= Solution
An <X-ray binary> contains a compact accretor supplied by a <donor star>. Most bright systems contain a <neutron star> or <black hole>. Gas arrives by <Roche-lobe overflow>, a captured <stellar wind>, or donor outflows, commonly forming an <accretion disk>. The primary energy source is the release of gravitational binding energy during <accretion>, with a characteristic <accretion luminosity>
$$
L\sim\frac{GM\dot M_{\rm acc}}{R_{\rm in}}\sim\epsilon\dot M_{\rm acc}c^2.
$$
For a <neutron star>, $R_{\rm in}$ can be near its material radius; for a <black hole>, radiation is produced by the flow outside the horizon. For $M\sim1.4M_\odot$ and $R\sim10\,\mathrm{km}$, $GM/(Rc^2)\sim0.2$, so accretion can release much more energy per unit mass than hydrogen burning. The hot inner flow, boundary layer or accretion column emits <X-rays>.
In a <high-mass X-ray binary>, a massive, relatively short-lived donor often supplies gas through a strong wind or an equatorial outflow; some systems instead undergo <Roche-lobe overflow>. These objects trace young stellar populations. In a <low-mass X-ray binary>, a lower-mass donor commonly fills its <Roche lobe> and feeds a disk. Such systems can persist in older populations. These mass labels refer to the donor, not the compact accretor.
A magnetized <neutron star> can channel accretion onto its poles, producing an <accreting X-ray pulsar> as the star rotates. Accretion transfers <angular momentum>, so changes in spin constrain the flow and magnetic coupling. A <Type I X-ray burst> has a different origin: accumulated <hydrogen> or <helium> undergoes unstable thermonuclear burning on a <neutron star> surface. It rises rapidly and then cools as the fuel is exhausted. A <black hole> has no material surface supporting the same surface-fuel mechanism.
Orbital motion and optical observations of the donor constrain masses, with inclination and donor-model uncertainties. A compact mass exceeding plausible stable <neutron star> masses supports a <black hole> interpretation. Rapid variability probes the small emitting region, while disk spectra and recurrent outbursts probe <accretion> and its instabilities. The <Eddington luminosity>,
$$
L_{\rm Edd}=\frac{4\pi GMc}{\kappa},
$$
is obtained by balancing radiative acceleration $\kappa L/(4\pi r^2c)$ against $GM/r^2$; it is a useful luminosity scale under the assumed isotropic, opacity-controlled force law. Geometry and time dependence can complicate its application. \b[X-ray binaries reveal compact stars through efficient gravitational accretion, with pulsations, bursts and orbital dynamics distinguishing their physical components.]
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