1. Accretion

The brightest sources in the X-ray sky are Galactic X-ray binaries. The brightest is usually Sco X-1 although its intensity is often surpassed by transient sources. In an X-ray binary, a compact star accretes matter from its companion. The gravitational potential energy of this matter is converted to kinetic energy and eventually to radiation, giving rise to the high observed luminosities. The compact star may be a white dwarf, neutron star, or black hole. In optical astronomy it is usual to refer to the heavier star in a binary system as the primary as it is usually the brighter star. In a high-mass X-ray binary the lighter, compact component is the X-ray emitter. Thus, in this dissertation I will refer to the compact, accreting component of the X-ray binary as the primary. I will refer to the donor star as the companion.

The energy that can be extracted from accretion increases as the radius of the compact object decreases. This is because the amount of gravitational potential energy that infalling matter loses increases as the radius of the accreting object decreases. For a star of radius R_x and mass M_x which accretes matter at a rate $\dot{M}$, the accretion luminosity is (see Frank et al. (1985) and references therein)

$${GM_{\rm x}\dot M\over R_{\rm x}}$$ (1)

assuming that all the kinetic energy of the accreted matter is converted to radiation at R_x. Neutron stars convert accreted mass to energy with an efficiency $\varepsilon$ = ${L_{\rm x}\over \dot M c^2}$ of $\sim$ 0.1 compared with 0.007 for thermonuclear fusion. An accreting neutron star emits radiation mostly in the energy range 1 keV-50 MeV (Frank et al. (1985)). A crude estimate of the upper limit to the luminosity of these sources may be obtained by equating the outward force on electron-proton pairs with the gravitational force. The resulting luminosity

$${4\pi G M m_{\rm p} c \over \sigma_{\rm T}}$$ L_Edd = (2)

$$\approx \left(\vphantom{{M\over M_{\odot}}}\right. {M\over M_{\odot}} \left.\vphantom{{M\over M_{\odot}}}\right)$$ (3)

is known as the Eddington limit. If the luminosity exceeds this value the radiation pressure from the source overcomes the gravitational force and accretion stops. This is only a rough guide as it assumes steady-state, spherical accretion.