Around 1911 to 1913, Ejnar Hertzsprung and Henry Norris Russell each plotted stars by two numbers: their spectral class (temperature) and their luminosity. Instead of a random scatter, the stars fell into a few distinct groups. This Hertzsprung–Russell (H–R) diagram is the most useful picture in stellar astronomy.
- Axes: luminosity goes up (on a log scale, from $10^{-4}$ to $10^{6}$ Suns); surface temperature goes along the bottom, increasing to the left, so O stars are on the left and M stars on the right.
- Main sequence: a band from hot and bright (upper left) to cool and dim (lower right). About 90% of stars, including the Sun, are here, fusing hydrogen in their cores.
- Giants and supergiants: upper right: cool but very luminous.
- White dwarfs: lower left: hot but very dim.
Why it works
Why must cool, luminous stars be huge, and hot, dim ones tiny? Because of luminosity, size and temperature: $L = 4\pi R^2\sigma T^4$. A star on the right is cool, so each square meter gives off little light; to be very luminous it must have an enormous surface. A star at the lower left is hot, so each square meter is very bright; to be dim overall it must be very small. Lines of equal radius run diagonally across the diagram: supergiants hundreds of times the Sun's radius, white dwarfs about the size of Earth.
Key idea
On the H–R diagram, luminosity increases upward and temperature increases to the left. Main-sequence stars lie on a diagonal band; giants sit above it to the right (big), white dwarfs below it to the left (small).
Worked examples
Worked example: A giant
A star has the Sun's temperature but is $400$ times as luminous. How big is it, and where does it sit?
- $L = R^2T^4$ with $T = 1$: $R = \sqrt{400} = 20$ solar radii.
- Same temperature as the Sun (class G), but far above the main sequence: a giant.
Answer: $20$ solar radii, in the giant region.
Worked example: Hot but dim
A star is $10{,}000$ times dimmer than the Sun ($L = 0.0001$) and twice as hot. How big is it?
- $R = \frac{\sqrt{L}}{T^2} = \frac{\sqrt{0.0001}}{2^2} = \frac{0.01}{4} = 0.0025$ solar radii.
- About $1700$ km: a white dwarf at the lower left.
Answer: $0.0025$ solar radii.
Common mistake
On almost every other graph, values increase to the right. On the H–R diagram temperature increases to the left, a tradition from when the axis was spectral class (O, B, A … M). Read the axis labels before reading a position. Check: blue O stars and the hot white dwarfs are on the left, red M stars and red giants on the right.