Eddington Luminosity

\[L_E=\frac{4\pi GMm_p c}{\sigma_T}\]

Variables

LeEddington luminosity (W)

Ggravitational constant (m³/kg·s²)

Mmass of the object (kg)

mpproton mass (kg)

cspeed of light in vacuum (m/s)

sigmaTThomson scattering cross section (m²)

Description

What is this formula?

The Eddington luminosity is the maximum luminosity a celestial object can achieve when the outward radiation pressure balances the inward gravitational attraction acting on ionized gas.

When to use it

Use this formula in astrophysics when studying stars, quasars, neutron stars, or black holes accreting matter, especially when radiation pressure becomes significant.

Example

Calculate the Eddington luminosity for a star with solar mass.

Given:

M=1.989×10^30 kg

G=6.67430×10^-11 m³/kg·s²

mp=1.6726219×10^-27 kg

c=2.99792458×10^8 m/s

sigmaT=6.6524587×10^-29 m²

Formula:

Le=(4*pi*G*M*mp*c)/sigmaT

Substitution:

Le=(4*pi*(6.67430×10^-11)*(1.989×10^30)*(1.6726219×10^-27)*(2.99792458×10^8))/(6.6524587×10^-29)

Result:

Le≈1.26×10^31 W

This is approximately the Eddington luminosity of the Sun.

Applications

- Black hole accretion physics

- Stellar structure studies

- Quasar luminosity limits

- High-energy astrophysics

- Radiation pressure analysis