Account for the production of emission and absorption spectra and compare these with a continuous black body spectrum; investigate stellar evolution using the Hertzsprung-Russell diagram and account for the synthesis of elements heavier than iron in supernovae

What this dot point is asking

NESA wants you to use the Hertzsprung-Russell diagram to describe stellar properties and evolution, explain the sequence of fusion reactions that build elements up to iron in stellar cores, and account for the supernova production of elements heavier than iron. The thread linking these is the binding energy curve and the observation that fusion releases energy only up to iron.

The answer

The Hertzsprung-Russell diagram

The H-R diagram plots stars by their luminosity (vertical, increasing upward) against their surface temperature (horizontal, increasing to the left, by historical convention). Stars do not fill the diagram uniformly; they cluster in well-defined regions.

• Main sequence. A diagonal band from the upper left (hot, luminous, blue) to the lower right (cool, dim, red). Stars on this band fuse hydrogen to helium in their cores. About 90% of all stars are here. The Sun sits in the middle.
• Red giants and supergiants. Upper right: cool but very luminous because of large radii. Stars enter this region after core hydrogen runs out.
• White dwarfs. Lower left: hot but very dim because of small radii (Earth-sized). The exposed cores of low-mass post-red-giant stars.

The diagram is a snapshot of populations: any individual star moves through these regions in a particular order set by its mass.

Life of a Sun-like star (about 1 solar mass)

1. Pre-main-sequence. A protostar contracts under gravity, heats, and ignites hydrogen fusion when the core reaches about 10 million K.
2. Main sequence (about 10 billion years). Hydrogen burns to helium in the core via the proton-proton chain. The Sun is currently here.
3. Subgiant and red giant. Core hydrogen runs out, the core contracts and heats, the envelope expands and cools. The star moves up and to the right on the H-R diagram.
4. Helium core fusion. Core helium ignites (triple alpha process), fusing helium to carbon and oxygen.
5. Planetary nebula. After helium exhaustion, the carbon-oxygen core contracts but cannot reach carbon-fusion temperatures. The outer envelope is ejected as a glowing nebula.
6. White dwarf. The bare core, supported by electron degeneracy pressure, slowly radiates its heat over many billions of years. It moves to the lower-left of the H-R diagram and fades.

Life of a massive star (above about 8 solar masses)

The first stages are the same (main sequence, red supergiant), but the higher core mass allows successive ignitions of heavier elements:

• carbon burns to neon, magnesium and oxygen,
• neon burns to magnesium and oxygen,
• oxygen burns to silicon,
• silicon burns to iron.

Each new fuel burns for a shorter time (helium-burning may last a few million years; silicon-burning days). The result is an onion-skin structure: an iron core surrounded by shells of silicon, oxygen, neon, carbon, helium and hydrogen.

When the iron core mass exceeds the Chandrasekhar limit (about 1.4 solar masses), it collapses. Protons capture electrons to form neutrons, releasing neutrinos. The neutrino burst and the rebound of the collapsing core drive a core-collapse supernova, blowing the outer layers into interstellar space and leaving a neutron star or black hole.

Why iron is the cutoff

The binding energy per nucleon as a function of mass number $A$ has a maximum at iron-56 (and the closely competing nickel-62). Below iron, fusion of light nuclei releases energy because the product has higher binding energy per nucleon. Above iron, fusion costs energy. Therefore stellar cores cannot produce elements heavier than iron by exothermic fusion. Iron accumulates as ash and the core eventually collapses for lack of an energy source.

Elements heavier than iron: the r-process

During the supernova explosion, the collapsing core releases a flood of free neutrons. Heavy seed nuclei (already present from earlier stages) absorb many neutrons in quick succession, far faster than the timescale for beta decay. This is the r-process (rapid neutron capture). The neutron-rich nuclei subsequently beta-decay to stable isotopes of elements up to and beyond uranium.

Neutron star mergers, detected as gravitational-wave events, are now known to be another major site of r-process nucleosynthesis. Either way, the heavy elements (gold, platinum, uranium) are made in cataclysmic events, blown into space, and incorporated into later generations of stars and planets.

