In physics, luminosity is the density of luminous intensity in a given direction.

In astronomy, luminosity is the amount of energy a body radiates in unit time. It is typically expressed in the SI unit watts or in terms of solar luminosities, L_s; that is, how many times more energy the object radiates than the Sun.

Luminosity is an intrinsic constant independent of distance, while in contrast apparent brightness observed is related to distance with an inverse square relationship. Brightness is usually measured by apparent magnitude, which is a logarithmic scale.

In measuring star brightnesses, luminosity, apparent magnitude (brightness), and distance are interrelated parameters. If you know two, you can determine the third. Since the sun's luminosity is the standard, comparing these parameters with the sun's apparent magnitude and distance is the easiest way to remember how to convert between them.

Computing between brightness and luminosity

Given a luminosity, one can calculate the apparent magnitude of a star from a given distance:

where

m_star is the apparent magnitude of the star, measured in

m_sun is the apparent magnitude of the reference sun, measured in

L_star is solar luminosity of the star, measured in multiples of the Sun's luminosity

L_sun is solar luminosity of the reference sun, which can be taken as 1

Dist_star is the distance to the star, measured in light years

Dist_sun is the distance to the reference sun, measured in light years

Or simplified, given m_sun = −26.73, dist_sun = 1.58 × 10⁻⁵ lyr:

m_star = − 2.72 − 2.5 · log(L_star/dist_star²)

Example:

How bright would a star like the sun be from 4.3 light years away? (The distance to the next closest star Alpha_Centauri)

m_sun (@4.3lyr) = −2.72 − 5 · log(1/4.3) = 0.45

0.45 magnitude would be a very bright star, but not quite as bright as Alpha Centauri.

Also you can calculate the luminosity given a distance and apparent magnitude:

L_star/L_sun = (dist_star/dist_sun)² · 10^{{(m_sun −m_star) · 0.4}}

L_star = 0.0813 · dist_star² · 10^{(−0.4 · m_star)} · L_sun

Example:

What is the Luminosity of the star Sirius?

Sirius is 8.6 lyr distant, and magnitude −1.47.

Lum(Sirius) = 0.0813 · 8.6² · 10^{−0.4·(−1.47)} = 23.3 × Lum_sun

You can say that Sirius is 23 times brighter than the sun, or it radiates 23 suns.

A bright star with bolometric magnitude ·10 has a luminosity of 10⁶L_s, whereas a dim star with bolometric magnitude +17 has luminosity of 10⁻⁵L_s. Note that absolute magnitude is directly related to luminosity, but apparent magnitude is also a function of distance. Since only apparent magnitude can be measured observationally, an estimate of distance is required to determine the luminosity of an object.

Hertzsprung-Russell diagram

The Hertzsprung-Russell diagram relates luminosity to color, stellar classification or surface temperature.

SI light units

SI light units
Quantity	SI unit	Symbol	Notes
Luminous energy	joule	J
Luminous flux	lumen or ( candela · steradian )	lm	also called Luminous power
Luminous intensity	candela	cd
Luminance	candela / square metre	cd/m2	also called Luminosity
Illuminance	lux or (lumen / square metre)	lx
Luminous efficacy	lumens per watt	lm/w