Eddington luminosity

The Eddington luminosity is a fundamental concept in astrophysics. It represents the maximum brightness, or luminosity, a celestial body can achieve while remaining stable. This stability occurs when there is a perfect balance between two opposing forces. Gravity pulls the material of a star inward toward its center. Simultaneously, radiation pressure creates an outward push. When these forces are equal, the star reaches a state called hydrostatic equilibrium.

At this point, the mean acceleration within the star is zero. If a star exceeds this limit, the outward radiation pressure overcomes gravity. This imbalance triggers an intense, radiation-driven stellar wind that pushes the star's outer layers away.

The mechanism behind this limit involves a complex interaction between light and matter. In the outer layers of a star, radiation pressure primarily acts on electrons. Because electrons have very little mass, they are easily pushed outward from the center. This movement creates a separation of electric charges between the electrons and the heavier protons. This separation generates a radially directed electric field. This field acts to lift the positive protons against the pull of gravity. When the electric field becomes strong enough to levitate these protons, both the electrons and protons are expelled together into space.

Different chemical compositions change the value of the Eddington limit. The standard derivation assumes a plasma made of pure ionized hydrogen. In this scenario, the limit is tied to the mass of a proton and the Thomson scattering cross-section. However, the limit shifts if the material changes. For instance, an evolved star with a pure helium atmosphere requires more energy to lose mass. A helium nucleus, or alpha particle, is nearly four times as massive as a proton. Consequently, a star would need twice the usual Eddington luminosity to drive off a pure helium atmosphere.

Extreme environments like black holes or neutron stars create even more unique conditions. At very high temperatures, high-energy photons can interact with nuclei or other photons. This process can create an electron-positron plasma. In such a state, the combined mass of the charge carriers is approximately 918 times smaller than the proton-to-electron mass ratio. Additionally, the radiation pressure on the positrons doubles the effective upward force per unit mass. Because of these factors, the limiting luminosity is reduced by a factor of approximately 1,836.

History shows how our understanding of this limit has evolved. Sir Arthur Eddington originally calculated this value by considering only electron scattering. This version is known as the classical Eddington limit. Modern scientists now use a modified Eddington limit. This updated model accounts for other radiation processes, such as bound-free and free-free radiation interactions. These refinements allow researchers to explain the observed luminosities of accreting black holes, such as quasars.

We observe many phenomena that challenge or exceed these theoretical boundaries. Some systems undergo super-Eddington accretion, where material falls onto a black hole at rates far above the limit. In these cases, the luminosity may saturate due to photon trapping. Photon trapping occurs when photons are reabsorbed by the dense, flowing material. Other events, like gamma-ray bursts, novae, and supernovae, exceed the Eddington luminosity by large factors for very short times. These events result in highly intensive mass loss. The star Eta Carinae provides a famous example. Its outbursts between 1840 and 1860 required super-Eddington winds to explain its massive loss of material.

Scientists also study why some objects remain stable even when they appear to exceed the limit. One theory involves atmospheric porosity. In this model, the stellar atmosphere consists of dense regions surrounded by lower-density gas. This structure might reduce the coupling between radiation and matter. Another possibility is the photon bubble effect. In radiation-dominated atmospheres, photon bubbles can develop spontaneously. These bubbles allow radiation to move more efficiently through the atmosphere than a uniform gas would allow. This effect may explain why some accretion discs maintain high luminosities without becoming unstable.