Physics/Option Modules/Astrophysics/Neutron Stars
Physics · Astrophysics · A2 Level

Neutron Stars

A teaspoon of neutron-star material would weigh about as much as a mountain. When a collapsing stellar core is too massive to become a white dwarf, gravity crushes it into something even more extreme — a ball of almost pure neutrons, held up by a quantum effect pushed to its absolute limit.

8 min read

Beyond the Chandrasekhar limit

The previous lesson showed that electron degeneracy pressure can support a stellar remnant only up to the Chandrasekhar limit, roughly 1.4 solar masses. For a more massive star, the collapsing core left behind after its nuclear fuel is exhausted can exceed this limit — and when it does, electron degeneracy pressure alone is no longer strong enough to halt the collapse. Gravity wins, and the core continues to collapse far beyond the point at which a white dwarf would have stabilised.

As the collapse proceeds to even more extreme densities, the electrons are forced so close to the protons in the core's nuclei that they are effectively forced to combine with them, in a process similar to inverse beta decay: an electron and a proton merge to form a neutron (releasing a neutrino in the process). This happens on a vast scale throughout the collapsing core, converting what was a mix of electrons, protons and nuclei into an extraordinarily dense ball made up almost entirely of neutrons.

Neutron degeneracy pressure

Collapse of the core is eventually halted by a new form of the same underlying quantum-mechanical effect encountered in the previous lesson: neutron degeneracy pressure. Just as the Pauli exclusion principle prevents electrons from being squeezed into the same quantum states, it also applies to neutrons, generating an outward pressure that resists further compression once the neutrons themselves are forced close enough together.

Because neutrons are far more massive than electrons, and are not electrically charged (so there's no additional repulsion from like charges to worry about), neutron degeneracy pressure can support a far greater density before failing than electron degeneracy pressure can. The result of this second stage of collapse, halted by neutron degeneracy pressure, is a neutron star.

Order-of-magnitude estimateJust how dense is a neutron star?
1
A typical neutron star has a mass of roughly 1.4–2 solar masses, packed into a radius of only about 10–20 km.
Compare this to the Sun's actual radius of around 700,000 km — a neutron star squeezes a comparable mass into a sphere tens of thousands of times smaller across.
2
Using $\rho = \dfrac{M}{\frac{4}{3}\pi r^3}$ with $M \approx 2.8\times10^{30}\,\text{kg}$ and $r \approx 1.2\times10^{4}\,\text{m}$ gives a density of order $10^{17}$–$10^{18}\,\text{kg m}^{-3}$.
This is comparable to, and in some cases exceeds, the density of matter packed inside an atomic nucleus itself — a neutron star is, in effect, a single object with roughly the density of a nucleus but the size of a city.
3
A teaspoon (roughly 5 cm³) of neutron-star material at this density would have a mass of the order of a billion tonnes.
A genuinely useful way to convey the scale: matter this dense simply cannot exist under everyday conditions anywhere on Earth.
estimate
$$\rho = \frac{M}{\frac{4}{3}\pi r^3} \approx \frac{2.8\times10^{30}}{\frac{4}{3}\pi (1.2\times10^4)^3} \approx 4\times10^{17}\,\text{kg m}^{-3}$$

Pulsars: neutron stars we can actually observe

Neutron stars are far too small and faint to observe directly by their visible light in most cases, but many are detected through a striking observational signature: pulsars. A pulsar is a rapidly rotating, highly magnetised neutron star that emits intense beams of electromagnetic radiation from its magnetic poles. Because the magnetic axis is typically misaligned with the rotation axis, these beams sweep around like a lighthouse beam as the neutron star spins.

If one of these beams happens to sweep across the Earth's line of sight during each rotation, radio telescopes detect it as an extremely regular, rapid series of pulses — some pulsars rotate (and therefore pulse) many times per second, with a regularity so precise that pulsars are sometimes used as extraordinarily accurate natural clocks. This regular pulsing is what first revealed the existence of neutron stars observationally.

Connecting forward: gamma-ray bursts

Gamma-ray bursts are associated with the sudden, violent collapse of massive or supergiant stars, releasing an intense, short-lived burst of gamma radiation as the core collapses. Depending on the mass of the collapsing core, this violent collapse can result either in a neutron star, as covered in this lesson, or — for even more massive cores that even neutron degeneracy pressure cannot support — an object with no known lower limit to its further collapse: a black hole, the subject of the next lesson.

The key idea to take from this lesson

A neutron star represents the second and far more extreme stage of degeneracy-pressure support in stellar remnants. Where electron degeneracy pressure fails above the Chandrasekhar limit, neutron degeneracy pressure — the same exclusion-principle effect, now acting between neutrons rather than electrons — can support a far higher density, but it too has its own upper mass limit, beyond which even a sea of neutrons cannot resist gravity. What lies beyond that final limit is the subject of the next lesson.

Key takeaways

  • When a collapsing stellar core exceeds the Chandrasekhar limit, electron degeneracy pressure can no longer halt the collapse.
  • Collapse continues until electrons combine with protons (inverse beta decay), converting the core into a ball composed almost entirely of neutrons.
  • The collapse is eventually halted by neutron degeneracy pressure, the same quantum exclusion effect as before, now acting between neutrons.
  • A neutron star typically has a radius of only 10–20 km but a mass of roughly 1.4–2 solar masses, giving densities comparable to an atomic nucleus.
  • A teaspoon of neutron-star material would have a mass of roughly a billion tonnes, conveying just how extreme this density is.
  • Pulsars are rapidly rotating, highly magnetised neutron stars whose beams of radiation sweep across space, detected on Earth as extremely regular pulses.
  • Gamma-ray bursts are linked to the violent collapse of massive stars, forming either a neutron star or, for even more massive cores, a black hole.
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