Stellar Evolution

Trace the life cycles of stars from main sequence to their final states — white dwarfs, neutron stars, or black holes — and follow their tracks on the HR diagram.

AQA A-Level Physics · Astrophysics Option

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Describe main sequence lifetimes and what determines stellar mass evolution path

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Describe the red giant and supergiant stages

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Explain white dwarf formation and the Chandrasekhar limit (1.4 M_☉)

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Describe neutron stars and pulsars

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State the conditions for black hole formation

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Trace evolutionary tracks on the HR diagram

Main Sequence: Hydrostatic Equilibrium

A star spends most of its life on the main sequence, where it is in hydrostatic equilibrium: the inward gravitational force is balanced by the outward radiation pressure from nuclear fusion in the core.

Main sequence lifetime depends on mass:

t ∝ M / L ∝ M / M⁴ = M⁻³ (approximately)

Stellar mass	Main sequence lifetime	Final fate
< 0.5 M_☉ (red dwarf)	>100 billion years	White dwarf directly
0.5–8 M_☉ (Sun-like)	~1–50 billion years	Red giant → white dwarf
8–20 M_☉ (massive)	~10–100 million years	Red supergiant → supernova → neutron star
>20 M_☉ (very massive)	<10 million years	Red supergiant → supernova → black hole

More massive stars are far more luminous (L ∝ M^3.5 approximately) and exhaust their fuel much faster, even though they have more of it. The most massive O-type stars live only a few million years.

Red Giants and Supergiants

When core hydrogen is exhausted, the inward gravitational force wins briefly. The core contracts and heats up, which ignites hydrogen shell burning around the inert helium core.

The outer layers expand enormously, surface temperature drops — the star becomes a red giant (for low/medium mass) or red supergiant (for high mass):

Radius increases by factor ~100–1000
Surface temperature drops to ~3000–4000 K
Luminosity increases overall (L = 4πr²σT⁴ — r increases faster than T⁴ decreases)
On the HR diagram: the star moves to the upper right

Eventually, core temperatures reach ~10⁸ K, igniting helium fusion (triple-alpha process: 3 ⁴He → ¹²C). For massive stars, carbon, oxygen, silicon burning stages follow in sequence.

Low/Medium Mass Stars: White Dwarfs

For stars with initial mass < ~8 M_☉ (after mass loss, the remnant core is < 1.4 M_☉):

Outer layers are shed as a planetary nebula
The exposed core becomes a white dwarf

White dwarf properties:

Mass: typically ~0.6 M_☉; Size: ~Earth-sized (~10⁴ km diameter)
Density: ~10⁹ kg/m³ (one teaspoon ≈ 15 tonnes)
No fusion — supported by electron degeneracy pressure
Cools gradually from hot-white to cold-black over billions of years

The Chandrasekhar limit is 1.4 M_☉. If a white dwarf exceeds this mass (e.g. by accreting matter from a companion), electron degeneracy pressure is overcome, triggering a Type Ia supernova explosion.

Massive Stars: Supernovae and Neutron Stars

For stars with initial mass > ~8 M_☉, fusion proceeds through successively heavier elements until the core becomes iron. Since iron fusion is endothermic, energy generation ceases:

The iron core collapses in milliseconds
Protons and electrons combine: p + e⁻ → n + ν_e (neutronisation)
The core rebounds — a supernova explosion ejects the outer layers
The remnant core is a neutron star

Neutron star properties:

Mass: 1.4–3 M_☉; radius: ~10 km
Density: ~10¹⁷ kg/m³ (nuclear density)
Supported by neutron degeneracy pressure

A pulsar is a rotating neutron star with a strong magnetic field that emits narrow beams of electromagnetic radiation. If the beam sweeps past Earth, we detect regular pulses — like a cosmic lighthouse.

Black Holes and HR Diagram Tracks

If the remnant core mass exceeds ~3 M_☉, neutron degeneracy pressure is also overcome and the core collapses to a black hole — a region of spacetime from which nothing, not even light, can escape.

