quantity

luminosity

The total amount of energy a star emits per unit time.
11 related articles · 6 formulas

Description

Luminosity is the total amount of energy a star radiates into space every second. It is a fundamental measure of a star's power, often expressed in units of the Sun's luminosity. Unlike apparent brightness, which depends on distance, luminosity is an intrinsic property of the star itself, telling us how much nuclear fuel it is burning in its core.

History

The concept of luminosity as a measure of a star's total energy output was formalized in the late 19th and early 20th centuries, with key contributions from astrophysicists like Ejnar Hertzsprung and Henry Norris Russell, who used it in their famous diagram.

How it works

Luminosity is determined by the star's radius and surface temperature, following the Stefan-Boltzmann law: a hotter or larger star radiates more energy per unit area and thus has higher luminosity. For main-sequence stars, luminosity scales strongly with mass, so more massive stars are dramatically more luminous. In practice, astronomers measure a star's apparent brightness and distance to calculate its luminosity.

In practice

Luminosity is used to determine distances to stars and galaxies (via standard candles like Cepheid variables) and to classify stars into evolutionary stages.

Fun fact

The most luminous known stars, like R136a1, are millions of times more luminous than the Sun, but they live only a few million years because they burn fuel so rapidly.

Concept graph →

Formulas

$$\log_{10}(M/M_\odot) = a \log_{10}(L/L_\odot) + b$$
Relates stellar mass to luminosity.
What is in the formula
Mvariablestellar mass — mass kilogram
Lvariablestellar luminosity — luminosity watt
M_sunvariablesolar mass — mass kilogram
L_sunvariablesolar luminosity — luminosity watt
aconstantempirical slope of the relation — empirical slope = 3.5
bconstantempirical intercept of the relation — empirical intercept = 0
log10operatorbase-10 logarithm — logarithm base 10
$$L_{\rm Edd} = \frac{4\pi G M c}{\kappa}$$
Radius where radiation pressure balances gravity defines Eddington limit.
What is in the formula
L_{\rm Edd}variableEddington luminosity — luminosity watt
MvariableMass of the object — mass kilogram
cvariableSpeed of light — speed metre per second
GconstantNewtonian gravitational constant — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared
\kappaconstantOpacity of the stellar material — opacity = 0.034 square metre per kilogram
$$\dot{n}_{\text{ion}} = \frac{L}{R \, c \, (1-f_{\text{esc}})}$$
Ionization rate equals line luminosity divided by escape fraction and emission coefficient.
What is in the formula
\dot{n}_{\text{ion}}variableionization rate per unit volume — ionization rate metre per second per cubic metre
Lvariableline luminosity — luminosity watt
Rvariableemission coefficient — emission coefficient watt per cubic metre per steradian
cvariablespeed of light — speed of light metre per second
f_{\text{esc}}variableescape fraction of ionizing photons — escape fraction
$$M_{\rm BH} \propto L^\alpha \, {\rm FWHM}^\beta$$
Black hole mass scales with luminosity and line width.
What is in the formula
M_BHvariableBlack hole mass — mass kilogram
LvariableContinuum luminosity (e.g., at 5100 Å) — luminosity watt
FWHMvariableFull width at half maximum of emission line — line width metre per second
αvariablePower-law index for luminosity — power law index
βvariablePower-law index for line width — power law index
$$L_{\rm Edd} = \frac{4\pi G M c}{\kappa}$$
Maximum luminosity where radiation pressure balances gravity.
What is in the formula
L_EddvariableEddington luminosity — luminosity watt
MvariableMass of the object — mass kilogram
κvariableOpacity of the accreting material — opacity square metre per kilogram
GconstantNewtonian gravitational constant — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared
cconstantSpeed of light in vacuum — speed of light = 299792458 metre per second
$$L = 4\pi R^2 \sigma T^4$$
Luminosity relates to radius and temperature.
What is in the formula
LvariableLuminosity (total power radiated) — luminosity watt
RvariableRadius of the radiating body — radius metre
TvariableEffective temperature of the surface — temperature kelvin
\sigmaconstantProportionality constant relating blackbody radiated power to temperature — stefan boltzmann constant = 5.670374419e-8 watt per metre squared per kelvin to the fourth

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