The elements in your body that are heavier than iron were forged in supernovae or neutron star mergers in previous generations of stars.

Spectra revisited

The continuous part of a stellar spectrum is a near-blackbody curve from the dense photosphere (see the Module 7 dot point on spectra and stars). The cooler outer atmosphere imprints absorption lines whose pattern reveals composition and (with line-ratio analysis) temperature. Nebulae and hot rarefied gas glow with emission lines instead. Together these spectra are the observational tool by which stellar nucleosynthesis is checked: the predicted abundances of elements in the surfaces of stars (and in interstellar gas clouds) can be matched against observations.

Worked example: locating a star on the H-R diagram

A star has surface temperature 25000 K and luminosity 10000 $L_{\odot}$. Where is it on the H-R diagram, and what is its evolutionary stage?

High temperature (blue, far left) and very high luminosity place it in the upper-left of the diagram, on the upper main sequence. This is a massive O-type or early B-type star, probably 20-40 solar masses, burning hydrogen in its core via the CNO cycle. Its lifetime is short (a few million years) and it will end as a core-collapse supernova.

Examples in context

Example 1. Hydrogen fusion in a Sun-like star modelled at ANU Mt Stromlo. The pp-chain fuses 4 protons into $^4$He: $4 m_p - m_{He} = 4 \times 1.00728 - 4.0026 = 0.02652 \text{ u}$, releasing $0.02652 \times 931.5 = 24.7 \text{ MeV}$. Per second, the Sun fuses $3.8 \times 10^{38}$ protons, converting $4.3 \times 10^{12}$ kg of mass to energy ($E = \Delta m c^2 = 4.3 \times 10^{12} \times 9 \times 10^{16} = 3.9 \times 10^{29} \text{ W}$). This sustains the Sun's luminosity for $\sim 10 \text{ Gyr}$. Mt Stromlo's helioseismology programs cross-check core temperatures ($1.5 \times 10^7 \text{ K}$) against the pp-chain reaction rate, confirming standard-solar-model predictions.

Example 2. Type Ia supernova r-process at GW170817-style merger detected by SKA precursors in WA. A neutron-star merger creates extreme neutron densities ($n \sim 10^{32}/\text{cm}^3$), driving rapid neutron capture (r-process) that builds elements like gold and platinum. Per kg of ejecta: $\sim 10^{-3}$ kg of $^{197}$Au is produced. Earth's $\sim 4 \times 10^{17}$ kg gold reserves required $\sim 4 \times 10^{20}$ kg of r-process ejecta in supernovae/kilonovae over Galactic history. The Murchison Widefield Array (and future SKA-Low) detect the radio afterglow of such mergers, complementing optical observations of the kilonova fade.

Try this

Q1. Sketch the main features of the Hertzsprung-Russell (H-R) diagram and identify the main sequence, red giant and white dwarf regions. [3 marks]

• Cue. Axes: luminosity (vertical, log) vs surface temperature (horizontal, reversed). Main sequence runs upper-left to lower-right; red giants upper-right; white dwarfs lower-left.

Q2. Calculate the surface temperature of a star whose spectrum peaks at $\lambda_{\max} = 290 \text{ nm}$. [2 marks]

• Cue. $T = 2.898 \times 10^{-3} / 2.90 \times 10^{-7} = 9{,}993 \text{ K} \approx 10{,}000 \text{ K}$.

Q3. A $20 M_\odot$ star ends its life as a supernova. (a) State the heaviest element typically formed by core nuclear fusion before collapse. (b) Explain why elements heavier than iron require the r-process. (c) Outline how supernova nucleosynthesis seeded the Solar System with heavy elements. [1+3+3 marks]

• Cue. (a) Iron ($^{56}$Fe). (b) Beyond Fe, fusion is endothermic; r-process needs rapid neutron capture in supernova or NS-merger conditions. (c) Ejected metals enriched the molecular cloud that collapsed to form the Sun and planets $\sim 4.6 \text{ Gyr}$ ago.