The Hertzsprung-Russell diagram

A map of stars

The Hertzsprung-Russell diagram, or H-R diagram, plots stars by luminosity and surface temperature. It is one of the most important tools in astronomy because it reveals patterns in stellar structure and evolution.

A common version places luminosity $L$ on the vertical axis and surface temperature $T$ on the horizontal axis, with temperature decreasing to the right. Hot blue stars lie on the left; cool red stars lie on the right.

Luminosity and temperature

A star's luminosity is the total power it radiates. The Stefan-Boltzmann law relates luminosity, radius, and effective temperature:

$L=4pi R^2sigma T^4$

This equation means that a star can be bright because it is hot, large, or both.

Lines of constant radius can be drawn on the H-R diagram. Giants are luminous partly because they are huge. White dwarfs are dim despite being hot because they are small.

The main sequence

Most stars lie on the main sequence, a diagonal band from hot, luminous stars to cool, faint stars. Main-sequence stars fuse hydrogen into helium in their cores.

Mass is the main property determining where a star lies on the main sequence. Massive stars are hotter and more luminous. Low-mass stars are cooler and fainter.

An approximate mass-luminosity relation for main-sequence stars is

$Lpropto M^{3.5}$

though the exponent varies by mass range.

Stellar lifetimes

A star's main-sequence lifetime is roughly fuel supply divided by luminosity. Since fuel scales approximately with mass, while luminosity rises steeply with mass,

t_{MS}sim rac{M}{L}

Using $Lpropto M^{3.5}$ gives

$t_{MS}propto M^{-2.5}$

Massive stars have more fuel but burn it vastly faster, so they live shorter lives.

Giants and supergiants

Giants and supergiants occupy the upper right region of the diagram. They are cool at the surface compared with hot main-sequence stars, but very luminous because their radii are enormous.

These stars are usually evolved objects that have exhausted core hydrogen and expanded dramatically.

White dwarfs

White dwarfs occupy the lower left region: hot but faint. Their small luminosity comes from their tiny radii, roughly Earth-sized. They are stellar remnants supported by electron degeneracy pressure, not by ordinary fusion.

Over time, white dwarfs cool and fade.

Color and spectral type

The H-R diagram is often labeled by spectral types O, B, A, F, G, K, M. O stars are hottest and bluest; M stars are coolest and reddest. The Sun is a G-type main-sequence star.

Spectral lines reveal temperature, composition, gravity, and other properties.

Evolutionary tracks

A star does not stay fixed on the H-R diagram forever. As it evolves, its luminosity and temperature change, tracing a path called an evolutionary track. Star clusters are especially useful because their stars formed at nearly the same time. The main-sequence turnoff reveals cluster age.

The big idea

The H-R diagram organizes stars by luminosity and temperature and reveals the physics of stellar structure and evolution. The main sequence represents core hydrogen fusion, while giants and white dwarfs represent later stages. A star's position on the diagram is a clue to its mass, radius, age, and fate.