Physics • Year 12 • Module 8 • Lesson 10
Supernovae and Neutron Stars
Apply your understanding of supernova types, neutron star properties, and the significance of GW170817 to data scenarios and quantitative calculations.
1. Neutron star density calculations
The density of a neutron star can be estimated using \(\rho = M / \tfrac{4}{3}\pi R^3\). Use \(1\,M_\odot = 2.0 \times 10^{30}\) kg. 9 marks
| Neutron star | Mass (\(M_\odot\)) | Radius (km) | Density (kg/m³) |
|---|---|---|---|
| NS-Alpha | 1.4 | 12 | |
| NS-Beta | 2.0 | 11 | |
| NS-Gamma | 2.0 | 13 |
1.1 Calculate the density of each neutron star. Show your full working for NS-Alpha. 6 marks (2 per row)
1.2 Nuclear density is approximately \(2.8 \times 10^{17}\) kg/m³. Compare your calculated density for NS-Alpha to nuclear density and comment. 2 marks
1.3 NS-Gamma has the same mass as NS-Beta but a larger radius. Explain what this implies about density using the formula, without doing the full calculation. 1 mark
2. Interpret supernova light curve data
The table below shows approximate peak absolute magnitudes for five supernovae observed by a student. The absolute magnitude of the Sun is +4.83. 8 marks
| Supernova | Type | Peak absolute magnitude | Host galaxy distance (Mpc) | Suitable standard candle? |
|---|---|---|---|---|
| SN-1 | Ia | −19.3 | 250 | |
| SN-2 | Ia | −19.1 | 320 | |
| SN-3 | II | −16.2 | 180 | |
| SN-4 | II | −18.5 | 400 | |
| SN-5 | Ia | −19.5 | 410 |
2.1 Complete the “Suitable standard candle?” column (Yes / No) and justify your choices. 3 marks
2.2 Using the three Type Ia supernovae, calculate the mean peak absolute magnitude and the range of values. Comment on whether these values are consistent with Type Ia supernovae being standard candles. 3 marks
2.3 The Type II supernovae show a large range in peak absolute magnitude. Explain why this makes them unreliable as standard candles, with reference to their progenitors. 2 marks
3. Predict and justify — supernova remnant classification
For each stellar scenario, predict the type of supernova (if any) and the final remnant. Justify each prediction using the mass thresholds from the lesson. 6 marks (1 per prediction + 1 justification each)
3.1 A white dwarf of initial mass 0.9 M☉ accretes matter from its companion until it reaches 1.4 M☉. Predict the type of supernova and the remnant left.
3.2 A massive star with initial mass 20 M☉ ends its life with a collapsing iron core. The remnant core mass after collapse is 1.8 M☉. Predict the type of supernova and the remnant.
3.3 A second massive star has a collapsing core remnant mass of 4.5 M☉. Predict the type of supernova and the remnant.
4. Analyse — the significance of GW170817
In August 2017, the LIGO and Virgo detectors detected gravitational waves from two merging neutron stars (GW170817). Two seconds later, a short gamma-ray burst was detected. Over the following days, a kilonova was observed showing spectral signatures of strontium and other heavy elements. 6 marks
4.1 Explain what a kilonova is and how it differs from a supernova. 2 marks
4.2 Explain why the detection of heavy elements in the kilonova afterglow supports r-process nucleosynthesis in neutron star mergers. 2 marks
4.3 Strontium (Z = 38) is heavier than iron (Z = 26). Explain why strontium cannot be produced by fusion in stellar cores but can be produced during a neutron star merger. 2 marks
Q1.1 — Neutron star densities
NS-Alpha: \(M = 1.4 \times 2.0\times10^{30} = 2.8\times10^{30}\) kg. \(R = 12\times10^3 = 1.2\times10^4\) m. \(V = \tfrac{4}{3}\pi(1.2\times10^4)^3 = \tfrac{4}{3}\pi \times 1.728\times10^{12} = 7.24\times10^{12}\) m³. \(\rho = 2.8\times10^{30} / 7.24\times10^{12} \approx 3.9\times10^{17}\) kg/m³.
