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I am studying accretion disks around active galactic nuclei (AGN). I have seen two sets of models, sub-Eddington and super-Eddington accretion disks. What do these terms refer to in this case? I understand that the Eddington luminosity has something to do with the maximum luminosity of a body.

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The Eddington limit is a theoretical maximum accretion rate onto an accreting body under certain idealised circumstances.

The limit is calculated by assuming that the gravitational acceleration felt by the accreted material is exactly balanced by radiation pressure, under the assumptions that the material is completely ionised hydrogen, that the opacity is provided by Thomson scattering by electrons and that the accretion is spherically symmetric. Finally, it is assumed that the luminosity of the central object is proportional to the accretion rate onto it and usually the relationship used is that $L = \epsilon \dot{M}c^2$, with the efficiency $\epsilon=0.1$.

Sub-Eddington accretion is simply any mass accretion rate smaller than $10 L_{\rm Edd}/c^2$. Super-Eddington accretion is an accretion rate larger than this.

Super-Eddington accretion is possible because the accretion is not spherically symmetric (think of a disk) and $\epsilon$ may be much less than 0.1 think- of throwing a brick into a black hole; how much radiation does that emit?

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The Eddington luminosity is given by: $$L_{Eddington}=\frac{4\pi c GMm}{\sigma_T}.$$

This represents the maximum luminosity of a body, when there is a balance between the two primary forces - that of the radiation, acting out of the body, and that of the gravitational force of the star, acting inwards.

The terms sub-Eddington and super-Eddington refer to whether the body is above or below its Eddington limit. The Eddington limit does not give the maximum luminosity of a body.

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