Schwarzschild radius: r_s = 2GM / c²

HR diagram evolutionary tracks:

Low-mass star: Main sequence (lower right) → expands right → red giant (upper right) → contracts to white dwarf (lower left)
High-mass star: Main sequence (upper left) → expands right → red supergiant → supernova → off the HR diagram (neutron star/black hole)

The Sun will become a red giant in ~5 billion years, expanding to engulf Mercury and possibly Venus and Earth, before shedding its outer layers as a planetary nebula and leaving a white dwarf remnant.

Example 1: Main sequence lifetime estimate

A star has mass 4 M_☉ and luminosity 40 L_☉. Estimate its main sequence lifetime compared to the Sun (lifetime ~10 billion years).

1 t ∝ M/L → t_star/t_☉ = (M_star/M_☉) / (L_star/L_☉) = 4/40 = 0.10

2 t_star = 0.10 × 10 billion = 1.0 billion years

The star lives ~1 billion years — only 1/10 of the Sun's main sequence lifetime, despite being 4× more massive.

Example 2: Chandrasekhar limit application

A white dwarf in a binary system accretes matter from its companion star at a rate of 10⁻⁸ M_☉/year. If the white dwarf currently has mass 1.3 M_☉, how long before a Type Ia supernova occurs?

1 Mass needed: ΔM = 1.4 − 1.3 = 0.1 M_☉

2 Time = ΔM / accretion rate = 0.1 / 10⁻⁸ = 10⁷ years

The supernova will occur in ~10 million years. Type Ia supernovae are extremely useful as "standard candles" in cosmology because they all have roughly the same peak luminosity (at the Chandrasekhar limit).

Example 3: Schwarzschild radius of a black hole

A stellar black hole has mass 10 M_☉. Calculate its Schwarzschild radius. (M_☉ = 2.0 × 10³⁰ kg, G = 6.67 × 10⁻¹¹ N m² kg⁻², c = 3.0 × 10⁸ m/s)

1 M = 10 × 2.0 × 10³⁰ = 2.0 × 10³¹ kg

2 r_s = 2GM/c² = 2 × 6.67 × 10⁻¹¹ × 2.0 × 10³¹ / (3.0 × 10⁸)²

3 r_s = 2.668 × 10²¹ / 9.0 × 10¹⁶ = 2.965 × 10⁴ m

r_s ≈ 30 km — a stellar black hole with 10 solar masses has an event horizon of only 30 km radius

Example 4: Tracing an evolutionary track

A 15 M_☉ star begins on the main sequence. Describe and trace its path on the HR diagram until its death.

1 Begins upper left of main sequence: very hot (T ~ 25,000 K), very luminous (L ~ 10⁵ L_☉), spectral class O or B.

2 Core H exhausted after ~10 million years. Moves rightward on HR diagram — becomes a red supergiant (upper right): T drops to ~3500 K, L remains very high.

3 Successive nuclear burning stages: He → C → O → Si → Fe. Iron core collapse triggers supernova explosion.

Final state: Neutron star (if remnant core 1.4–3 M_☉) or black hole (if remnant > 3 M_☉). The star is no longer on the HR diagram. The supernova ejects heavy elements into interstellar space.

Q1. Why do massive stars have shorter main sequence lifetimes than low-mass stars?

Q2. What is the Chandrasekhar limit and why is it significant?

Q3. A pulsar emits radio pulses every 0.033 seconds. What does this tell us about its rotation rate?

Q4. In which direction does a main-sequence star move on the HR diagram when it becomes a red giant?

Q5. What prevents a white dwarf from collapsing further under gravity?

Challenge 1. A neutron star has mass 1.4 M_☉ and radius 10 km. Calculate its mean density and compare it to nuclear density (~2.3 × 10¹⁷ kg/m³). (M_☉ = 2.0 × 10³⁰ kg)

Challenge 2. Explain why Type Ia supernovae are used as "standard candles" in cosmology, and state what assumption must hold for this to work.

Challenge 3. The Sun will eventually become a red giant with radius ~200 R_☉ and temperature ~3500 K. Calculate the Sun's luminosity as a red giant and express it as a multiple of the current solar luminosity. (Current: L_☉ = 3.85 × 10²⁶ W, T_☉ = 5778 K, r_☉ = 6.96 × 10⁸ m)