Stellar spectra and the Hertzsprung–Russell diagram

The spectrum–luminosity diagram (Hertzsprung–Russell, 1911–1913) places stars by spectral class (or temperature, increasing to the left) and absolute magnitude (or luminosity). Most stars (≈ 90 %) lie on the main sequence, which runs from upper left to lower right – they fuse hydrogen to helium in their cores (so does the Sun). At upper right are cool but large red giants and supergiants, at lower left small, hot, faint white dwarfs. On the main sequence luminosity depends on mass: roughly L ∝ M³·⁵ (for ≈ 2–20 M☉); the lifetime is t ∝ M / L ∝ M⁻²·⁵: the Sun lives ≈ 10 billion years, a 10 M☉ star about 30 million years, red dwarfs trillions of years. Spectroscopic parallax: find M from the star’s class on the diagram, then compute the distance from m – M = 5 lg d – 5.