The HR diagram. The Hertzsprung-Russell diagram plots the luminosity (power output) of a star against its surface temperature, with hot stars on the left. Most stars lie on a diagonal band, the main sequence: this is where a star spends most of its life, fusing hydrogen into helium in its core. As a star changes, it moves across the diagram. The lines of equal radius come from the Stefan-Boltzmann law, L = 4πR²σT⁴: a star that is hotter and brighter than another of the same radius lies up and to the left.

R / R_Sun = √(L / L_Sun) / (T / 5772 K)²

Mass decides everything. A heavy star has a much higher pressure and temperature in its core, so it fuses hydrogen far faster. Its luminosity is about L ∝ M^3.5, and since the fuel is only proportional to M, the time on the main sequence is about t ≈ 10 billion years × (M/M_Sun)^−2.5. The Sun lasts 10 billion years. A 15 solar-mass star lasts about 10 million years, and a 0.3 solar-mass red dwarf for hundreds of billions of years (longer than the age of the universe).

Low-mass stars (up to about 8 solar masses). When the hydrogen in the core runs out, the core (now helium) shrinks and heats up, and hydrogen fuses in a shell around it. The outer layers swell up and cool: the star becomes a red giant. When the core reaches 100 million kelvin, helium fuses to carbon and oxygen. Later the helium runs out too, and the star becomes a giant again (the asymptotic giant branch), and throws off its outer layers as a planetary nebula. The core is left as a white dwarf, which is about the size of the Earth, and cools for ever. It does not fuse anything. It is held up by electron degeneracy pressure.

High-mass stars. A star of more than about 8 solar masses can fuse heavier and heavier elements: helium, carbon, neon, oxygen and silicon, each in its own shell, like an onion. Each stage is quicker than the last (silicon burning takes a day). Iron is the end of the line, because fusing iron takes in energy instead of giving it out. When the iron core cannot support itself, it collapses in a fraction of a second, and the outer layers are thrown off in a supernova. The remnant is a neutron star (for stars up to about 25 solar masses, at the start) or a black hole (for heavier ones).

Size. As a star leaves the main sequence its outer layers swell enormously. The Sun will become a red giant about 100 times its present radius, and a red supergiant can be about 1000 times the radius of the Sun. These sizes cannot be drawn to scale next to the main-sequence star, so the picture of the star is illustrative; use the radius bar to compare real sizes.

What the tracks leave out. The tracks are schematic. They are drawn through approximate values taken from published evolution models, and the colours and sizes of the shells in the cross-section are not to scale (the cores of giants are really tiny compared with the star). The ages are approximate. The masses at which stars end as white dwarfs, neutron stars and black holes depend on the details of the models (and on the chemical composition of the star).

Things to try. (1) Play the life of the Sun. What happens to its radius? (2) Compare how long a 1 and a 15 solar-mass star spend on the main sequence. (3) Which stars end as white dwarfs? (4) Turn on the lines of equal radius. How much bigger than the Sun does a red giant get? (5) Where is the red dwarf after 13.8 billion years (the age of the universe)?