# Luminosity

The luminosity  L is a term used mainly in astronomy for the radiated power (energy per time). If the total radiated power over all areas of the electromagnetic spectrum is considered, the luminosity is a synonym for " radiated power ".

All units of power can be used to specify the luminosity . In addition to the SI unit watt , erg per second was also common in astronomy in the past . In addition, the luminosity of the sun (L ) is used as a unit.

## Luminosity determination

If a radiation source emits its power uniformly in a solid angle , the result at a distance from the source is an energy flux density (energy per time and area) of: ${\ displaystyle L}$ ${\ displaystyle \ Omega}$${\ displaystyle R}$${\ displaystyle f}$

${\ displaystyle f = {\ frac {L} {\ Omega R ^ {2}}}}$

With isotropic radiation in all directions, the solid angle is and the following applies: ${\ textstyle \ Omega = 4 \ pi}$

${\ displaystyle L = 4 \ pi R ^ {2} \ cdot f}$

This equation is used to determine the luminosity of astronomical objects such as planets , stars, galaxies, etc. If one considers very large distances, as in the case of distant quasars or galaxy clusters , the equation must be expanded or interpreted differently, since relativistic effects become important.

Often the complication of determining luminosity is to determine the distance and the energy flux density . ${\ displaystyle R}$${\ displaystyle f}$

Determining distances is an important field in astronomy and is often very complex. The distance to nearby stars can be determined by measuring the parallax . A large number of such parallaxes were measured , for example, as part of the Hipparcos mission. A whole range of methods can be used to determine the distance of distant objects such as star clusters , galaxies, quasars, etc. Objects of known luminosity play an important role in this. They are called standard candles . If one measures the energy flow and sets z. For example , assuming isotropy , the formula for luminosity can be used to calculate distance.

Suitable detectors are required to measure the flow . In astronomy, CCD detectors are used in many places , which have displaced the previously used photo plates . In general, however, only part of the entire spectrum is observed, so that the measurement of the total luminosity is only possible to a limited extent.

## Luminosity of astronomical objects

The luminosity is usually a measure of the energy emission of a star in the form of electromagnetic radiation . In general, this is how a star gives off most of its energy, but not all of it. Other possibilities are for example energy loss as neutrino radiation or stellar wind .

The luminosity depends on the radius of the stars and their effective temperature . The relationship with the effective temperature is by definition, and the term temperature should not be taken too seriously here.

For stars, the luminosity in visible light with the spectral class is a parameter in the Hertzsprung-Russell diagram that describes the star evolution . The term is often restricted to a specific band (section of the electromagnetic spectrum) for specific research topics . It is common to speak of “X-ray luminosity” when referring to the radiation power integrated over the X-ray band .

### Luminosity classes

Even if the effective temperature of two stars is similar, their luminosity can differ significantly from one another, since their radii do not have to be the same. The determination of the effective temperature, which is reflected in the spectral type , is therefore not sufficient to classify the stars according to their luminosity.

In order to be able to classify stars according to their luminosity, the luminosity class was introduced instead . It is determined from the width of the spectral lines of a star, which in turn is a measure of its radius.

See also: Hertzsprung-Russell diagram , main series , giant star , mass-luminosity relation

### Luminosity of the sun

The sun is an isotropic radiator. At a distance of R  = 1  AU  = 1.496 · 10 11  m from the center of the sun, an energy of 1367 J per m² occurs every second  . The quantity 1367 J / (m² · s) is also known as the solar constant and is to be equated with the energy flux density in the luminosity formula. ${\ displaystyle f}$

The energy of 1367  J can be distributed over significantly more than 1 m² of the earth's surface, since the surface of the earth is not perpendicular to the direction of incidence of sunlight wherever the sun is not in the zenith ; the changing orientation of the earth's surface to the sun is the reason for the seasons .

The entire radiation of the sun is distributed over a spherical surface of the size

${\ displaystyle O = 4 \ pi R ^ {2} = 2 {,} 812 \ cdot 10 ^ {23} \, \ mathrm {m} ^ {2}}$

If you put this value and the solar constant in the formula for the luminosity, you get:

${\ displaystyle L = O \ cdot 1367 \, \ mathrm {\ frac {J} {m ^ {2} \ cdot s}} = 3 {,} 845 \ cdot 10 ^ {26} \, \ mathrm {W} }$

This represents the mean luminosity of the sun, which is often indicated with the symbol L .