Star brightness and colour

Five magnitudes is exactly a factor of 100 in brightness, so Sirius looks about 25 times brighter than Polaris.

A scale that runs backwards

Astronomers measure how bright a star looks with the magnitude scale, and it surprises everyone at first: smaller numbers are brighter. The idea is ancient. Ptolemy's star catalogue in the second century sorted stars into six classes, the brightest "of the first magnitude" and the faintest visible ones of the sixth. In 1856 Norman Pogson turned this into mathematics. He defined a difference of five magnitudes as exactly a factor of 100 in brightness. One magnitude is then the fifth root of 100, about 2.512.

The scale had to stretch past 1 for the brightest objects, so very bright stars have magnitudes near zero or below it. In the Bright Star Catalogue, Vega is 0.03 and Sirius, the brightest star of the night sky, is −1.46. Planets can go further: Venus reaches about −4. At the other end, Pogson took magnitude 6 as the faintest a person can see without a telescope, though under a truly dark sky sharp eyes can do a little better.

Working out brightness ratios

To compare two stars, take the difference in magnitude, Δm, and work out 2.512 to the power Δm, or more exactly 10^(0.4 × Δm). Sirius (−1.46) and Polaris (2.02) differ by 3.48 magnitudes, so Sirius looks 10^(0.4 × 3.48) ≈ 24.7 times brighter. Sirius against Deneb (1.25) is 2.71 magnitudes, about 12 times. A 6th-magnitude star is about 244 times fainter than Vega. These are apparent brightnesses, how bright stars look from Earth. Deneb is actually one of the most luminous stars we can see; it only looks modest because it is very far away.

How many stars can you see?

The Bright Star Catalogue lists 9,110 objects, nearly every star down to magnitude 6.5. Count its entries and 5,080 are magnitude 6.0 or brighter over the entire sky. At any moment only half the sky is above the horizon, and stars near the horizon are dimmed by the thick air they shine through, so even on a perfect night you see a couple of thousand at most. In a city the glow of street lights brightens the background sky and drowns the faint ones; often only stars brighter than magnitude 3 or 4 remain. There are just 518 stars of magnitude 4.0 or brighter in the whole catalogue, and those 518, plus a few fainter ones in the lines, are the stars in this course's model.

Star colours

Look carefully and stars are not all white. Betelgeuse is clearly orange, Rigel blue-white, Antares reddish, Capella yellowish. The colour tells the temperature of the star's surface: cooler stars glow red and orange, hotter ones white and blue. Astronomers measure colour by comparing brightness through a blue filter (B) and a yellow-green filter (V). The difference B−V is the colour index. A hot blue-white star such as Rigel has B−V near zero (−0.03 in the catalogue); Betelgeuse has 1.85 and Antares 1.83. The model turns each star's B−V into a colour with a standard approximation, so the orange giants of winter and summer stand out.

Why do faint stars look white even when they are red? The colour-sensing cells in the eye, the cones, need more light than the rod cells that work in the dark. Below a certain brightness only the rods respond, and rods do not see colour. That is why colour is easiest to see in the brightest stars, and why binoculars, which gather more light, show star colours far better than the naked eye.