Hertzsprung-Russell Diagram
The Hertzsprung-Russell diagram is a graph of stars by brightness and surface temperature that reveals the main sequence, giants, and white dwarfs.
Definition
The Hertzsprung-Russell diagram, or H-R diagram, is a graph that sorts stars by how bright and how hot they are: hot stars on the left, cool stars on the right, bright stars at the top, dim stars at the bottom, with most stars falling along a diagonal stripe called the main sequence. Precisely, it plots luminosity (or absolute magnitude) against surface temperature (or spectral type or color index), with temperature decreasing to the right; about $90\%$ of stars lie on the main sequence, red giants and supergiants occupy the upper right, and white dwarfs the lower left. Because $L = 4\pi R^2 \sigma T^4$, lines of constant radius run diagonally across the diagram, which is why giants sit upper right and white dwarfs lower left. The main sequence is a sequence in mass, and a star's track across the diagram over time traces its evolution.
Example
The Sun sits near the middle of the main sequence, Betelgeuse is cool but very bright and sits upper right, and a white dwarf is hot but dim and sits lower left. Sirius A, at about $9{,}900^\circ\text{C}$ and $25$ times the Sun's luminosity, sits above and left of the Sun, while its companion Sirius B is hotter yet only about $1/40$ as bright as the Sun. Plotting a globular cluster shows a main sequence ending at a turnoff point; the turnoff mass of around $0.8$ solar masses for the oldest clusters gives ages of $12$ to $13$ billion years.
Key Insight
The H-R diagram is not a map of where stars are in space; it is a chart of what kind of star each one is. A cool star can only be very bright if it is enormous, and a hot star can only be dim if it is tiny, so the diagram reveals size even though size is not one of its axes. Hertzsprung and Russell built it independently around 1910 with no theory of stellar structure, and the fact that stars fell into bands instead of scattering randomly was the clue that stars obey simple physical laws.