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Spec mapping: OCR H556 Module 5.5 — Astrophysics and Cosmology (structure of the Hertzsprung–Russell diagram: luminosity (logarithmic) versus surface temperature (decreasing to the right); identification of main sequence, red giants, supergiants and white dwarfs; qualitative use to describe stellar evolutionary state). Refer to the official OCR H556 specification document for exact wording.
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.
The HR diagram is a scatter plot of stars with:
T (in kelvin), usually plotted decreasing from left to right — hot stars on the left, cool stars on the right.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:
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:
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:
L \propto M^{3.5} approximately for intermediate masses).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.
Above the main sequence, in the upper right corner, sit the red giants and red supergiants. They are cool (T \approx 2500\text{–}4500\text{ K}) but extraordinarily luminous. How can that be? The Stefan–Boltzmann law gives the answer:
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.
In the lower-left corner of the diagram sit the white dwarfs. They are hot (T \approx 8000\text{–}30 000\text{ 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.
White dwarfs are not powered by fusion. They are the cooling cores of dead low-mass stars. Once a star has exhausted its fuel and blown off its outer layers, the dense core that remains gradually radiates away its residual heat over billions of years. Lesson 6 traces the journey from main sequence to red giant to white dwarf in detail.
Between the main sequence and the red giant branch there is a nearly-empty region known as the Hertzsprung gap. Stars cross this gap quickly as they evolve off the main sequence and towards the red-giant phase. At any given moment, few stars are caught in transit — so few lie in this region. The gap is not empty because the physics forbids it; it is empty because the time a star spends there is short compared with the main-sequence lifetime or the red-giant lifetime.
This is a nice reminder that the HR diagram is a statistical snapshot: the density of points at each location reflects both the fundamental physics (certain configurations are stable, others aren't) and the time spent (long-lived stages are heavily populated).
When you see an HR diagram in an exam question, ask yourself:
graph LR
subgraph "HR Diagram"
MS["Main sequence<br/>hot L high<br/>cool L low"]
RG["Red giants<br/>cool L high"]
WD["White dwarfs<br/>hot L low"]
SG["Supergiants<br/>top of diagram"]
end
MS -. evolves to .-> RG
RG -. evolves to .-> WD
MS -. if massive .-> SG
A star has T = 3500 K and L = 10⁴ L_☉. What kind of star is it?
Therefore it lies in the upper-right corner of the HR diagram. Combined with the Stefan–Boltzmann law:
r2=L/(4πσT4)=(104×3.83×1026)/(4π×5.67×10−8×(3500)4)=(3.83×1030)/(1.07×108)=3.58×1022m2r=1.89×1011m≈270R☉A radius of 270 R_☉ and temperature 3500 K identify this as a red supergiant, similar in size to a large red supergiant.
A star has T = 20 000 K and L = 10⁻³ L_☉. Classify it.
Lower-left corner of the HR diagram: a white dwarf. Compute the radius:
r2=(10−3×3.83×1026)/(4π×5.67×10−8×(2×104)4)=(3.83×1023)/(4π×5.67×10−8×1.6×1017)=(3.83×1023)/(1.14×1011)=3.36×1012m2r=1.83×106mAbout 1800 km — a quarter the radius of Earth. A small, dense white dwarf.
A star has T = 10 000 K and L = 10² L_☉. Where does it sit?
Compute radius:
r2=(100×3.83×1026)/(4π×5.67×10−8×1016)=(3.83×1028)/(7.13×109)=5.37×1018m2r=2.32×109m≈3.3R☉A star with T=10000 K, L=100L⊙ and r=3.3R⊙ is a main-sequence A star — massive, hot, bright, but still a main-sequence object. This is the kind of star Vega is.
The four principal regions correspond to four very different physical situations:
The Sun lies near the middle of the main sequence: T=5800 K, L=1L⊙, a G2V main-sequence dwarf. Always mark its position when sketching the diagram in an exam — it anchors all the others.
Question (10 marks): The diagram below represents the principal regions of the Hertzsprung–Russell diagram.
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