Eddington Luminosity
The maximum steady luminosity before radiation blows a star apart.
Formula
Variables
Example
≈ 1.26×10³¹ W for each solar mass
How it works
The Eddington luminosity is the point where the outward push from a star’s light on ionized gas exactly balances the inward pull of gravity. It comes from comparing radiation pressure on free electrons, via Thomson scattering, with gravitational attraction on the proton-electron plasma; because the gas is electrically neutral, electrons and protons are effectively held together, so pushing on the electrons can drive the whole gas outward. If an object shines above this limit for long enough, material is no longer stably bound and accretion or the outer layers can be driven away.
When to use it
Use this when studying the brightness limit of stars, accreting neutron stars, black holes, and quasars, especially in problems involving radiation pressure or mass-dependent maximum luminosity. It is also useful for checking whether an observed source can be powered by steady spherical accretion.
Worked example, step by step
Find the Eddington luminosity of a 10-solar-mass object. Step 1: Write the formula L_Edd = (4πG M m_p c) / σ_T Step 2: Substitute values G = 6.674×10^-11 m^3 kg^-1 s^-2 M = 10 × 1.989×10^30 kg = 1.989×10^31 kg m_p = 1.673×10^-27 kg c = 2.998×10^8 m/s σ_T = 6.652×10^-29 m^2 Step 3: Compute the numerator 4πG M m_p c ≈ 4π × (6.674×10^-11) × (1.989×10^31) × (1.673×10^-27) × (2.998×10^8) ≈ 8.35×10^3 Step 4: Divide by the Thomson cross-section L_Edd ≈ (8.35×10^3) / (6.652×10^-29) ≈ 1.26×10^32 W Final answer: L_Edd ≈ 1.26×10^32 W for a 10-solar-mass object.
Common mistakes to avoid
- Using the mass of the Sun instead of the object’s mass in the calculation
- Forgetting that the formula assumes ionized gas and Thomson scattering, not arbitrary opacity
- Dropping the factor of 4π or mixing up cgs and SI units
Did You Know?
Beyond this limit radiation pressure overwhelms gravity, capping how fast black holes and massive stars can grow.
Share this formula
More in Astronomy & Space
View allEscape Velocity
IntermediateMinimum speed to escape a body's gravity.
Orbital Velocity
IntermediateSpeed of a circular orbit.
Kepler's Third Law
AdvancedRelates orbital period to semi-major axis.
Schwarzschild Radius
AdvancedEvent horizon radius of a black hole.
Hubble's Law
AdvancedRecession velocity of galaxies with distance.
Stefan–Boltzmann Law
AdvancedLuminosity of a star from radius and temperature.