Theme E — Nuclear and Quantum Physics

E.5.5 The Hertzsprung–Russell (HR) Diagram — IB Physics HL Revision Notes & Topical Questions

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E.5.5 The Hertzsprung–Russell (HR) Diagram — IB PHYSICS SL notes: Interpret the HR diagram using luminosity, temperature and mass relationships to place stars and follow their evolution.Hertzsprung and Russell independently plotted luminosity against temperature.Luminosity L = to…

Temperature T is surface temperature in kelvin
The Sun is class G
The diagram shows only stable phases
A star radiates as a black body
What the symbols mean
For two stars L1/L2

Part 1 of 7Axes of the diagram

Hertzsprung and Russell independently plotted luminosity against temperature.

2Luminosity L

Luminosity L total power radiated by a star, in watts or relative to the Sun (L☉ = 3.83 × 10²⁶ W).

The axis is logarithmic — each gridline is a factor of ten or more, not an equal addition.

3Temperature T is surface temperature in kelvin

Temperature T is surface temperature in kelvin plotted backwards, hot on the left, cool on the right.
Hot stars are about 40 000 K and cool stars about 3000 K.

The temperature axis may be labelled by spectral class O, B, A, F, G, K, M or by colour from blue to red.

Part 2 of 7Regions of the diagram

Region	Position	Features
Main sequence	Diagonal band, top left to bottom right	Stars fusing hydrogen; about 90% of stars; luminosity rises with surface temperature
Red giants	Above the main sequence, right	Cool but luminous, so very large
Red supergiants	Very top right	Luminosity up to 10⁶ L☉; larger still
White dwarfs	Bottom left	Hot but dim, so very small

1The Sun is class G

5800 K and 1 L☉.

2The diagram shows only stable phases

The diagram shows only stable phases transitions are short; black holes emit no light.

Part 3 of 7Stefan–Boltzmann law and radius

Stefan–Boltzmann law and radius

A star radiates as a black body

L = σAT⁴ = 4πR²σT⁴.
What the symbols mean: L = luminosity, the total power emitted (W) · σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴ · r = radius of the star (m) · A = surface area (m²) · T = surface temperature (K)
σ = 5.67 × 10^-8 W m^-2 K^-4, R is the radius and T is in kelvin.

For two stars L1/L2

(R₁/R₂)²(T₁/T₂)⁴.

Giants are large

Giants are large they have similar or lower temperature than the Sun yet far greater luminosity, so their area is large.

Lines of constant radius run diagonally

Lines of constant radius run diagonally with larger radii toward the top right.

Two stars at the same point have the same radius

Two stars at the same point have the same radius whatever their mass.

Part 4 of 7Mass–luminosity relation

1For main-sequence stars L ∝ M3.5

For main-sequence stars L ∝ M3.5 with M in solar masses.
A star of twice the Sun's mass is about 2^3.5, roughly 11 times as luminous.

2Lifetime goes as M/L ∝ M-2.5

Lifetime goes as M/L ∝ M-2.5 so heavy stars live short lives.

Mass increases from bottom right to top left along the main sequence.

The relation does not apply to giants, supergiants or white dwarfs.

Part 5 of 7Evolution on the diagram

A protostar moves down and left toward the main sequence.

2After leaving the main sequence a star moves up and right

After leaving the main sequence a star moves up and right it expands and cools to the giant region.

A low-mass star later moves left across the diagram, then down to the white dwarf region as it fades.

A massive star moves across to the supergiant region.

5Cluster turn-off point

Cluster turn-off point stars above it have left the main sequence; its position gives the cluster's age.
A turn-off at lower luminosity means an older cluster.

Part 6 of 7Using the diagram

Use temperature, colour or class for the horizontal position.

Use luminosity for the vertical position.

Find the radius from L = 4πR²σT⁴.

Classify the star as main sequence, giant or white dwarf.

1Plot a star by temperature and luminosity relative to the Sun

Plot a star by temperature and luminosity relative to the Sun the Sun is at 1 on the luminosity axis.

2Stars in a cluster are at the same distance

Stars in a cluster are at the same distance matching apparent brightness against a standard main sequence gives the cluster distance.

Part 7 of 7More from the specification

Stellar spectra and energy levels

Stellar spectra and energy levels absorption line classifications on HR diagrams correspond to quantum electron jumps between distinct atomic energy levels.

The Hertzsprung-Russell (HR) Diagram and Stellar Classes

The HR diagram plots stellar luminosity against surface temperature (or spectral class, in reverse temperature order); main sequence stars occupy a diagonal band, red giants and supergiants lie at the upper right,
- (or absolute magnitude)
and white dwarfs lie at the bottom left.

Nuclear Fusion and Hydrostatic Equilibrium in Main Sequence Stars — In main sequence stars, hydrogen nuclei undergo nuclear fusion reactions in the core to produce helium nuclei (via the proton-proton chain or CNO cycle); the vast thermal energy released creates outward gas and radiation pressure that balances inward gravitational collapse.

Stellar Evolution and Post-Main-Sequence Core Collapse

When core hydrogen is exhausted, fusion ceases and radiation pressure drops,
causing gravitational contraction of the helium core; outer layers expand and cool into a giant star,
where stellar atmospheres produce characteristic dark absorption lines in their continuous emission spectra.

Wavelength

Distance between a point on one wave and the same point on the next wave

Stellar parallax

Apparent shift of a nearby star against distant stars as Earth orbits the Sun.

Binding energy

The minimum energy required to separate the nucleons of a nucleus to infinity.

Emission spectrum

The set of discrete wavelengths emitted by excited atoms of an element.

Energy level

A discrete energy an electron in an atom can have

Kinetic energy

K = ½mv², energy of motion.

Continuous spectrum

Spectrum with no gaps between the regions.

Fusion

Joining of light nuclei into a heavier one.

Pressure

Force per unit area, P = F/A.
What the symbols mean: p = pressure (Pa = N m⁻²) · F = force acting at right angles to the surface (N) · A = area (m²)

Helium

Product of the fusion of hydrogen in stars.

Nucleus

Small, dense, positively charged centre of the atom.

Absorption

The conversion of wave energy to internal energy of the medium.

Reaction

The partner force acting on the other object.

Parallax

Apparent shift between objects caused by viewing from different positions

Photon

A quantum of electromagnetic energy, E = hf
What the symbols mean: E = energy of one photon (J) · h = Planck constant (6.63 × 10⁻³⁴ J s) · f = frequency (Hz)

Key terms

Term	Meaning
Luminosity	Total power radiated by a star.
HR diagram	Plot of luminosity against surface temperature or spectral class.
Main sequence	Band of stars fusing hydrogen in their cores.
Stefan–Boltzmann law	L = σAT⁴ for a black body.
Turn-off point	Place where cluster stars leave the main sequence, showing the age.
Spectral class	Classification O, B, A, F, G, K, M by temperature.

Avoid these mistakes

Reading the temperature axis left to right as increasing — it decreases.

Thinking giants are hot — they are cool and large, luminous because of their area.

Applying L ∝ M³.5 to white dwarfs and giants — it is only for main-sequence stars.

Using temperature in degrees Celsius in L = 4πR²σT⁴ — use kelvin.

Treating the luminosity scale as linear — it is logarithmic.

Last updated: 18 October 2026