Does a teaspoon of neutron star really weigh billions of tonnes?

A 1.4 solar-mass neutron star is about 12 km in radius, so its mean density is about 4×10¹⁷ kg/m³, the same order as an atomic nucleus. Five millilitres is then about 2×10¹² kg, roughly 1.8 billion tonnes, a few times the combined weight of every human. A teaspoon of white dwarf is only a couple of tonnes, about one car.

What are the Chandrasekhar and TOV limits?

A white dwarf is held up by electron degeneracy pressure. Above about 1.44 solar masses (the Chandrasekhar limit) the electrons become relativistic and the pressure can no longer stop collapse. A neutron star is held up by neutron degeneracy and nuclear forces; its maximum mass, the TOV limit, depends on the equation of state of dense matter, and current evidence points to about 2.0–2.3 solar masses. Anything heavier becomes a black hole. The neutron star radius in this tool is an empirical ~12 km approximation, not a specific equation of state.

How reliable is the characteristic age P/2Ṗ?

It assumes the pulsar was born spinning much faster than now and has slowed by pure magnetic dipole radiation (braking index 3). For the Crab pulsar it gives about 1,260 years, close to the true age since the supernova of 1054. For many pulsars it is far off: a long birth period, a different braking index, field decay, or spin-up by accretion for millisecond pulsars all break it, so treat it as an order of magnitude.

Why do low frequencies arrive later, and how does that give a distance?

Free electrons in interstellar space make the group velocity of radio waves depend on frequency, slower at lower frequency, with a delay Δt ≈ 4.149 ms × DM × f⁻² (f in GHz). The dispersion measure DM is the electron column along the line of sight in pc/cm³. With a mean Galactic electron density of about 0.03 cm⁻³, the distance is d ≈ DM/⟨n_e⟩. In practice astronomers use Galactic electron models such as NE2001 or YMW16, good to a few tens of percent.

Why can you see part of a neutron star's far side?

A neutron star's Schwarzschild radius is about a third of its radius, so light bends strongly. Rays that graze the limb on their way to a distant observer actually leave from part of the back hemisphere. With Beloborodov's approximation the visible fraction is about 1/(2(1−Rs/R)), roughly three quarters of the surface for a 1.4 solar-mass star. The tool draws these rays by numerical integration and reports where the grazing ray lands.

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💫Neutron Star & Pulsar Explorer - Compact Objects, Lighthouse Model, P–Ṗ Diagram

Drag the remnant mass to compare a white dwarf, a neutron star and a black hole side by side: radius, mean density, the weight of a teaspoon, surface gravity, escape velocity and gravitational redshift, with the Chandrasekhar and TOV limits marked on a mass–radius chart. The light-bending view traces photons through Schwarzschild spacetime, so you can see why part of a neutron star's far side is visible. For pulsars there is a lighthouse animation with an observed pulse train, a pulse sound played at the real rate, spin-down estimates from P and Ṗ, a P–Ṗ diagram of famous pulsars, and distance from dispersion delay.

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How to use Neutron Stars & Pulsars

1On Compact objects, drag the mass and read the three objects' properties and the mass–radius chart
2On Light bending, change the stellar radius in units of Rs and watch the visible fraction of the surface
3On Pulsar lighthouse, pick a famous pulsar or enter P and Ṗ, set the inclination and viewing angle, then play the animation and the sound
4Click or drag on the P–Ṗ diagram, and on Dispersion distance change DM and the band to see the sweep and the distance

FAQ

Does a teaspoon of neutron star really weigh billions of tonnes?: A 1.4 solar-mass neutron star is about 12 km in radius, so its mean density is about 4×10¹⁷ kg/m³, the same order as an atomic nucleus. Five millilitres is then about 2×10¹² kg, roughly 1.8 billion tonnes, a few times the combined weight of every human. A teaspoon of white dwarf is only a couple of tonnes, about one car.
What are the Chandrasekhar and TOV limits?: A white dwarf is held up by electron degeneracy pressure. Above about 1.44 solar masses (the Chandrasekhar limit) the electrons become relativistic and the pressure can no longer stop collapse. A neutron star is held up by neutron degeneracy and nuclear forces; its maximum mass, the TOV limit, depends on the equation of state of dense matter, and current evidence points to about 2.0–2.3 solar masses. Anything heavier becomes a black hole. The neutron star radius in this tool is an empirical ~12 km approximation, not a specific equation of state.
How reliable is the characteristic age P/2Ṗ?: It assumes the pulsar was born spinning much faster than now and has slowed by pure magnetic dipole radiation (braking index 3). For the Crab pulsar it gives about 1,260 years, close to the true age since the supernova of 1054. For many pulsars it is far off: a long birth period, a different braking index, field decay, or spin-up by accretion for millisecond pulsars all break it, so treat it as an order of magnitude.
Why do low frequencies arrive later, and how does that give a distance?: Free electrons in interstellar space make the group velocity of radio waves depend on frequency, slower at lower frequency, with a delay Δt ≈ 4.149 ms × DM × f⁻² (f in GHz). The dispersion measure DM is the electron column along the line of sight in pc/cm³. With a mean Galactic electron density of about 0.03 cm⁻³, the distance is d ≈ DM/⟨n_e⟩. In practice astronomers use Galactic electron models such as NE2001 or YMW16, good to a few tens of percent.
Why can you see part of a neutron star's far side?: A neutron star's Schwarzschild radius is about a third of its radius, so light bends strongly. Rays that graze the limb on their way to a distant observer actually leave from part of the back hemisphere. With Beloborodov's approximation the visible fraction is about 1/(2(1−Rs/R)), roughly three quarters of the surface for a 1.4 solar-mass star. The tool draws these rays by numerical integration and reports where the grazing ray lands.

Features

White dwarf (Nauenberg mass–radius relation), neutron star and black hole compared side by side, including teaspoon weights
RK4 photon orbits in Schwarzschild spacetime, checked against Beloborodov's approximation
3D rotating-vector lighthouse animation with the observed pulse train, and pulses played as sound at the true period
Magnetic dipole spin-down: characteristic age, surface field, spin-down luminosity, light-cylinder radius
P–Ṗ diagram with constant-age and constant-field lines and the death line, showing the Crab, Vela, CP 1919, millisecond pulsars and magnetars
Dispersion dynamic spectrum: frequency vs arrival time, dedispersion and a distance estimate

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