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OCR H556 mapping. This lesson is the spine of Module 5.5.2 (post-main-sequence stellar evolution): the life cycle of low-mass stars (main sequence → red giant → planetary nebula → white dwarf) and high-mass stars (main sequence → red supergiant → supernova → neutron star or black hole), together with the Chandrasekhar limit (≈1.4M⊙) as the boundary between white-dwarf and core-collapse remnants. It builds on the Hertzsprung-Russell diagram (lesson 5) and on the Stefan-Boltzmann law and Wien's law (lessons 2 and 3), and it sets up Doppler red shifts and Hubble's law in the cosmology half of Module 5.5.
A star is not a fixed object. Its luminosity, temperature, radius and composition change over time, sometimes dramatically. When the nuclear fuel in a star's core runs low, the star cannot simply keep shining at the same rate; it must rearrange itself to find a new source of energy, and in doing so it moves across the Hertzsprung-Russell diagram.
This lesson traces the life story of a star from birth, through main-sequence burning, to death. The details depend strongly on the star's initial mass: low-mass stars (like the Sun) end as white dwarfs, while high-mass stars die spectacularly as supernovae and leave behind neutron stars or black holes. Along the way, the star's position on the HR diagram changes in characteristic ways — the evolutionary track.
Stars form from collapsing clouds of interstellar gas and dust — giant molecular clouds, consisting mostly of hydrogen with trace amounts of helium and heavier elements. A dense clump in such a cloud, triggered by a passing shockwave or by its own gravity, begins to collapse under its own weight. As it collapses:
When the core temperature reaches about 107 K, hydrogen fusion via the proton-proton chain (or the CNO cycle in more massive stars) ignites. The new star releases energy fast enough to counterbalance gravitational collapse, and it settles into hydrostatic equilibrium: outward radiation pressure and gas pressure balance inward gravity. A main-sequence star is born.
OCR does not assess the details of star formation in Module 5.5, so we shall not dwell on it further. The key point is that every star begins its main-sequence life with a mass set by its protostellar cloud, and that mass determines everything that follows.
Once on the main sequence, a star fuses hydrogen to helium in its core. This is by far the longest phase of its life. The main-sequence lifetime depends strongly on mass. Combining the mass-luminosity relation L∝M3.5 with the idea that a star's fuel supply scales with M gives:
tMS∝LM∝M3.5M=M−2.5A more massive star has more fuel, but it burns that fuel much faster. The net result is that a 10M⊙ star lives only about 107 years on the main sequence, while a 0.5M⊙ red dwarf would last 1012 years — longer than the current age of the universe.
| Mass (M⊙) | Main-sequence lifetime (years) |
|---|---|
| 50 | ≈5×106 |
| 10 | ≈2×107 |
| 1 (Sun) | ≈1010 |
| 0.5 | ≈1011 |
| 0.1 | ≈1012 |
The Sun is roughly half-way through its main-sequence life: ≈4.6 billion years so far, with another ≈5 billion to go. The slowest-evolving stars are the ones with the longest future ahead of them — a useful lever in synoptic questions where you are asked which kinds of star might still be on the main sequence at the present cosmological epoch.
When a low-mass star exhausts the hydrogen in its core, energy generation stops at the very centre. Without the outward pressure of fusion, the core begins to contract under gravity. Contraction heats the surroundings; in a thin shell just outside the dead helium core, temperatures rise high enough to ignite hydrogen-shell burning.
This has a counter-intuitive consequence. The shell burns more vigorously than the old core did, but the energy has to be transported out through the stellar envelope. The envelope expands to adjust. As it expands, it cools — and the star becomes a red giant: cool at the surface (3000-4000 K), but enormous in radius and therefore very luminous overall.
graph LR
MS["Main sequence<br/>H burning in core"] --> SGB["Subgiant branch<br/>H shell ignites"]
SGB --> RGB["Red giant branch<br/>envelope expands"]
RGB --> HB["Helium flash<br/>core He ignites"]
HB --> AGB["Asymptotic giant<br/>double-shell burning"]
AGB --> PN["Planetary nebula<br/>envelope ejected"]
PN --> WD["White dwarf<br/>cooling C/O core"]
On the HR diagram, the star moves from the main sequence upward and to the right — much more luminous (shell burning releases a great deal of power) and cooler at the surface (the envelope has expanded). This is the red giant branch.
Eventually, the contracting helium core becomes hot enough (≈108 K) to ignite helium fusion via the triple-alpha process (34He→12C). In lower-mass stars this ignition happens in a dramatic event called the helium flash, because the core is partially electron-degenerate and temperature runs away briefly before thermal pressure restores order. In higher-mass stars the transition is smoother. Either way, the star settles into a new equilibrium burning helium in its core and hydrogen in a shell above.
After core helium is exhausted, the star climbs the asymptotic giant branch (AGB), burning helium and hydrogen in alternating shells around an inert carbon-oxygen core. The outer layers become unstable, pulsate, and gradually drift away on stellar winds, eventually ejecting a planetary nebula — a glowing shell of gas illuminated by ultraviolet light from the hot exposed core. (The name is a historical misnomer: planetary nebulae have nothing to do with planets; Herschel called them "planetary" because their small greenish discs looked superficially like Uranus through early telescopes.)
What remains at the centre is a hot, dense, Earth-sized white dwarf made mostly of carbon and oxygen. It contains no fusion; its luminosity comes from residual heat, which it radiates away over billions of years, slowly fading in the lower-left corner of the HR diagram.
