Magnitude (astronomy)

In astronomy, magnitude refers to the brightness of stars. The magnitude scale is a logarithmic scale, with increasing brightness represented as lower numbers. The apparent magnitude of a star, planet, nebula, or other astronomical object is based on the brightness of the object as seen from earth (or, more properly, from the viewpoint of the observer). The absolute magnitude of an object is based on the brightness of the object to an observer 10 parsecs distant.

The original magnitude scale was a sorting of stars into "first magnitude" through "sixth magnitude". The scale has since developed to be continuous and open-ended, and logarithmic.

Apparent and absolute magnitudes of some well-known objects:

Magnitude

Based on a numbering system used by Hipparchus (sometime around 120-125 B.C. in Greece), stars are numbered according to their brightness as they are seen from Earth. The brightest are of the first magnitude, the next brightest the second magnitude, continuing to the sixth magnitude, which are the faintest naked-eye stars, and so on. Today this is called apparent magnitude. Without a telescope, Hipparchus created a catalogue of 1080 stars that could be seen in each constellation. He noted their positions, and rated their brightness.

Hipparchus' catalogue was later edited and increased by Ptolemy which he published in the Almagest (possibly between 127 and 150 A.D.), one of the most prominent works in the history of astronomy. Today, with ground based telescopes, we can see to about 22^nd magnitude.

In 1856, Norman Pogson replaced the system developed by Hipparchus and Ptolemy, with one based on mathematics but matching, as much as he could, the old system. He used the formula:

$m=-2.5*log{\frac {F}{F_{stand}}}\,$

• m - the magnitude
• F - is the flux from our star
• F_stand - is the flux from a standard star

Flux denotes the amount of energy emitted from a star that reaches Earth

• log - is a function denoting powers of ten in a number.

When the flux of the star is the same as the standard, then we have:

m = -2.5 log(1)

m = -2.5 * 0

m = 0

So if a star has the same flux as the standard star, its magnitude is zero. A negative magnitude indicates a star is brighter than the standard, usually the result when absolute magnitude is calculated. Absolute magnitude calculates apparent magnitude taking into consideration the distance of a star. By calculating the magnitude of all the stars as if they were a uniform distance away, the magnitude is measured in a uniform way. That distance is ten parsecs, about 32.6 light years distant. Apparent magnitudes are written in lower case m and absolute magnitudes are written with a upper case M.

Today, the standard star is Vega, with a defined absolute magnitude of M=0.0. Stars that have a brighter magnitude have a negative number and those that are dimmer have positive numbers.

Later investigations showed that the difference between each magnitude as denoted by Hipparchus was about 2.5 times brighter than the next greatest magnitude. In other words, a difference in 5 units of magnitude, e.g. from magnitude 1 to magnitude 6, corresponds to a change in brightness of 100 times. As technology developed to allow more accurate measurments, astronomers started assigning partial values rather than whole numbers, 2.45 or 2.75 for example, rather than rounding off to magnitude 2 or 3.

Stars that are brighter than the first magnitude are classed by numbers less than 1. The apparent magnitude of Rigel is m=0.12. Extremely bright stars have numbers that are less than zero or negative numbers. The brightest star in the night sky is Sirius with an apparent magnitude of m=-1.46 and the absolute magnitude of Rigel is M=-8.1. The Sun has an apparent magnitude of m=-26.7, since it is close, but an absolute magnitude of M=+4.8, the magnitude it would have if it were 10 parsecs from Earth.

At the present time there are no stars classified with an absolute magnitude brighter than -8.0 Some very dim stars have an apparent magnitude of 28, but absolute magnitude can be no fainter than about 16.