Investigate emission and absorption spectra, distinguish continuous, line emission and line absorption spectra, and analyse stellar spectra to identify chemical composition, surface temperature and motion

What this dot point is asking

NESA wants you to know the three types of spectrum, why atomic energy levels are quantised, and how spectroscopy is used to determine the composition, temperature and motion of stars. You should be able to read an absorption line in a stellar spectrum and explain what it tells you.

The answer

Quantised atomic energy levels

Electrons in atoms occupy discrete energy levels $E_1, E_2, E_3, \dots$ When an electron drops from a higher level $E_i$ to a lower level $E_f$, a photon of energy:

is emitted. The reverse is absorption: an electron absorbs a photon of exactly the right energy and jumps to a higher level. Because the levels are discrete, only certain photon energies (and therefore wavelengths) appear in atomic spectra. Each element has a characteristic set of levels and therefore a unique spectral "fingerprint".

Three types of spectrum (Kirchhoff's laws, 1859)

Continuous spectrum

A hot dense object (a glowing solid, liquid or high-pressure gas, or the interior of a star) emits a smooth distribution of wavelengths. The peak wavelength shifts with temperature (Wien's law); the total intensity follows the Stefan-Boltzmann law. The spectrum approximates a blackbody curve.

Line emission spectrum

A hot, low-density gas (a discharge lamp, the corona of a star, a nebula) emits only at specific wavelengths corresponding to its atoms' allowed downward transitions. The spectrum looks like bright lines on a dark background.

Line absorption spectrum

Continuum light passing through a cool gas loses the photons whose energies match the gas atoms' allowed upward transitions. The result is a continuous spectrum crossed by dark lines (Fraunhofer lines). Stellar spectra are predominantly of this type: the photosphere produces near-continuum light that is absorbed by the cooler outer atmosphere.

What stellar spectra reveal

A typical stellar spectrum is analysed for four things:

Chemical composition

Identify the absorption lines by wavelength and match to laboratory spectra. The most prominent lines in a Sun-like star are hydrogen Balmer lines (H-alpha at $656.3$ nm), neutral sodium, ionised calcium, magnesium and iron lines. Helium was discovered in 1868 from a solar absorption line that did not match any known terrestrial element.

Surface temperature

The relative strengths of different lines depend on temperature, because each transition has an optimal temperature for being populated. The shape of the underlying continuum (Wien's law: $\lambda\_{\text{peak}} T =$ constant) gives an independent temperature estimate. Together these classify stars into the spectral sequence O, B, A, F, G, K, M, from hottest (blue-white) to coolest (red).

Radial velocity (line of sight)

All lines are shifted from their laboratory wavelengths by the Doppler effect:

A redshift ($\lambda_{\text{obs}} > \lambda_0$) means the source is receding; a blueshift ($\lambda_{\text{obs}} < \lambda_0$) means it is approaching. This is how we know about the expansion of the universe (Hubble) and detect orbiting exoplanets (the star wobbles).

Rotation. A rotating star has one limb moving toward us and the other away, so each spectral line is broadened symmetrically into a profile whose width measures the equatorial rotation speed.

Other inferences include surface gravity (from line widths sensitive to pressure broadening), magnetic field (Zeeman splitting of lines) and turbulent motion.

Worked example: identifying composition

A stellar absorption spectrum shows strong lines at $588.99$ nm and $589.59$ nm. These match the laboratory sodium D doublet, so the star's atmosphere contains sodium. Comparing the doublet positions to laboratory values gives the radial velocity by the Doppler formula above.

Diffraction grating spectrometers

In practice, spectra are recorded by sending starlight through a slit, collimating it, dispersing it with a prism or diffraction grating, and imaging the result onto a CCD. A diffraction grating with line spacing $d$ produces principal maxima at:

$d \sin \theta = m \lambda$

so different wavelengths emerge at different angles and can be measured precisely. Gratings give much higher resolution than prisms and are standard in modern astrophysics.

Examples in context

Example 1. Mt Stromlo spectroscopy of a Cepheid variable. A spectrum taken at Mt Stromlo Observatory shows the calcium-K line at $\lambda_{\text{obs}} = 397.2 \text{ nm}$ instead of the laboratory rest value $\lambda_0 = 393.4 \text{ nm}$. The redshift is $z = \Delta\lambda / \lambda_0 = (397.2 - 393.4)/393.4 = 9.66 \times 10^{-3}$. For non-relativistic recession, $v = z c = 9.66 \times 10^{-3} \times 3.0 \times 10^8 = 2.90 \times 10^6 \text{ m/s} = 2900 \text{ km/s}$ away from us. Combined with Cepheid period-luminosity distance ($d = 40 \text{ Mpc}$), Hubble's constant $H_0 = v / d = 2900 / 40 = 72.5 \text{ km/s/Mpc}$, matching modern values.

Example 2. Helium discovery in the solar spectrum, replicated at Sydney Observatory. During the 1868 solar eclipse, astronomers including those at Sydney Observatory recorded a yellow emission line at $\lambda = 587.6 \text{ nm}$ in the Sun's chromosphere that did not match any terrestrial element. Photon energy $E = h c / \lambda = 1240 / 587.6 = 2.11 \text{ eV}$. This was the He I transition between the $1s2p$ and $1s2s$ levels in helium, an element not isolated on Earth until 1895. The discovery proved that astronomical spectra reveal compositions of objects we cannot sample, the cornerstone of all astrochemistry.

Try this

Q1. Distinguish between emission and absorption line spectra and state one source of each. [2 marks]

• Cue. Emission: hot dilute gas (e.g. street neon). Absorption: cold gas in front of hot continuum source (e.g. solar photosphere).

Q2. A spectral line of rest wavelength $656.3 \text{ nm}$ (H-alpha) is observed at $\lambda = 658.5 \text{ nm}$ in a distant galaxy. Calculate the recession velocity. [3 marks]

• Cue. $z = (658.5 - 656.3)/656.3 = 3.35 \times 10^{-3}$; $v = z c = 1006 \text{ km/s}$ away.

Q3. A star's spectrum shows strong hydrogen Balmer lines and weak helium lines. (a) Use Wien's law $\lambda_{\max} T = 2.898 \times 10^{-3} \text{ m K}$ to estimate temperature if $\lambda_{\max} = 480 \text{ nm}$. (b) Classify the star's spectral type. (c) Explain how Doppler broadening of the lines reveals stellar rotation. [2+2+2 marks]

• Cue. (a) $T = 2.898 \times 10^{-3} / 4.80 \times 10^{-7} = 6040 \text{ K}$. (b) F or G type. (c) Approaching/receding limbs blue/redshift, smearing the line; FWHM $\propto v \sin i$.