Eddington Luminosity Calculator Formula
Understand the math behind the eddington luminosity calculator. Each variable explained with a worked example.
Formulas Used
Eddington Luminosity
eddington_lum = 4 * pi * 6.674e-11 * mass * 299792458 / 0.034In Solar Luminosities
eddington_solar = 4 * pi * 6.674e-11 * mass * 299792458 / 0.034 / 3.828e26Variables
| Variable | Description | Default |
|---|---|---|
mass | Object Mass(kg) | 1.989e+30 |
How It Works
The Eddington Luminosity
The maximum luminosity where radiation pressure on infalling matter balances gravitational attraction.
Formula
L_Edd = 4π G M c / κ
Using electron-scattering opacity κ ≈ 0.034 m²/kg for ionised hydrogen. For a solar-mass object, L_Edd ≈ 3.3 × 10⁴ L_sun.
Exceeding L_Edd causes radiation-driven mass loss (stellar winds, super-Eddington outbursts).
Worked Example
A 1-solar-mass object.
- 01L_Edd = 4π G M c / κ
- 02= 4π × 6.674e-11 × 1.989e30 × 2.998e8 / 0.034
- 03Numerator = 4π × 3.979e28 = 4.988e29
- 04L_Edd = 4.988e29 / 0.034 ≈ 1.47e31 W ≈ 38 300 L_sun
Frequently Asked Questions
Can stars exceed the Eddington limit?
Briefly, yes. Super-Eddington luminosities drive powerful mass outflows. Some very massive stars and accreting objects transiently exceed it.
Why does the Eddington limit matter for black holes?
It sets the maximum accretion rate onto a black hole. Faster accretion would blow away the infalling material.
Does opacity affect the limit?
Yes. Higher opacity lowers L_Edd because radiation couples more effectively to matter. The electron-scattering value is a minimum opacity for ionised gas.
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Open Eddington Luminosity Calculator