Luminosity

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:

$m_{\mbox{star}}=m_{\mbox{sun}}-2.5\log _{10}\left({L_{\mbox{star}} \over L_{\mbox{sun}}}\cdot \left({{\mbox{dist}}_{\mbox{sun}} \over {\mbox{dist}}_{\mbox{star}}}\right)^{2}\right).$

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.