The Hertzsprung–Russell Diagram

Take every star whose luminosity and temperature you can determine, and plot one against the other. The result is not a random scatter — it's a diagram with clear structure, revealing that stars fall into a small number of distinct families. This single plot is the map astronomers use to make sense of the entire population of stars.

Setting up the axes

The Hertzsprung–Russell (H-R) diagram plots two properties of stars against each other: absolute magnitude (or, equivalently, luminosity) on the vertical axis, and surface temperature (or, equivalently, spectral class) on the horizontal axis.

• The vertical axis typically spans absolute magnitude from around $-10$ (extremely luminous) at the top down to around $+15$ (very dim) at the bottom — remembering that, as covered in an earlier lesson, smaller and more negative magnitude means brighter, so the most luminous stars sit at the top.
• The horizontal axis typically spans surface temperature from around $50\,000\ \text{K}$ down to around $2\,500\ \text{K}$.

The horizontal axis has one feature that catches almost everyone out the first time they see it: temperature decreases from left to right. The hottest stars are plotted on the left of the diagram, and the coolest stars on the right — the reverse of how a temperature axis would normally be drawn. This convention is a historical accident of how the diagram was first constructed from spectral classes, but it's essential to keep straight, since misreading the direction of the temperature axis will flip your interpretation of every feature on the diagram.

The main regions of the diagram

When large numbers of stars are plotted this way, they don't spread out evenly — they cluster into a small number of recognisable regions:

• The main sequence. A diagonal band running from the top-left (hot, highly luminous stars) down to the bottom-right (cool, dim stars). The great majority of stars, including the Sun, lie on the main sequence, and a star spends the vast majority of its life in this band.
• Giants. Occupying the upper-right region of the diagram — stars that are cool (so plotted toward the right) but nonetheless highly luminous (so plotted high up). By Stefan's law, a cool star can only be this luminous if it has an enormous surface area — so giants must be physically huge stars.
• White dwarfs. Occupying the lower-left region — stars that are hot (so plotted toward the left) but very dim (so plotted low down). Again by Stefan's law, a hot object radiating so little total power must have a very small surface area — so white dwarfs must be tiny, compact stars.

This is exactly the reasoning trailed at the end of the Stefan's law lesson: luminosity and temperature alone, once combined through $L = 4\pi r^2\sigma T^4$, are enough to tell you a star's approximate size, and that size is what separates the giants, the main sequence, and the white dwarfs into their distinct regions of the diagram.

The Sun is worth locating specifically on this diagram: it sits roughly in the middle of the main sequence, at a surface temperature of about $5800\ \text{K}$ and a fairly unremarkable absolute magnitude — a perfectly ordinary, middle-of-the-road main sequence star, neither unusually hot nor unusually cool, neither unusually luminous nor unusually dim.

Spectral classification

The horizontal axis of the H-R diagram is often labelled with spectral classes instead of (or alongside) a numerical temperature scale. Stars are sorted into seven main spectral classes, traditionally remembered in order from hottest to coolest as O, B, A, F, G, K, M.

Each spectral class is defined by the pattern of absorption lines seen in that star's spectrum, and this pattern is itself a consequence of surface temperature. A particularly instructive example is the strength of hydrogen absorption lines (the Balmer series, in the visible part of the spectrum):

• In the hottest stars (classes O and B), so much energy is available that most hydrogen atoms are already ionised — with their electron stripped away entirely, there's no electron left to produce a Balmer absorption line, so hydrogen absorption is comparatively weak.
• In class A stars, the temperature is just right for a significant fraction of hydrogen atoms to have their electron sitting in the $n=2$ energy level — precisely the level from which a Balmer-series photon can be absorbed — so hydrogen absorption lines are at their strongest here.
• In the coolest stars (classes K and M), there isn't enough thermal energy to excite many hydrogen atoms up to $n=2$ in the first place, so once again hydrogen absorption is comparatively weak, even though these stars still contain plenty of (mostly unexcited) hydrogen.

The result is that hydrogen absorption peaks in strength around class A, rather than at the very hottest stars — a good example of why you can't simply assume "hotter star, more of every absorption feature". You don't need to memorise exact temperature boundaries for each spectral class, but you should be comfortable with the overall hot-to-cool ordering O→M and with this reasoning for why hydrogen absorption peaks around class A specifically.

Class	Colour	Approx. temperature	Prominent absorption lines
O	Blue	25,000–50,000 K	Ionised helium, helium, hydrogen
B	Blue	11,000–25,000 K	Helium, hydrogen
A	Blue-white	7,500–11,000 K	Hydrogen (strongest), ionised metals
F	White	6,000–7,500 K	Ionised metals
G	Yellow-white	5,000–6,000 K	Ionised and neutral metals
K	Orange	3,500–5,000 K	Neutral metals
M	Red	Below 3,500 K	Neutral atoms, titanium oxide (TiO)

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