Hertzsprung-Russell diagram and stellar life cyclesEdexcel A-Level Physics: Revision notes

An HR diagram plots each star's luminosity against its surface temperature. Two conventions matter:

• surface temperature runs from hot on the left to cool on the right, so the axis is reversed
• luminosity increases upwards over many powers of ten, so it uses a logarithmic scale (often relative to the Sun)

To sketch one, draw the axes with the Sun in the middle (about $5800$ K and $1\,L_\odot$), then add the groups of stars below.

• Main sequence: a diagonal band from hot, luminous stars at the upper left to cool, dim stars at the lower right. Stars here fuse hydrogen in their cores. The Sun lies on it.
• Red giants and red supergiants: upper right, cool but very luminous because of their huge radii.
• White dwarfs: bottom left, hot but dim because they are very small.

From $L = 4\pi r^2\sigma T^4$, a star's position gives its radius. Stars of the same radius lie on a line running from the lower left to the upper right.

A white dwarf has $T = 12\,000$ K and $L = 1.0 \times 10^{-3}\,L_\odot = 3.85 \times 10^{23}$ W.

$r = \sqrt{L / 4\pi\sigma T^4} = \sqrt{3.85 \times 10^{23} / (4\pi \times 5.67 \times 10^{-8} \times (1.2 \times 10^{4})^4)} = 5.1 \times 10^{6}$ m.

This is about the size of the Earth, which explains the star's low luminosity despite its high temperature.

1. A cloud of gas and dust collapses under gravity to form a protostar, and the temperature rises.
2. When the core is hot enough, hydrogen fuses to helium. The star joins the main sequence, where outward gas and radiation pressure balances inward gravity.
3. When core hydrogen is used up, the core contracts and the outer layers expand and cool. The star moves to the upper right as a red giant.
4. The outer layers are ejected as a planetary nebula.
5. The core remains as a white dwarf, which cools and fades.

A star of much greater mass is hotter and far more luminous on the main sequence, and it fuses its hydrogen much faster, so it lives much less long.

After the main sequence it expands to a red supergiant. Fusion continues to heavier elements up to iron in the core. The core then collapses and the star explodes as a supernova. The remnant is a neutron star or, for a large enough mass, a black hole.

On the HR diagram, a massive star moves from the upper left of the main sequence across to the top right as a supergiant.