The white dwarf cannot be arbitrarily massive. Its support against gravitational collapse comes from electron degeneracy pressure — a quantum-mechanical effect in which electrons, forbidden by the Pauli exclusion principle from occupying the same state, resist being compressed beyond a certain limit. Degeneracy pressure has an upper bound. If the mass exceeds
MCh≈1.4M⊙then electron degeneracy cannot support the star and it collapses further. This is the Chandrasekhar limit, derived by Subrahmanyan Chandrasekhar in 1931 (for which he received the 1983 Nobel Prize in Physics). Any stellar remnant exceeding 1.4M⊙ cannot be a stable white dwarf.
For stars with initial main-sequence mass less than about 8M⊙, mass loss during the red-giant and AGB phases reduces the final core to well below 1.4M⊙. These stars therefore die as white dwarfs, and their fate is sealed.
Massive stars live fast and die young. Their main-sequence lifetimes are measured in tens of millions of years rather than billions. When their core hydrogen is exhausted, they follow a similar pattern to low-mass stars — shell burning, envelope expansion — but on a grander scale. They become red supergiants, with radii of hundreds to thousands of solar radii.
Unlike low-mass stars, they can ignite successive shells of heavier elements as their cores contract and heat up further:
graph TD
A[Hydrogen burning] --> B["Helium burning<br/>→ C, O"]
B --> C["Carbon burning<br/>→ Ne, Mg"]
C --> D["Neon burning<br/>→ O, Mg"]
D --> E["Oxygen burning<br/>→ Si, S"]
E --> F["Silicon burning<br/>→ Fe"]
F --> G["Core collapse<br/>→ Supernova"]
Each successive stage happens faster than the one before. Carbon burning takes about a thousand years for a 25M⊙ star; neon burning lasts a few years; oxygen burning a few months; silicon burning only a day. By the end, the star has an onion-like structure with shells of successively heavier elements burning around an iron core.
Iron is the end of the line. Fusion up to iron releases energy (the binding energy per nucleon rises from hydrogen to iron); fusion beyond iron costs energy. The iron core cannot sustain fusion and grows inert.
When the iron core exceeds the Chandrasekhar limit, electron degeneracy pressure fails and the core collapses catastrophically in a fraction of a second. Temperatures and densities surge. Electrons and protons combine to form neutrons and neutrinos. The core becomes, in effect, a gigantic atomic nucleus. The infalling outer layers bounce off this neutron core and are driven outward in a colossal type II core-collapse supernova that releases more energy in a few seconds than the Sun will in its entire lifetime.
What remains depends on the mass of the collapsed core:
Neutron stars frequently appear as pulsars, rotating rapidly and emitting beams of radio waves or X-rays that sweep past the Earth like a lighthouse. The first pulsar was discovered by Jocelyn Bell in 1967; it rotates 1.3 times per second. Young pulsars can rotate hundreds of times per second, dramatic evidence for the conservation of angular momentum of a collapsed stellar core.
| Initial mass | Main-sequence phase | Post-MS phase | Final state |
|---|---|---|---|
| 0.08-0.5M⊙ | Red dwarf (M) | Slow contraction | Helium white dwarf (eventually) |
| 0.5-8M⊙ | G or K dwarf | Red giant → AGB → planetary nebula | C/O white dwarf |
| 8-25M⊙ | O/B supergiant | Red supergiant → supernova | Neutron star |
| >25M⊙ | O supergiant | Red or blue supergiant → supernova | Black hole |
These mass boundaries are approximate; the precise fate of a star depends on metallicity, rotation, binary companions and more. But the qualitative pattern — low-mass stars become white dwarfs, high-mass stars supernova to neutron stars or black holes — is universal and examinable.
The journey of a star across the HR diagram is called its evolutionary track. The diagram below sketches the track for a Sun-like star (schematic, log-log axes).
For a low-mass star like the Sun:
For a massive star the track goes much further upward (to luminosities of ≈105L⊙ or more), enters the red supergiant phase, and terminates abruptly in a supernova — no white-dwarf remnant; instead, a neutron star or black hole that does not appear on the ordinary HR diagram at all.
The Sun is currently at (T,L)=(5800 K,1L⊙) on the main sequence. It has about 5 billion years of main-sequence life remaining. After that, working in Gyr from today:
The final Sun will be a Chandrasekhar-limit-safe white dwarf of about 0.55M⊙, composed mostly of carbon and oxygen, slowly fading in a cosmos far older than it is today.
A blue main-sequence star has mass M=20M⊙. Estimate its main-sequence lifetime, and describe its post-main-sequence evolution and likely remnant.
Lifetime. Using tMS≈1010yr×M−2.5:
tMS≈1010×20−2.5=1010/(202.5)≈1010/1789≈5.6×106yrSo the star lives only ≈5-6 million years on the main sequence, a thousandth of the Sun's lifetime.
Post-MS. After core hydrogen exhaustion the star enters its red-supergiant phase, igniting helium, then carbon, neon, oxygen and finally silicon in successive shells around an iron core. Within ∼104 years of leaving the main sequence the iron core grows beyond 1.4M⊙, degeneracy pressure fails, and a type II supernova ensues.
Remnant. A 20M⊙ progenitor leaves a core of perhaps 1.5-2.5M⊙ after the supernova — comfortably below the ≈3M⊙ neutron-star upper limit. So the most likely remnant is a neutron star, possibly observable as a pulsar. (For more massive progenitors, ≳25M⊙, the remnant is more likely to be a stellar-mass black hole.)
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