Physics • Year 12 • Module 8 • Lesson 9
Spectroscopy and Stellar Classification
Apply your understanding of spectral types, Doppler shifts, and spectroscopic analysis to real-data scenarios and diagram interpretation.
1. Interpret spectral data — classifying six stars
A student measured the dominant absorption features in the spectra of six stars and recorded them below. 10 marks
| Star | Dominant spectral feature(s) | Colour | Spectral type | Approx. surface temp. |
|---|---|---|---|---|
| Star 1 | Molecular TiO bands, no hydrogen | |||
| Star 2 | Ionised helium (He II) dominant | |||
| Star 3 | Strong hydrogen Balmer lines | |||
| Star 4 | Ionised Ca H & K lines; neutral metal lines | |||
| Star 5 | Neutral helium lines; some hydrogen | |||
| Star 6 | Hydrogen weaker; ionised Ca and iron lines |
1.1 Complete all empty cells in the table. 9 marks (1.5 per row)
1.2 Explain why Star 2 and Star 3 have the same spectral element (hydrogen is common to both stars’ compositions) but show very different hydrogen line strengths. 1 mark
2. Doppler radial-velocity calculations
Use \(\dfrac{\Delta\lambda}{\lambda_\text{rest}} = \dfrac{v_r}{c}\) and \(c = 3.0 \times 10^5\) km s−1. Show all working. 9 marks (3 each)
2.1 The Hα line (\(\lambda_\text{rest} = 656.3\) nm) in a star’s spectrum is observed at 654.6 nm.
(a) Is the line blueshifted or redshifted?
(b) Calculate the radial velocity and state its direction.
2.2 The Ca II K line (\(\lambda_\text{rest} = 393.3\) nm) in a galaxy spectrum is observed at 414.9 nm.
(a) Calculate the redshift \(z\).
(b) Estimate the recession velocity and comment on whether the non-relativistic approximation is valid here.
2.3 A star has a radial velocity of −42 km s−1 (negative = approaching). The Hβ line has a rest wavelength of 486.1 nm. Calculate the observed wavelength.
3. Compare the three types of spectra
Complete the two-column table contrasting the three spectra across four features. 8 marks (1 per cell, 2 × 4 pairs)
| Feature | Absorption spectrum | Emission spectrum |
|---|---|---|
| Appearance | ||
| Physical source | ||
| Astrophysical example | ||
| What it reveals about elements |
4. Predict and justify — an exoplanet detection scenario
An astronomer monitors the radial velocity of a star over 16 months and plots the data below. The radial velocity oscillates between +24 m s−1 and −24 m s−1 with a period of approximately 400 days.
Figure 1. Radial velocity curve for a star monitored over 500 days. Illustrative data.
4.1 Explain what causes the oscillating radial velocity. What does the period of the oscillation represent, and what does the amplitude indicate? 3 marks
4.2 A student claims that the periodic radial velocity is caused by the star pulsating (expanding and contracting). Identify one way the astronomer could test this alternative hypothesis using spectral analysis, and predict what result would confirm the exoplanet explanation. 2 marks
Q1.1 — Classification table
Star 1: red / M / below 3 700 K. Star 2: blue / O / above 30 000 K. Star 3: white / A / 7 500–10 000 K. Star 4: yellow / G / 5 200–6 000 K. Star 5: blue-white / B / 10 000–30 000 K. Star 6: yellow-white / F / 6 000–7 500 K.
Q1.2 — Hydrogen line strength contrast
Star 2 (O-type, >30 000 K) is so hot that hydrogen is almost completely ionised; ionised hydrogen cannot produce Balmer absorption lines, so they are absent. Star 3 (A-type, ~9 000 K) has the ideal temperature to populate the \(n=2\) hydrogen level, maximising Balmer line absorption. Spectral type reflects temperature, not merely composition.
Q2.1 — Hα Doppler calculation
(a) \(\Delta\lambda = 654.6 - 656.3 = -1.7\) nm (negative = shorter = blueshift, star approaching).
(b) \(v_r = c \cdot \Delta\lambda / \lambda_\text{rest} = (3.0 \times 10^5) \times (-1.7/656.3) = -777\) km s−1. The star is approaching at approximately 777 km s−1.
Q2.2 — Galaxy Ca II K Doppler
(a) \(z = \Delta\lambda / \lambda_\text{rest} = (414.9 - 393.3)/393.3 = 21.6/393.3 \approx 0.0549\).
(b) \(v_r = z \times c = 0.0549 \times 3.0 \times 10^5 \approx 16\thinsp;470\) km s−1 (≈ 16 500 km s−1). Since \(z \approx 0.055 < 0.1\), the non-relativistic approximation is marginally acceptable, but using the relativistic formula would give a more accurate result.
Q2.3 — Observed wavelength from known velocity
\(\Delta\lambda = \lambda_\text{rest} \times v_r / c = 486.1 \times (-42)/(3.0 \times 10^5) = -0.0680\) nm. \(\lambda_\text{obs} = 486.1 + (-0.068) = 486.032\) nm ≈ 486.03 nm (blueshifted).
Q3 — Compare absorption and emission spectra
Appearance: Absorption = dark lines on a continuous rainbow background; Emission = bright coloured lines on a dark background. Physical source: Absorption = continuous source (hot dense photosphere) behind cooler gas; Emission = hot low-density gas with no background. Astrophysical example: Absorption = stellar spectrum (photosphere + atmospheric gas); Emission = nebula, H II region, or hot gas cloud. What it reveals: Both spectra contain the same line positions for a given element, so both can identify composition; the temperature-dependence of line strength additionally reveals the physical conditions of the gas.
Q4.1 — Exoplanet radial velocity explanation (3 marks)
An orbiting planet gravitationally pulls the star around the common centre of mass, causing the star to undergo a small periodic wobble [1]. As the star wobbles toward Earth, its spectral lines blueshift; as it wobbles away, they redshift, producing the sinusoidal radial velocity curve [1]. The period (~400 days) equals the orbital period of the planet, and the amplitude (~24 m s−1) is related to the planet’s mass and orbital radius — a larger mass or smaller orbit produces a larger amplitude [1].
Q4.2 — Testing the pulsation hypothesis (2 marks)
Monitor the star’s brightness simultaneously; a pulsating star would also show periodic photometric variations (it would dim and brighten) synchronised with the velocity period [1]. If the brightness remains constant while the radial velocity oscillates, pulsation is ruled out and the exoplanet interpretation is confirmed [1].