Coaching Centre
Stellar spectra and classifying stars
How emission and absorption spectra are produced and how they compare with a continuous black-body spectrum, Wien's law, the Harvard spectral classes OBAFGKM, why the strength of hydrogen, helium, metal and molecular lines changes with temperature, Cecilia Payne's discovery of what stars are made of, and luminosity classes.
In 1925 a 25-year-old PhD student, Cecilia Payne, worked out that the Sun is made almost entirely of hydrogen and helium. Every senior astronomer believed the Sun had the same make-up as the Earth. The leading expert of the day told her the result was "clearly impossible", and she softened it in her thesis. Four years later he reached the same answer himself. Her thesis is now called one of the most brilliant ever written in astronomy.
Continuous, emission and absorption spectra
You met the three kinds of spectrum in Module 7. Here is the explanation you need for Module 8, in terms of energy levels.
- Continuous spectrum. A hot, dense object (a solid, a liquid, or a dense gas such as the inside of a star) gives out all wavelengths. Its atoms are packed so closely and interact so strongly that there are no separate energy levels: charged particles are accelerated in every possible way. The spectrum's shape depends only on temperature and is close to a black-body curve.
- Emission spectrum. A hot, low-density gas gives out only certain wavelengths. Electrons in its atoms are excited by collisions, then drop back to lower energy levels, each drop releasing a photon of energy $E = hf = E_{\text{upper}} - E_{\text{lower}}$. Because the levels are fixed, so are the wavelengths: bright lines on a dark background.
- Absorption spectrum. When continuous light passes through cooler, low-density gas, the gas atoms absorb photons with exactly the energy needed to lift an electron to a higher level. Those wavelengths are removed from the beam (the re-emitted photons go off in all directions), leaving dark lines on a continuous background. The dark lines sit at exactly the same wavelengths as the gas's emission lines.
A star is a combination: its hot dense interior produces a nearly black-body continuous spectrum, and the cooler gas of its outer atmosphere (the photosphere and above) absorbs particular wavelengths. So a star's spectrum is a black-body curve with absorption lines cut into it.
The continuous part: Wien's law
A black body's spectrum has a peak, and the peak moves to shorter wavelengths as the temperature rises. That is Wien's displacement law:
$$\lambda_{max} = \frac{b}{T}, \qquad b = 2.898 \times 10^{-3}\ \text{m K}$$
The peak gives a star's surface temperature (the temperature of the photosphere, where the light escapes), which also sets its colour. But for very hot stars, the peak is in the ultraviolet and can't be measured from the ground, and for all stars the absorption lines distort the curve. In practice astronomers use the pattern of absorption lines to classify a star, which is more precise.
The spectrum of Antares peaks at 850 nm. Find its surface temperature and describe its colour.
$T = \dfrac{b}{\lambda_{max}} = \dfrac{2.898 \times 10^{-3}}{850 \times 10^{-9}} = 3.4 \times 10^{3}$ K
The peak is in the near infrared and the star gives out much more red than blue light: it looks orange-red. A temperature of 3400 K puts it in class M.
The spectral classes OBAFGKM
In the 1890s to 1920s, a team at Harvard College Observatory sorted the spectra of hundreds of thousands of stars. Annie Jump Cannon, who classified about 350 000 stars by eye, arranged the classes into the order used today, which turned out to be a temperature sequence:
| Class | Surface temperature (K) | Colour | Strongest absorption features | Example |
|---|---|---|---|---|
| O | above 30 000 | blue | Ionised helium (He II); weak hydrogen | Naos (ζ Puppis) |
| B | 10 000–30 000 | blue-white | Neutral helium (He I); hydrogen getting stronger | Rigel; Achernar |
| A | 7500–10 000 | white | Hydrogen Balmer lines at their strongest | Sirius A; Vega |
| F | 6000–7500 | yellow-white | Hydrogen weaker; ionised calcium and metals getting stronger | Procyon A; Canopus |
| G | 5200–6000 | yellow | Ionised calcium (Ca II H and K) strong; many metal lines | The Sun; α Centauri A |
| K | 3700–5200 | orange | Neutral metals strong; hydrogen weak | Arcturus; α Centauri B |
| M | 2400–3700 | red | Molecular bands, especially titanium oxide (TiO) | Betelgeuse; Proxima Centauri |
Each class is split into ten subclasses, 0 to 9 (the Sun is G2, slightly hotter than G5). Classes L, T and Y have since been added for brown dwarfs, which are cooler than M stars.
Why the lines change with temperature
Almost all stars have nearly the same composition: about 74% hydrogen, 24% helium and 2% everything else by mass. The huge differences between their spectra come from temperature, which controls which energy levels the atoms' electrons are in. Take the visible hydrogen (Balmer) lines as the example. They are absorbed only by hydrogen atoms whose electron is already in the $n = 2$ level.
