The Hertzsprung-Russell Diagram — Quick Summary

Mr Toogood's Physics · Astrophysics

AQA 3.9.2.5
M: +15 → −10
y-axis (bottom→top)
T: 50 000K → 2 500K
x-axis (left→right)
P_A/P_B = A_A/A_B
Same class → same T
r ∝ √A
Since A = 4πr²

The HR diagram: axes & shape

Basic Hertzsprung-Russell diagram showing the main sequence, giants, supergiants and white dwarfs

Learn this basic shape — commonly examined.

  • Both axes are reversed from normal convention: M runs +15 (bottom) to −10 (top); T runs 50 000 K (left) to 2 500 K (right) — or OBAFGKM.
  • Main sequence: a curved band (not a line) running top-left to bottom-right — where stars spend most of their lives.
  • Giants/supergiants (top-right): cool but very bright → enormous surface area.
  • White dwarfs (bottom-left): hot but dim → tiny.
Drawing rules: giants have M < 0; dwarfs have M > 10; neither cloud touches the main sequence; supergiants don't need to be drawn.

The Sun's life path

The path traced by the Sun across the HR diagram during its lifetime

Nebula → main sequence → red giant → white dwarf.

The Sun forms from a nebula (too cool and dim to appear on the diagram), joins the main sequence at its current position, later expands into a red giant as it runs low on fuel (cooler, much brighter), then sheds its outer layers and collapses to a white dwarf (hot, dim). You're expected to know this path.

Comparing stars on the HR diagram

HR diagram comparing two stars of the same spectral class but different absolute magnitudes

Same class (same T), different M → must differ in size.

Two stars of the same spectral class share the same temperature. If their absolute magnitudes differ, Stefan's law (T cancels) shows the brighter one must have a larger surface area — and therefore a larger radius.

P_A/P_B = A_A/A_B

Worked example

A red giant (T=3000 K) and a main sequence star (T=15 000 K) share the same absolute magnitude, M=0 — so the same power output:

A_RG/A_MS = (T_MS/T_RG)⁴ = 5⁴ = 625

Since A=4πr², the radius ratio is √625 = 25 — the red giant's radius is 25× that of the main sequence star.

Exam essentials

Axis conventions

  • y: M, +15 (bottom) → −10 (top).
  • x: T, 50 000 K (left) → 2 500 K (right), or OBAFGKM.

Region identification

  • Main sequence: curved band.
  • Giants: M<0, top-right, cool but huge.
  • Dwarfs: M>10, bottom-left, hot but tiny.

Common slips

  • Both axes run "backwards" — check direction before plotting or reading values.
  • Same spectral class ⇒ same T; a magnitude difference must come from size (Stefan's law), not temperature.
  • Remember A∝r² — take a square root to get the radius ratio, not the area ratio.