NS-Beta: \(M = 4.0\times10^{30}\) kg, \(R = 1.1\times10^4\) m, \(V = 5.58\times10^{12}\) m³, \(\rho \approx 7.2\times10^{17}\) kg/m³.
NS-Gamma: \(M = 4.0\times10^{30}\) kg, \(R = 1.3\times10^4\) m, \(V = 9.20\times10^{12}\) m³, \(\rho \approx 4.3\times10^{17}\) kg/m³.
Q1.2 — Comparison to nuclear density
NS-Alpha density (≈3.9×1017 kg/m³) is comparable to nuclear density (2.8×1017 kg/m³) [1]. This confirms that neutron star matter is as dense as atomic nuclei; the entire star is essentially one enormous nucleus-like object [1].
Q1.3 — NS-Gamma vs NS-Beta
NS-Gamma has the same mass as NS-Beta but a larger radius, so its volume is larger; since \(\rho = M/V\), NS-Gamma will be less dense than NS-Beta.
Q2.1 — Standard candle column
SN-1 (Ia): Yes. SN-2 (Ia): Yes. SN-3 (II): No. SN-4 (II): No. SN-5 (Ia): Yes. Award 1 mark for all Ia = Yes and all II = No; 1 mark for justification (Ia = consistent mass at explosion → consistent luminosity; II = variable progenitor mass); 1 mark for identifying that both Type IIs have very different magnitudes (−16.2 vs −18.5).
Q2.2 — Type Ia statistics
Mean = (−19.3 + −19.1 + −19.5)/3 = −19.3 [1]. Range = −19.5 to −19.1 = 0.4 magnitudes [1]. The range of 0.4 magnitudes is small, consistent with Type Ia being standard candles (small scatter in intrinsic luminosity) [1].
Q2.3 — Why Type II are not standard candles
Type II supernovae arise from massive stars (>8 M☉) that span a wide range of initial masses, envelope sizes, and energies [1]. This produces a large variation in peak luminosity (SN-3 and SN-4 differ by over 2 magnitudes), making them unreliable standard candles [1].
Q3.1 — White dwarf at Chandrasekhar limit
Type Ia supernova [1]. No remnant — the entire white dwarf is destroyed in the thermonuclear runaway [1].
Q3.2 — Massive star with 1.8 M☉ remnant core
Type II (core-collapse) supernova [1]. Neutron star — the remnant core mass (1.8 M☉) is below the TOV limit (~3 M☉), so neutron degeneracy pressure can support it [1].
Q3.3 — Massive star with 4.5 M☉ remnant core
Type II (core-collapse) supernova [1]. Black hole — the remnant core mass (4.5 M☉) exceeds the TOV limit (~3 M☉), so even neutron degeneracy pressure cannot prevent collapse [1].
Q4.1 — What is a kilonova?
A kilonova is a luminous optical-infrared transient produced by r-process nucleosynthesis in the debris ejected from a neutron star merger [1]. Unlike a supernova (which arises from a single star), a kilonova requires the collision of two neutron stars and is powered by the radioactive decay of freshly synthesised r-process nuclei [1].
Q4.2 — Heavy elements supporting r-process
Elements heavier than iron (such as strontium, gold, platinum) cannot be produced by stellar fusion because fusion beyond iron is endothermic [1]. Their detection in the kilonova spectrum demonstrates that extreme neutron fluxes during the merger produced these elements via rapid neutron capture (r-process), confirming neutron star mergers as r-process sites [1].
Q4.3 — Why strontium needs neutron star merger
Strontium (Z = 38) lies beyond iron on the binding energy curve; fusing nuclei heavier than iron absorbs energy rather than releasing it, so stellar cores cannot produce strontium via fusion [1]. A neutron star merger provides the extreme neutron flux needed for r-process: nuclei rapidly capture many neutrons faster than they beta-decay, building strontium and other heavy elements that are impossible to form by fusion [1].