Star colour and temperature

Betelgeuse looks orange-red at about 3,600 K; Rigel looks blue-white at about 12,100 K.

Hot things glow, and the colour tells the temperature

Heat an iron poker in a fire and it first glows dull red, then orange, then yellow-white. Stars follow the same rule. Every hot object gives off light across many wavelengths, and the hotter it is, the shorter the wavelength where its output peaks. The relation is called Wien's law: peak wavelength = 2.898 million nanometre-kelvins divided by the temperature. For the Sun at 5,772 K that is about 502 nm, in the blue-green part of the spectrum.

Wait, the Sun is not blue-green. The curve is broad, and the Sun gives off plenty of red, yellow and violet light too. Our eyes mix the whole spread and the result is white; the Sun looks yellow mainly near the horizon, where the air scatters away blue. That is also why there are no green stars. A star whose peak is in the green also shines strongly in red and blue, and the mix looks white. A cool star such as Betelgeuse, at about 3,600 K, peaks near 805 nm in the infrared, so the visible part of its light is weighted to red and orange. Rigel at about 12,100 K peaks near 240 nm in the ultraviolet and looks blue-white.

Hotter means much brighter per square metre

Temperature also controls how much light each square metre of surface sends out. The Stefan-Boltzmann law says the output per area grows with the fourth power of temperature. Double the temperature and each square metre shines 2⁴ = 16 times as much. Sirius A, at about 9,900 K, emits (9,900 ÷ 5,772)⁴ ≈ 8.7 times as much light per square metre as the Sun. Total luminosity is that output times the surface area, which grows with radius squared. Put together: luminosity in Suns = radius² × (temperature ÷ 5,772)⁴. The model's readout uses exactly this formula, and the next units build on it.

In practice astronomers rarely measure a whole spectrum curve just to get a temperature. A quicker way is to photograph a star through two coloured filters, one passing blue light and one passing yellow-green "visual" light, and compare the two brightnesses. The difference is the colour index, written B−V. A hot star is brighter through the blue filter and has a small or negative index; a cool star has a large positive one. The Sun's B−V is about 0.66, Arcturus about 1.23 and Aldebaran about 1.54. Once the index has been matched to temperature using stars with well-studied spectra, two photographs are enough to estimate the temperature of thousands of stars at once.

O, B, A, F, G, K, M

When astronomers spread starlight into a spectrum, they see dark lines where atoms in the star's atmosphere absorb particular colours. The pattern of lines depends mostly on temperature. At Harvard College Observatory, Annie Jump Cannon simplified an earlier alphabetical scheme into seven classes ordered from hottest to coolest: O, B, A, F, G, K, M. Each class splits into ten subclasses, 0 to 9, so the Sun's G2 is a little hotter than G5. The International Astronomical Union adopted her system in 1922, and it is still used.