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We know Eddington Limit (Eddington Luminosity) is calculated with this formula:

$$L_{Ed} \approx 3 * 10^4 * L_{sun} * \frac{M}{M_{sun}}$$

Example: For a black hole with $10^4 M_{sun}$, we get $$L_{Ed} = 1.16 * 10^{35} W$$

My question is what does it really show? What do we get by calculating this Number? Is this formula really used to calculate the luminosity or it is used for calculating mass?

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The Eddington limit represents the maximum luminosity that can be achieved by a body (such as the star) when there is hydrostatic equilibrium (http://astronomy.swin.edu.au/cosmos/H/Hydrostatic+Equilibrium). For luminosity greater than Eddington limit, the radiative force of the luminosity on matter exceeds the gravitational force on the matter. If the luminosity radiated by an accretion disk exceeds the Eddington limit, the matter falling towards the supermassive black hole can be blown away.

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    $\begingroup$ Welcome to Astronomy SE. Thanks for this useful answer. The question asks about black holes; does that have any bearing the answer? $\endgroup$
    – James K
    Apr 17, 2017 at 11:16
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    $\begingroup$ Note that the Eddington luminosity is just a type of luminosity unit. It does not represent an absolute maximum because Super-Eddington accretion rates are possible - see physics.stackexchange.com/questions/269393/… $\endgroup$
    – ProfRob
    Apr 17, 2017 at 12:58

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