18.4 The H–R Diagram

The Hertzsprung-Russell (H-R) Diagram

The Hertzsprung-Russell diagram is one of the most useful tools in astronomy. It plots a star's luminosity against its surface temperature, and in doing so, reveals patterns that connect a star's brightness, temperature, size, and evolutionary stage. Once you understand how to read it, you can look at a star's position on the diagram and immediately learn a lot about what that star is and where it's headed.

Stars spend most of their lives on the main sequence, a diagonal band where they fuse hydrogen in their cores. Their position along that band depends on their mass. As stars age and exhaust their hydrogen fuel, they move off the main sequence into other regions of the diagram, becoming giants, supergiants, or white dwarfs.

Luminosity, Temperature, and Size Relationships

The H-R diagram has two axes, but pay attention to the unusual setup:

• Vertical axis: Luminosity (increasing from bottom to top), often expressed relative to the Sun's luminosity or as absolute magnitude.
• Horizontal axis: Surface temperature (increasing from right to left). This catches a lot of people off guard. The hottest stars are on the left side, not the right.

The diagram reveals a clear relationship between these properties. Hotter stars tend to be more luminous, and cooler stars tend to be less luminous, at least along the main sequence.

You can also infer a star's size from where it sits on the diagram. This works because luminosity depends on both temperature and surface area. The relationship is captured by the Stefan-Boltzmann law: $L = 4\pi R^2 \sigma T^4$, where $L$ is luminosity, $R$ is the star's radius, $T$ is surface temperature, and $\sigma$ is the Stefan-Boltzmann constant.

That equation tells you something important: if two stars have the same temperature but one is far more luminous, the brighter one must be larger. This is how you can read size off the diagram:

• Upper right (cool but very luminous): These stars must be enormous to produce so much light at low temperatures. These are the red giants and red supergiants.
• Lower left (hot but dim): These stars are very hot, yet their luminosity is low. That means they must be tiny. These are the white dwarfs.

Main Sequence Significance

The main sequence is the prominent diagonal band running from the upper left (hot, luminous, massive stars) to the lower right (cool, dim, low-mass stars). Stars on the main sequence are all doing the same basic thing: fusing hydrogen into helium in their cores.

What keeps a main sequence star stable is hydrostatic equilibrium. The outward pressure from nuclear fusion and radiation balances the inward pull of gravity. As long as a star has hydrogen fuel in its core, this balance holds and the star stays on the main sequence.

A star's mass is the single most important factor determining where it sits on the main sequence and how long it stays there:

• High-mass stars (upper left) are extremely luminous, but they burn through their hydrogen fuel quickly. A star 10 times the Sun's mass might spend only about 20 million years on the main sequence.
• Low-mass stars (lower right) are dim but incredibly fuel-efficient. A red dwarf with 0.2 solar masses could remain on the main sequence for hundreds of billions of years.

The Sun, for reference, has a main sequence lifetime of roughly 10 billion years and sits near the middle of the band.

Once a star exhausts the hydrogen in its core, it leaves the main sequence. Where it goes next depends on its mass: lower-mass stars swell into red giants and eventually shed their outer layers to become white dwarfs, while the most massive stars become supergiants and may end their lives in supernova explosions.

Stellar Classifications on the H-R Diagram

Giants, Supergiants, and White Dwarfs

Stars that have left the main sequence occupy distinct regions of the H-R diagram.

Giants are evolved stars whose cores have run out of hydrogen. They expand dramatically and cool at the surface, which shifts them to the upper right of the diagram. They have higher luminosities but lower surface temperatures than main sequence stars of similar mass. Arcturus, a red giant about 25 times the Sun's diameter, is a well-known example.

Supergiants sit across the very top of the H-R diagram. These are the most luminous stars, and they come in a range of temperatures. Betelgeuse is a cool red supergiant (around 3,500 K) with a radius roughly 700 times the Sun's. Rigel is a blue supergiant (around 12,000 K) that is extremely luminous and hot. Supergiants descend from the most massive main sequence stars and live relatively short lives.

White dwarfs occupy the lower left corner: hot but very faint. A white dwarf like Sirius B has a surface temperature around 25,000 K (hotter than the Sun) but is only about the size of Earth. That tiny surface area is why its luminosity is so low despite the high temperature. White dwarfs are the remnant cores of low- to intermediate-mass stars that have shed their outer layers. They no longer undergo fusion and slowly cool over billions of years.

Stellar Properties and Classification

A few key properties determine how a star is placed on the H-R diagram:

• Effective temperature is the surface temperature of the star, plotted on the horizontal axis. It's determined from the star's spectrum and color.
• Absolute magnitude measures a star's intrinsic brightness (how bright it would appear from a standard distance of 10 parsecs). This relates directly to luminosity on the vertical axis. Don't confuse it with apparent magnitude, which depends on how far the star is from us.
• Spectral classification organizes stars by their spectral features, which reflect surface temperature. The Harvard system uses the sequence O, B, A, F, G, K, M (from hottest to coolest). The Sun is a G-type star. This sequence maps directly onto the horizontal axis of the H-R diagram.
• Stellar composition also plays a role. Stars with different chemical abundances can have slightly different positions on the diagram and follow different evolutionary tracks, though for an intro course, mass and age are the dominant factors.