Calculate the total amount of energy radiated per second by a star

By , 22nd April 2008 in Solar Physics

A star's luminosity is the total amount of energy radiated per second by the star and is used to compare stars in a way that does not depend on viewing position or the distance to the star.

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).

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 relation 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

We can see that for every additional distance unit, r, the light is spread over an additional area, r2.

We will use luminosity calculations in the next tutorial when we look at apparent and absolute magnitudes.

Further Reading

There are no comments for this post. Be the first!

Leave a Reply

Your email address will not be published.