Neutron Star
A neutron star is an extraordinarily dense stellar remnant formed when the core of a massive star (8–20 M☉) collapses during a Type II supernova, compressing a mass of 1.2–2.1 M☉ into a sphere only ~10–13 km in radius, resulting in densities comparable to atomic nuclei (~10¹⁴ g/cm³). The star is supported against further gravitational collapse by neutron degeneracy pressure—a quantum mechanical effect arising from the Pauli exclusion principle—rather than thermal or radiation pressure. Neutron stars often manifest as rapidly rotating pulsars, emitting beams of electromagnetic radiation from their magnetic poles at highly regular intervals, and they are key sources of gravitational waves when in binary systems.
Key Formula
Neutron star radius ≈ (3M / 4π ρ₀)^(1/3); Core density ≈ 10¹⁴–10¹⁵ g/cm³
LaTeX: R_{\text{NS}} \approx \frac{3M}{4\pi\,\rho_0},\quad \rho_{\text{core}} \approx 10^{14}\text{–}10^{15}\,\text{g cm}^{-3}
| Symbol | Meaning | Unit |
|---|---|---|
| R_NS | Radius of the neutron star | km |
| M | Mass of the neutron star | kg |
| ρ₀ | Nuclear saturation density (~2.3×10¹⁴ g/cm³) | g/cm³ |
| ρ_core | Core density of the neutron star | g/cm³ |
Worked Example
Problem
A neutron star has a mass of 1.4 M☉ (M☉ = 2×10³⁰ kg) and a radius of 12 km. Calculate its average density and compare to the density of atomic nuclei (~2.3×10¹⁴ g/cm³).
Solution
Step 1 – Convert mass: M = 1.4 × 2×10³⁰ = 2.8×10³⁰ kg. Step 2 – Convert radius: R = 12 km = 1.2×10⁴ m. Step 3 – Calculate volume: V = (4/3)π R³ = (4/3) × π × (1.2×10⁴)³ = (4/3) × π × 1.728×10¹² = 7.24×10¹² m³. Step 4 – Calculate density: ρ = M/V = 2.8×10³⁰ / 7.24×10¹² = 3.87×10¹⁷ kg/m³ = 3.87×10¹⁴ g/cm³.
Answer
Average density ≈ 3.87×10¹⁴ g/cm³, which is close to nuclear saturation density, confirming neutron star matter is essentially nuclear-density material throughout.
Comparing Neutron Stars to Other Stellar Remnants
| Property | White Dwarf | Neutron Star | Black Hole | Sun (for reference) |
|---|---|---|---|---|
| Typical mass (M☉) | 0.5–1.4 | 1.2–2.1 | >3 (stellar) | 1.0 |
| Radius | ~7,000 km | 10–13 km | rs~3 km/M☉ | 696,000 km |
| Density (g/cm³) | 10⁵–10⁷ | 10¹⁴–10¹⁵ | singularity | 1.41 |
| Support mechanism | Electron degeneracy | Neutron degeneracy | None (collapsed) | Radiation pressure |
| Progenitor | < 8 M☉ star | 8–20 M☉ star | > 20 M☉ star | N/A |
Interactive Tools
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Related Terms
Supernova
A supernova is an extraordinarily energetic stellar explosion that marks the catastrophic death of certain types of stars, releasing in seconds as much energy (roughly 10⁴⁴ J) as the Sun will radiate over its entire 10-billion-year lifetime, and briefly outshining an entire galaxy. Type Ia supernovae occur when a white dwarf in a binary system accretes enough mass to exceed the Chandrasekhar limit (~1.4 M☉), triggering runaway nuclear fusion; Type II supernovae occur when the iron core of a massive star (>8 M☉) collapses under gravity, producing a shockwave that ejects the outer layers. Supernovae are the primary source of elements heavier than iron in the universe and are used as "standard candles" in cosmology to measure vast intergalactic distances.
White Dwarf
A white dwarf is the dense, compact stellar remnant left behind after a low-to-intermediate mass star (0.5–8 M☉) has shed its outer layers as a planetary nebula, leaving an Earth-sized sphere of electron-degenerate matter composed primarily of carbon and oxygen at densities of ~10⁶ g/cm³. Unlike main sequence stars, white dwarfs are not powered by nuclear fusion; they simply radiate their residual thermal energy, cooling over billions to trillions of years from initially blue-white temperatures through yellow and orange to the theoretical endpoint of a cold, dark "black dwarf". The maximum mass a white dwarf can have before collapsing is the Chandrasekhar limit of ~1.4 M☉.
Stellar Nuclear Fusion
Stellar nuclear fusion is the thermonuclear process occurring in a star's core whereby lighter atomic nuclei are forced together under extreme temperature and pressure to form heavier nuclei, releasing enormous amounts of energy according to Einstein's mass–energy equivalence. In main-sequence stars like the Sun, the dominant process is the proton–proton (pp) chain, which converts hydrogen into helium; more massive stars rely on the CNO (carbon–nitrogen–oxygen) cycle. This energy release provides the radiation pressure that counteracts gravitational collapse, maintaining a star's long-term equilibrium known as hydrostatic balance.
The term "neutron star" was proposed by Walter Baade and Fritz Zwicky in 1934, just two years after James Chadwick's discovery of the neutron (1932). "Neutron" derives from Latin "neuter" (neither), reflecting that it carries no electric charge. The existence of neutron stars was confirmed observationally with the discovery of the first pulsar by Jocelyn Bell Burnell in 1967.