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Physics HL · Chapter 25: Nuclear Fusion and Stars

25.2 Stellar Properties and the Hertzsprung-Russell Diagram

Use luminosity, temperature, and radius relationships to interpret HR-diagram regions and classify stellar populations.

Estimated time: 52 minutes

What an HR Diagram Encodes

The Hertzsprung-Russell diagram plots stellar luminosity against surface temperature (with temperature decreasing to the right). Because stellar luminosities span many orders of magnitude, both axes are typically logarithmic. This is not cosmetic: it is what allows physically meaningful clustering, such as the main sequence, giants, and white dwarfs, to appear clearly on one chart.

The position of a star on the HR diagram is not its position in space. Two stars can be close on the diagram and very far apart in the galaxy. The HR plane is a classification map of physical state, not a coordinate map of distance.

Luminosity-Temperature-Radius Coupling

L=4πR2σT4,R=L4πσT4L = 4\pi R^2\sigma T^4,\qquad R = \sqrt{\frac{L}{4\pi\sigma T^4}}

At fixed temperature, larger luminosity implies larger area and radius; at fixed luminosity, hotter stars are smaller.

This relationship explains why red giants can be very bright despite relatively low surface temperature: their radii are enormous. It also explains why white dwarfs can be hot but dim: their surface areas are tiny. When comparing two stars, make sure you hold the right variable fixed before drawing conclusions.

Main Sequence, Giants, and White Dwarfs

Most stars lie on the main sequence where hydrostatic balance is maintained by core hydrogen fusion. Giant branches represent stars that have left this stable phase and expanded substantially. White dwarfs are dense stellar remnants that no longer generate significant fusion power and cool over time. These regions reflect different internal energy-support mechanisms, not just cosmetic color differences.

Color still provides useful thermal intuition through Wien reasoning: bluer stars are generally hotter and redder stars cooler. But color alone does not determine luminosity or radius. HR placement requires combining color/temperature with brightness-derived luminosity information.

Simulation: HR Diagram Placement and Radius Inference

Move a star across temperature and luminosity ranges, classify its HR region, and inspect inferred radius plus spectral-peak shifts.

Place stars on a logarithmic HR plane and connect luminosity-temperature position to radius and spectral peak.
Hertzsprung-Russell diagram (log L vs temperature, hot to the left)main sequence trendselected star32000 K2800 K10^610^-4

Luminosity

1.585 Lsun

Radius

1.09 Rsun

Wien peak

467.3 nm

Classification

main sequence

Test Yourself

Two stars have the same surface temperature, but star A has luminosity 10,000 times larger than star B. Which statement is correct?