The Eddington luminosity (also referred to as the Eddington limit) of a source is defined as the maximum luminosity where the continuum radiation force outwards balances the gravitational force inwards in hydrostatic equilibrium. When exceeding the Eddington luminosity, a star would initiate a very intense continuum-driven stellar wind from its outer layers. Since most massive stars have luminosities far below the Eddington luminosity, however, their winds are mostly driven by the less intense line absorption. The Eddington limit is invoked to explain the observed luminosity of accreting black holes such as quasars.
Originally, Sir Arthur Stanley Eddington took only the electron scattering into account when calculating this limit, something that now is called the classical Eddington limit. Nowadays, the modified Eddington limit also counts on other continuum processes such as bound-free and free-free interaction.
Read more about Eddington Luminosity: Derivation, Super-Eddington Luminosities, Other Factors