole and a neutron star, as discussed in Sect. 16.4.3.
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