A star can only be so bright. Its own light pushes outward on its gas (radiation pressure); its gravity pulls inward. Push out harder than gravity pulls and the star blows its outer layers off — so there’s a maximum luminosity for a given mass, the Eddington limit. It caps how fast black holes can eat and how massive stars can get. Slide the mass and read the ceiling.
The Eddington luminosity is the maximum luminosity at which an object’s outward RADIATION PRESSURE balances its inward GRAVITY: Lᴱₐₐ = 4πGMc/κ (mass M, opacity κ) — proportional to mass. Shine brighter than this and radiation pressure exceeds gravity, driving the outer layers away in a wind: it caps the luminosity (and hence mass) of stable stars and the accretion rate of black holes and quasars (super-Eddington accretion blows off the infalling gas). It is why the most massive stars hover near their Eddington limit and shed mass violently. A fail-loud self-check throws unless the Eddington luminosity scales linearly with mass. ◆ real astrophysics, node-verified.
The classic Lᴱₐₐ = 4πGMc/κ with constant electron-scattering opacity (exact under those assumptions); real objects can briefly exceed it (super-Eddington) via geometry — the radiation-pressure ceiling scaling with mass is exact.