Background Information

Magnitudes

Astronomers use a very old, archaic, and annoying method to determine the brightness of celestial objects: the magnitude system. An object’s magnitude is a measure of its flux, or brightness, as measured through a specific filter. A bright star will have a low magnitude, and a dim star will have a high magnitude. Therefore, if star A has a magnitude of 1 and star B has a magnitude of 2, star A will be brighter than star B. Although stars A and B are separated in brightness by only one magnitude, this does not mean that star A is twice as bright as star B. In the magnitude system, star A is actually about 2.5 times brighter than star B. This means magnitudes are logarithmic (and not linear). If we say that star C has a magnitude of 3, then star A will be 2.5*2.5 = 6.25 times brighter than star C.

There are two definitions of magnitude: apparent magnitude and absolute magnitude. Apparent magnitude is the brightness of an object as observed on Earth. This makes finding apparent magnitude very simple. All we do is look at a star and measure its brightness, and we have its apparent magnitude! Absolute magnitude, on the other hand, is a bit more complicated. Absolute magnitude is the brightness of an object, or apparent magnitude of an object, measured as if it were 10 parsecs away from the observer. For example, the Sun has an apparent magnitude of -26.74, as measured in the visual filter, but if we were able to move the Sun to a location 10 parsecs from Earth, then we would see it as a star with an apparent magnitude of 4.83. So the absolute magnitude of the Sun is 4.83. Notice that magnitudes do not have to be positive! Many objects have negative magnitudes.

Apparent and absolute magnitude are related to distance through the following equation, called the distance modulus:

M - m = 5·log(d) - 5

Where m = apparent magnitude, M = absolute magnitude, and d = distance, measured in parsecs. So if we can find the apparent and absolute magnitudes of a star, we can calculate its distance from us using the above equation.

Note: Many websites will give the magnitude of a star without saying which filter the magnitude was measured in. The stated magnitude is generally assumed to have been measured in the visual (V) filter, but this is sloppy. We will state the filter the absolute magnitude was measured in as a subscript (Mr = absolute magnitude in the red filter), and the apparent magnitude of a filter will be given as the filter’s notation, without the prime (r = apparent magnitude in the red filter).