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Luminosity of Stars

How to calculate the total amount of energy radiated per second by a star

By , in Solar Physics

Luminosity of Stars
In astronomy, luminosity is the total amount of energy radiated by a star, galaxy, or another astronomical object per unit time. It is related to the brightness, which is the luminosity of an object in a given spectral region. In SI units luminosity is measured in joules per second or watts.

Luminosity, L, is the total outward flow of energy from a radiating body per unit time, in all directions and over all wavelengths.

The SI units of luminosity are Watts (W) which quantify the rate of energy transfer in joules per second.

Luminosity is the rate at which a star, or any other body, radiates its energy. It is the same as the classification of light bulbs. A 40W bulb radiates less energy than a 100W bulb. The same is true for stars, however, they radiate far greater quantities of energy. The energy output of our Sun is around 3.89x1026 W (that's 389 followed by 24 zeros!), and our Sun isn't even a bright star! As stars go, our Sun is a 20W bulb.

Because of the large quantities involved with luminosity, astronomers prefer to use a more convenient unit called a solar luminosity, given the symbol L. One solar luminosity is equal to the luminosity of our Sun, but even so, stars can be as high as 1x106L? so very large numbers cannot be avoided!

A star which has a luminosity of 2L is twice as luminous as our Sun, and a star of 0.5L is half as luminous.

Whereas flux is the energy received over a unit area, luminosity is the total energy output of the star. Since the star radiates in all directions (isotropically) we only receive a tiny fraction of the energy radiated which is how we observe flux and calculate apparent magnitude. It would be helpful to know the relationship between the flux observed at Earth and the star's luminosity (total energy output).

Imagine a star at a distance d radiating equally in all directions. Flux is measured with a detector (whatever type) and has a surface area of 1 m2 and is perpendicular to the star. From the diagram above we can see that as the star radiates in all directions and forms a sphere around the star.

From previous definitions, luminosity (L) is the total energy output per second and flux (F) is the total energy per second crossing a unit area of surface we can determine the relationship between flux and luminosity. The surface area of a sphere of radius d is:

Area=4 pi r^2
Equation 21 - Sphere, Surface Area of

So the flux, F, measured at Earth by the detector of unit area is given by:

Flux=L/{4 pi r^2}
Equation 22 - Flux and Luminosity

We can see from the equation that flux decreases as distance increases and we can also see that distance is squared. It follows from this that light obeys the inverse square law - the observed flux from a star is inversely proportional to the square of the distance between it and an observer. This is more clearly illustrated in the diagram below.

The Inverse Square Law

The brightness of a star seen from the Earth depends its intrinsic luminosity and also on its distance from the Earth. The observed brightness of a given star decreases inversely proportionally to its distance away. The presence of interstellar gas will further decrease the observed brightness. From the diagram we can see that for every additional distance unit, r, the light is spread over an additional area, r2.

Last updated: 2017-07-21

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