- In a cool M or K star, nearly every hydrogen atom has its electron in the ground state ($n = 1$). Few can absorb Balmer photons, so the lines are weak.
- At about 10 000 K (class A), collisions keep a useful fraction of hydrogen atoms in $n = 2$, so the Balmer lines are at their strongest.
- In O and B stars, most hydrogen is ionised: the electron has gone completely, so there is nothing left to absorb. The lines weaken again.
The same reasoning explains the others. Helium needs a lot of energy to excite and even more to ionise, so its lines appear only in the hottest stars (neutral helium in B stars, ionised helium only in O stars). Molecules like TiO are broken apart by collisions above about 4000 K, so molecular bands appear only in M stars.
That is what Cecilia Payne realised. She used the new physics of ionisation to correct for temperature, and showed that the Sun's spectrum is dominated by metal lines not because metals are common but because hydrogen at 5800 K is in the wrong state to absorb visible light. Hydrogen is in fact about a million times more abundant than the metals.
- Choose Star 3. Move the cursor to the peak of the black-body curve: it is near 502 nm, giving $T \approx 5770$ K. Then look at the lines: strong ionised calcium, moderate hydrogen. Which class?
- Choose Star 1. The peak is near 293 nm, giving about 9900 K, and the hydrogen lines are the strongest of any star. Classify it.
- Choose Star 4. Its peak is at about 85 nm, far into the ultraviolet. Why can't astronomers find this temperature from a ground-based measurement of the peak? Which line tells you it is class O?
- Choose Star 2. Its peak is about 805 nm. What feature shows in the spectrum that no hotter star has?
- Classify all seven stars. Then put them in order of temperature without looking at the cursor readings, using only their lines.
Luminosity classes
Two stars of the same spectral class can have very different luminosities. A K-type giant like Arcturus is several hundred times as luminous as a K-type main-sequence star like α Centauri B, because it is far larger. The spectra can tell them apart. A giant's atmosphere is huge and thin, so its atoms collide less often and its absorption lines are narrower than a dense main-sequence star's (you saw this pressure broadening in Module 7).
The full Morgan–Keenan classification adds a Roman numeral for luminosity class: I supergiant, II bright giant, III giant, IV subgiant, V main sequence (dwarf), plus white dwarfs (D). The Sun is G2 V. Betelgeuse is M1–2 Ia. With both the spectral class and the luminosity class, a star's position on the H–R diagram (page 8D) is fixed, so its luminosity, and therefore its distance, can be estimated from its spectrum alone.
Test yourself
A star's spectrum peaks at 290 nm. Its surface temperature is about
$T = 2.898 \times 10^{-3} / 290 \times 10^{-9} = 9990$ K ≈ 10 000 K.
Which spectral class has the strongest hydrogen Balmer absorption lines?
At about 10 000 K many hydrogen atoms have electrons in n = 2, ready to absorb Balmer photons.
Strong titanium oxide bands in a star's spectrum indicate that the star is
Molecules are broken apart in hotter atmospheres; TiO bands are the signature of class M.
Dark lines in the Sun's spectrum are produced by
The continuum comes from the hot interior; cooler overlying gas absorbs at its characteristic wavelengths. (Earth's atmosphere adds a few lines too, but not most of them.)
Two G-type stars have the same temperature but one has much narrower absorption lines. That star is most likely
A giant's thin atmosphere has less pressure broadening, so narrower lines, and it has a higher luminosity class.
Label the three types of spectrum.
Put these spectral classes in order from hottest to coolest.
Which kind of spectrum does each produce?
A hot, dense object gives a spectrum. A low-density gas absorbs photons whose energy equals the difference between two energy . As a star's temperature rises, its peak wavelength becomes . The differences between stellar spectra are mainly due to .
Account for the production of the absorption spectrum of a star and explain how the absorption lines can be used to classify the star. Refer to energy levels in your answer.
The hot, dense interior of a star emits a continuous spectrum close to a black-body curve. As this light passes out through the cooler, less dense gas of the star's outer atmosphere, atoms absorb photons whose energy exactly matches the difference between two of their electron energy levels, $hf = E_2 - E_1$. The excited atoms re-emit this energy in random directions, so fewer photons of those wavelengths travel towards us, leaving dark lines on the continuous spectrum.
Which lines appear, and how strong they are, depends mainly on the temperature of the atmosphere, because temperature controls which energy levels are occupied and whether atoms are ionised. For example, the hydrogen Balmer lines need electrons in n = 2: they are strongest at about 10 000 K (class A), weak in cool stars where electrons are in the ground state, and weak in very hot stars where hydrogen is ionised. Ionised helium lines appear only in O stars, ionised calcium is strongest in G and K stars, and molecular TiO bands only in cool M stars. Matching the pattern of lines places the star in a spectral class, O, B, A, F, G, K or M, from hottest to coolest.