## Luminosity (or Absolute Magnitude)

The Luminosity of a star is the total amount of energy it emits per second. The absolute magnitude of a star usually refers to the total amount of energy of a certain kind of light (like visual or radio), but can be corrected to include all kinds of light. (Absolute magnitude is really just the apparent magnitude a star would have if it were at a distance of 10 parsecs from the Earth.) The range of stellar luminosities is enormous! The most luminous stars have luminosities 100,000 times greater than the Sun; the least luminous stars have luminosities 10,000 times smaller than the Sun.

Luminosity, or absolute magnitude, is not as easy to measure as flux, or apparent brightness. To measure a star's flux, you simply point a telescope at the star and calculate how much energy reaches the telescope per second. The measurement tells us how bright the star looks. However, to find luminosity, we need to know how bright the star really is, how much energy it is emitting.

Stars may look bright (or faint) for two reasons. The first is that it may really be bright (or faint). The second is that it may be relatively close (or very far away). Suppose we have two stars with exactly the same true luminosity. Imagine that we put one of those stars where the Sun is and put the other one trillions of miles away. The star that is farther away will look fainter to us, even though we know that it is really emitting the same amount of energy as the star that is close to us. This means that in order to find the luminosity of a star, we must first determine its distance. (We can do this by the method of parallax , or by using some other method.)

Once we know the star's distance, it is easy to use the apparent magnitude to find its absolute magnitude and estimate its luminosity. All we have to do is use a simple formula (right).

This formula states that the absolute magnitude of a star is simply its apparent magnitude + 5 - (5 times the log of the star's distance). This may sound complicated, but it is easy to plug into a calculator. Once you do the calculation, you have the Absolute Magnitude (and the Luminosity)!

There is a simple formula which relates the luminosity of a star to its mass for stars on the Main Sequence. It is usually more difficult to find a star's mass than its distance. However, if the star is part of a binary system, we may be able to determine its mass (and therefore its luminosity) without calculating its distance. (Actually, in this case we could use the formula above to find the distance to the star; this is important for stars which are too far away for us to be able to measure their distance through the method by parallax.) The relation between a star's mass and its luminosity is simply that the more massive a star is, the more luminous it is. This is because more massive stars have more gravity and therefore must fuse hydrogen faster to produce enough radiation pressure to support the star against gravity. Lighter stars, which do not have as much mass, have lower gravities and therefore do not fuse their materials as fast. The mass luminosity relation is shown below: