Home > Luminosity

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.

1 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 starFor alternate meanings see star (disambiguation Hubble Space Telescope of the Sagittarius Star Cloud in the Milky Way Galaxy. A star is any massive gaseous celestial body in outer space. Stars appear as shining points in the nighttime sky that twinkle bec with bolometric magnitudeIn astronomy, absolute magnitude is the apparent magnitude, m an object would have if it were at a standardized distance away. It allows the overall brightnesses of objects to be compared without regards to distance. Absolute Magnitude for stars M In stel ·10 has a luminosity of 10⁶L_s, whereas a dim star with bolometric magnitude +17 has luminosity of 10⁻⁵L_s. Note that absolute magnitudeIn astronomy, absolute magnitude is the apparent magnitude, m an object would have if it were at a standardized distance away. It allows the overall brightnesses of objects to be compared without regards to distance. Absolute Magnitude for stars M In stel 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.