20 Introduction to the Magnitude System

Before proceeding, we need an introduction to the magnitude system. This system was developed in Ancient Greece, before telescopes or cameras or CCDs; so it may seem a little outdated.  It’s still in very common use among astronomers, however, probably because it is a very human system.

Imagine doing the following.  Go outside on a dark night and find a handful of the brightest stars in the sky; call these first magnitude stars.  Then find a handful that are a bit dimmer, call these second magnitude stars. Now take it down another step; find stars that look like they are as dim compared to the second magnitude stars as the second magnitude stars are to the first magnitude stars – call them third magnitude stars.  Keep going until you reach the faintest stars that you can see. Congratulations, you’ve developed a magnitude system.

One interesting thing to notice about this system is that the smaller the magnitude of a star, the brighter the star is.  A star with a magnitude of 1 is brighter than a star with a magnitude of 3. And a star with a magnitude of -1.47 (Sirius) is brighter than a star with a magnitude of 0.03 (Vega). “Where exactly do negative magnitudes come from?” you ask. History… stuff happened.

Another interesting thing about the magnitude scale is that it’s logarithmic; not because the Ancient Greeks liked math, but because your eyes’ response to light is logarithmic.  The brightest things you can see are many times brighter than the faintest things you can see, even if it doesn’t seem this way.

What this means for the magnitude system is that an object with a magnitude of 1 is about 2.5 times brighter than an object with a magnitude of 2, which is about 2.5 times brighter than an object with a magnitude of 3, and so on.  You can chain these factors of 2.5 together to find that an object with a magnitude of 1 is about [latex]2.5\times2.5\approx6[/latex]  times brighter than an object with a magnitude of 3 and about [latex]2.5\times2.5\times2.5\approx16[/latex]  times brighter than an object with a magnitude of 4.

The magnitude system is designed so that a star that is 100 times fainter has a magnitude that is +5 larger. Return to the star Proxima Centauri as an example.  This star has an apparent visual magnitude of 11.5, which is 5 magnitudes fainter than 6.5, which is about the faintest magnitude star your eyes can see. So Proxima Centauri is 100 times fainter than your eyes can see. (Chaining together 5 factors of 2.5 you get [latex]2.5\times2.5\times2.5\times2.5\times2.5[/latex] which is not quite 100, which is why a star with a magnitude of 1 is about 2.5 times brighter than one with a magnitude of 2.)

Some Example Stars

The table shows the name and apparent visual magnitude for several stars. Apparent magnitude means the magnitude that you see (that is apparent). Visual means that the magnitude was measured in the V-band. As the magnitude system has evolved, it has become simultaneously more convoluted and more precise. These magnitudes give the brightness of visual light (measured in the V-band) compared to an established brightness standard. (Since Sirius, Arcturus, and Rigil Kentaurus A are all brighter than this standard, they have negative apparent visual magnitudes.)