Eddington luminosity

Picture an object so bright that its own light starts to blow away the very gas trying to fall onto it. Light, remember, carries a tiny push (radiation pressure). For most things this push is negligible, but a fiercely glowing object feeding on infalling gas can shine so intensely that the outward shove of its light balances the inward pull of its gravity. The brightness at which these two exactly cancel is the Eddington luminosity — a natural speed limit on how brightly a body of a given mass can shine while still accreting.

The balance is between gravity pulling gas inward and radiation pressure pushing it outward, and both scale in predictable ways: gravity grows with the object's mass, while the light's push depends on its luminosity. Setting them equal gives a simple rule — the maximum luminosity is proportional to the mass. For each solar mass, the Eddington luminosity is roughly 30,000 times the Sun's own brightness. Push past it and radiation drives a powerful outflow, choking off the supply of fuel and limiting how fast the object can grow.

This limit shapes the cosmos at every scale. It caps how fast a black hole can feed and therefore how quickly supermassive black holes could have grown in the early universe — a real puzzle, since we see billion-solar-mass black holes when the universe was very young. It explains why the brightest stars shed mass in fierce winds and why X-ray binaries and quasars rarely outshine their Eddington brightness for long. An honest caveat: real systems can briefly exceed the limit ('super-Eddington' accretion) if the geometry lets radiation escape sideways while gas keeps falling in elsewhere.