Eddington limit

Radiation carries momentum. When photons from a luminous star or an accretion flow interact with nearby gas, the resulting outward force can oppose gravity. The Eddington limit names the luminosity at which these forces balance in a simplified model. For a spherical source whose opacity is dominated by electron (Thomson) scattering, a commonly used estimate is L_E ≈ 1.3 × 10^38 (M/M☉) erg s⁻¹, where M is the central object's mass and M☉ is the Sun's mass. The coefficient varies slightly with adopted constants and assumptions about composition and opacity. This is a luminosity scale, not a universal maximum mass for every star or black hole.

In a star, strong radiation pressure can help drive material away from the outer layers, so the Eddington balance is relevant to stellar structure and mass loss. In an accreting system, infalling gas releases gravitational energy; radiation from the hot flow can push against the incoming material. The simple balance therefore offers a benchmark for how rapidly a roughly spherical, radiatively efficient flow can shine while continuing to accrete. The outcome in real stars, disks and compact objects depends on their internal structure and on how energy and matter move.

The textbook derivation simplifies the system, notably by assuming spherical symmetry and a specified opacity. Accretion disks are not spherical, and matter, radiation and energy can be transported in ways the idealized calculation omits. Instabilities, convection, radiation trapping and direction-dependent emission can change the relationship between total luminosity and the force acting on gas. Astronomers use the term super-Eddington for systems whose inferred luminosity or accretion rate exceeds a chosen Eddington reference. Such reports do not mean that the underlying force balance is irrelevant: they point to departures from the assumptions of the simplest model, and the detailed physics remains an active research area.

The Eddington luminosity is often used to form the Eddington ratio, the luminosity divided by the estimated Eddington luminosity. This dimensionless comparison helps characterize how strongly a source radiates relative to the reference balance. It is also important in discussions of black-hole growth: the rate needed to build very massive black holes early in cosmic history motivates study of phases of rapid, potentially super-Eddington accretion. The ratio is an interpretive tool, not by itself a direct measurement of accretion rate or proof that an object is in a particular physical state.