The Hertzsprung–Russell Diagram

By the early twentieth century, astronomers had measured surface temperatures and luminosities for thousands of nearby stars — using photometry, parallax, and the physics you saw in Lessons 1–4. Somebody, eventually, had the obvious idea: plot all those stars on a single chart, with one quantity on each axis. When they did, something astonishing happened. The stars did not scatter randomly. Instead they fell into well-defined groups — a long diagonal band, a few scattered clumps, and two compact regions at the extremes.

The resulting diagram — conceived independently by Ejnar Hertzsprung (a Danish astronomer) and Henry Norris Russell (an American) around 1911–13 — is now known as the Hertzsprung–Russell (HR) diagram. It is the single most important visualisation in stellar astrophysics, and it is the centrepiece of OCR Module 5.5.2.

This lesson introduces the HR diagram, explains its axes and principal features, and prepares you for Lesson 6 on stellar evolution, where we trace how individual stars move around the diagram throughout their lives.

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What The HR Diagram Plots

The HR diagram is a scatter plot of stars with:

• x-axis: surface temperature T (in kelvin), usually plotted decreasing from left to right — hot stars on the left, cool stars on the right.
• y-axis: luminosity L (often expressed as L/L_☉), plotted on a logarithmic scale, increasing upwards.

This unusual convention — temperature decreasing to the right — is a historical accident, but it is universal, and OCR expects you to draw diagrams in this orientation. If you reverse the axis, you will lose marks. An equivalent version uses spectral class (O, B, A, F, G, K, M) on the x-axis instead of temperature, which is just a categorical version of the same axis.

graph TD
    subgraph HRD
    A[Upper Left:<br/>Hot<br/>Luminous]
    B[Upper Right:<br/>Cool<br/>Luminous<br/>= Giants]
    C[Lower Left:<br/>Hot<br/>Faint<br/>= White Dwarfs]
    D[Lower Right:<br/>Cool<br/>Faint<br/>= Red Dwarfs]
    end
    A -. main sequence .- D
    B -. red giants .- A

The four corners tell you the basic architecture:

• Upper left: hot and luminous (O and B supergiants).
• Upper right: cool but luminous (red giants and supergiants — they are large, not hot).
• Lower left: hot but faint (white dwarfs — they are small, not cool).
• Lower right: cool and faint (red dwarfs and M-type main-sequence stars).

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The Main Sequence

The dominant feature of the HR diagram is a diagonal band running from the upper left to the lower right — the main sequence. Roughly 90% of all stars, including the Sun, lie on this band. On the main sequence:

• Stars fuse hydrogen to helium in their cores via the proton–proton chain or the CNO cycle.
• Their luminosity and temperature are tightly correlated: more massive stars are both hotter and more luminous.
• They stay on the main sequence for most of their lives — the Sun spends about 10¹⁰ years there.

The main sequence is not a path that an individual star follows; it is a locus of stable configurations. A star born with a given mass settles onto the main sequence and stays there, roughly in one place, until its core hydrogen runs out. The position on the main sequence is determined by mass: from roughly 0.08 solar masses (just massive enough to sustain hydrogen fusion) at the lower end, up to 100 or more solar masses at the upper end.

The main sequence relation is approximately:

• Mass increases → luminosity increases steeply (L propto M^{3.5} approximately for intermediate masses).
• Mass increases → temperature increases (hotter cores, hotter surfaces).
• Mass increases → radius increases (larger stars).

A massive O star might have M = 30 M_☉, L = 10⁵ L_☉, T = 40 000 K, R = 10 R_☉. A red dwarf might have M = 0.3 M_☉, L = 10⁻² L_☉, T = 3500 K, R = 0.3 R_☉. Between these extremes lies the entire main sequence.

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Red Giants And Red Supergiants

Above the main sequence, in the upper right corner, sit the red giants and red supergiants. They are cool (T approx 2500 ext{–}4500 ext{ K}) but extraordinarily luminous. How can that be? The Stefan–Boltzmann law gives the answer:

L = 4π r² σ T⁴

If T is low but L is high, then r must be enormous. Red giants have radii of tens or hundreds of solar radii. Red supergiants like Betelgeuse and Antares have radii of hundreds to over a thousand solar radii — large enough to swallow the inner planets if placed at the centre of our solar system.

Red giants are not a separate sequence of stars in the sense that main-sequence stars are. They are post-main-sequence stars — stars that have finished burning hydrogen in their cores, and have expanded and cooled as a result. We shall trace this process in detail in Lesson 6.

A useful distinction:

Type	Radius	Typical T	Typical L
Red giant	10–100 R_☉	3000–4000 K	100–10³ L_☉
Red supergiant	100–1500 R_☉	3500–4000 K	10⁴–10⁶ L_☉

Red giants evolve from low-mass main-sequence stars (less than 8 M_☉), and red supergiants from high-mass main-sequence stars (more than 8 M_☉). The dividing line matters enormously for what happens next.

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White Dwarfs

In the lower-left corner of the diagram sit the white dwarfs. They are hot (T approx 8000 ext{–}30 000 ext{ K}) but intrinsically faint — far below the main sequence. Again the Stefan–Boltzmann law explains this: if T is high but L is low, r must be small.

White dwarfs have radii of about 5000–10 000 km — roughly the size of the Earth. They contain about half the mass of the Sun in a volume smaller than the Earth, giving densities of 10⁹ kg m⁻³. A teaspoonful of white-dwarf material would weigh several tonnes on Earth.