The Hertzsprung-Russell diagram and stellar evolution

Drawing the HR diagram

• y-axis: luminosity (often relative to the Sun, on a logarithmic scale, from about 10^-4 to 10⁶).
• x-axis: surface temperature, on a logarithmic scale, with temperature decreasing from left (about 40 000 K) to right (about 2500 K).

Hot stars are on the left; luminous stars are at the top.

The main groups

• Main sequence: a band from top left (hot, luminous, massive) to bottom right (cool, dim, low mass). Stars spend most of their lives here, fusing hydrogen into helium in their cores.
• Red giants and supergiants: top right, cool but very luminous, so (by L = σ4πr^2T4) very large.
• White dwarfs: bottom left, hot but dim, so very small.

Life cycles

• A star forms when a cloud of gas and dust collapses under gravity until its core is hot and dense enough for hydrogen fusion. It joins the main sequence.
• Low and medium mass stars (like the Sun): when core hydrogen runs out, the star swells into a red giant, fusing helium. It then sheds its outer layers as a planetary nebula, leaving a white dwarf that slowly cools.
• High mass stars: become red supergiants, fusing heavier elements up to iron. The core collapses, causing a supernova, leaving a neutron star or, for the most massive, a black hole.

More massive main-sequence stars are hotter and more luminous, and use up their fuel much faster.

Worked example

Two stars have the same surface temperature but one is 400 times more luminous. How do their radii compare?

1. L = σ4πr^2T4 with T the same, so L is proportional to r²
2. r ratio = sqrt(400)

Answer: The brighter star has 20 times the radius

Check yourself

1. Two stars have the same surface temperature. One is 400 times as luminous as the other. What is the ratio of their radii?
   Show answer

   20. L is proportional to r² at fixed T, so r ratio = sqrt(400) = 20.

2. A white dwarf has radius 7.0 x 10⁶ m and surface temperature 10 000 K. Find its luminosity, in units of 10²³ W, to 3 s.f.
   Show answer

   3.49 x 10²³ W. L = 5.67 x 10^-8 x 4π x (7.0 x 10⁶)² x (1.0 x 10⁴)⁴ = 3.49 x 10²³ W, about a thousandth of the Sun's.

3. How is the temperature axis of an HR diagram arranged?
   • Temperature increases from left to right
   • It is a linear scale starting at zero
   • Temperature is on the vertical axis
   • Temperature decreases from left to right
   Show answer

   Temperature decreases from left to right. By convention, hot stars are plotted on the left.

4. What process powers a star on the main sequence?
   • Fusion of hydrogen into helium in its core
   • Fusion of helium into carbon
   • Gravitational collapse alone
   • Fission of heavy elements
   Show answer

   Fusion of hydrogen into helium in its core. Main-sequence stars are fusing hydrogen in their cores.

5. Red giants are cool but very luminous. What does this tell you?
   • They are very close to Earth
   • They are very hot inside their surface
   • They have very large radii
   • They are very small
   Show answer

   They have very large radii. L = σ4πr^2T4: low T but high L requires a large r.

6. What will the Sun eventually become?
   • A white dwarf
   • A neutron star
   • A black hole
   • A supernova remnant
   Show answer

   A white dwarf. Low and medium mass stars end as white dwarfs after the red giant stage.

7. Where are white dwarfs found on the HR diagram?
   • Top right: cool but bright
   • Top left: hot and bright
   • Bottom left: hot but dim
   • Bottom right: cool and dim
   Show answer

   Bottom left: hot but dim. They are hot but very small, so they have low luminosity.

8. How does a high-mass main-sequence star compare with a low-mass one?
   • It is cooler and lives longer
   • It is dimmer and lives longer
   • It has the same temperature but a longer life
   • It is hotter, more luminous and has a shorter life
   Show answer

   It is hotter, more luminous and has a shorter life. It burns its fuel much faster.

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Sources

• Pearson Edexcel International Advanced Subsidiary/Advanced Level in Physics specification (XPH11/YPH11), Issue 3
• Pearson qualifications: International Advanced Levels Physics (2018)

Last updated 7 November 2026. Spotted a mistake? Tell us.