--- title: Neutron star summary: The collapsed core of a massive star, more massive than the Sun yet only about 24 km across; seen as radio pulsars, millisecond pulsars, magnetars and X-ray pulsars. science_status: [observed, model, sim] categories: [Neutron stars, Stellar remnants, Compact objects, Pulsars] aliases: [Neutron stars, Pulsar, Pulsars, Radio pulsar, Millisecond pulsar, Magnetar, Magnetars, X-ray pulsar, Accreting pulsar, XDINS, Magnificent Seven, Central compact object, PSR, MSP, MGR, XRP] infobox: type: neutron_star image: File:Neutron_star_hot_caps_sim.png image_caption: "Sim reference render: a 12 km neutron star, its light bent so that both hot polar caps show at the edges" classes: [rotation-powered radio pulsar, millisecond pulsar, magnetar, accreting X-ray pulsar, X-ray dim isolated neutron star (XDINS), central compact object (CCO), neutron-star X-ray binary] spin_period_s: "0.0014 (716 Hz) to 76 for radio pulsars; accreting pulsars up to hours" period_derivative_s_per_s: "about 1e-21 (millisecond pulsars) to about 1e-10 (magnetars)" characteristic_age_yr: "a few hundred (magnetars, young pulsars) to about 1e10 (millisecond pulsars)" dipole_field_g: "about 1e8 to 1e9 (millisecond pulsars); about 1e12 (ordinary pulsars); 1e14 to 1e15 (magnetars)" spin_down_luminosity_erg_s: "up to about 5e38 (the Crab pulsar)" mass_msun: "about 1.2 to 2.35 measured; heaviest well measured 2.08 +/- 0.07 and 2.35 +/- 0.17" maximum_mass_msun: "not pinned down; above about 2.1, most analyses below about 2.3" radius_km: "about 12 (12.0, 95 percent range 11.3 to 12.6, at 1.4 solar masses)" mean_density_kg_m3: 4e17 surface_gravity_m_s2: 1e12 escape_speed: "about 0.6 c" surface_temperature_k: "about 1e6 when young; below 1e5 after about 10 million years unless reheated" distance_methods: [radio parallax (VLBI), timing parallax, dispersion measure, association with a supernova remnant or cluster] dispersion_measure_pc_cm3: "about 2.6 (nearby) to over 1,000 (far side of the Galaxy)" known_count: "4,393 radio and high-energy pulsars in the ATNF Pulsar Catalogue v2.8.1; about 30 magnetars" nearest_known: "RX J1856.5-3754, 123 pc" catalogue_ids: "ATNF PSR J name (e.g. PSR J0534+2200 for the Crab)" source_catalogue: [ATNF Pulsar Catalogue v2.8.1, McGill Magnetar Catalog] sim_stops: [Crab Pulsar, Vela Pulsar, Geminga, RX J1856.5-3754, PSR J0437-4715, Hercules X-1, SGR 1806-20] sim: entity: stellar_class.neutron_star catalogue: [atnf_psrcat_2.8.1, known_neutron_stars.json] refs: - id: hewish1968 type: article-journal author: [{family: Hewish, given: A.}, {family: Bell, given: S. 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M.}, {family: Sunyaev, given: R. A.}] title: "The Limiting Luminosity of Accreting Neutron Stars With Magnetic Fields" container-title: Monthly Notices of the Royal Astronomical Society issued: 1976 volume: 175 page: "395-417" DOI: 10.1093/mnras/175.2.395 - id: staubert2019 type: article-journal author: [{family: Staubert, given: R.}, {literal: "et al."}] title: "Cyclotron lines in highly magnetized neutron stars" container-title: Astronomy & Astrophysics issued: 2019 volume: 622 page: "A61" DOI: 10.1051/0004-6361/201834479 - id: walter2010 type: article-journal author: [{family: Walter, given: F. M.}, {literal: "et al."}] title: "Revisiting the Parallax of the Isolated Neutron Star RX J185635-3754 Using HST/ACS Imaging" container-title: The Astrophysical Journal issued: 2010 volume: 724 page: "669-677" DOI: 10.1088/0004-637X/724/1/669 images_wanted: - file: File:Neutron_star_hot_caps_sim.png subject: "Reference render: a 1.4 solar-mass, 12 km neutron star (2.9 Schwarzschild radii) against a lensed star field; its two hot polar caps both visible at the edges of the disc" source: sim source_ref: "BHIMG:b4_neutron_star_r2p9_caps_limbs.png" credit: "Pax Abyssi (sim reference render)" note: "prefix legend in content/wiki/_notes/writer-c.md; confirm with the renderer lane whether this is an in-game capture or the desk oracle before captioning" - file: File:Crab_pulsar_bent_light_sim.png subject: "Four-panel reference render of the Crab pulsar: flat space with a spin graticule, bent light in false colour, bent light as the eye sees it, and averaged over a turn" source: sim source_ref: "NSIMG:n0_crab.png" credit: "Pax Abyssi (sim reference render)" note: "prefix legend in content/wiki/_notes/writer-c.md; the panel header text is internal (prints physical values); crop the header or regenerate a clean version before publishing" - file: File:Crab_Nebula_Webb.jpg subject: "The Crab Nebula in infrared, JWST NIRCam and MIRI: the supernova remnant of 1054 energised by the Crab pulsar at its centre" source: esa-webb page_url: "https://esawebb.org/images/weic2326a/" image_url: "https://cdn.esawebb.org/archives/images/large/weic2326a.jpg" credit: "NASA, ESA, CSA, STScI, T. Temim (Princeton University)" licence: "CC BY 4.0" --- A **neutron star** is the collapsed core of a massive star: typically more massive than the Sun, yet only about 24 km across, the size of a city. Its matter is packed as tightly as the inside of an atomic nucleus. Neutron stars are born in supernova explosions, spin up to hundreds of times a second, carry the strongest magnetic fields known, and cool over millions of years from a million degrees. Astronomers meet them in several guises: as **radio pulsars** whose beams sweep past Earth like a lighthouse's, as **millisecond pulsars** that keep time as well as atomic clocks, as **magnetars** that erupt in flares of gamma rays, and as **X-ray pulsars** fed by a companion star. The ATNF Pulsar Catalogue lists 4,393 pulsars in its version 2.8.1 :cite[atnf]. ::figure{src="File:Crab_Nebula_Webb.jpg" size=wide alt="A cage-like cloud of orange and red filaments around a pale, smoky interior against a dark sky." caption="Observation: the Crab Nebula in infrared, seen by the James Webb Space Telescope. The remnant of a supernova recorded in 1054 is kept glowing by the Crab pulsar, a neutron star spinning 30 times a second at its centre. Credit: NASA, ESA, CSA, STScI, T. Temim (Princeton University)."} ## What a neutron star is When the iron core of a massive star exceeds what electron pressure can hold up, it collapses in under a second. Electrons are forced into protons, making neutrons, and the fall stops only when the neutrons are packed to nuclear density and resist further squeezing. The outer layers rebound and are blown off as a supernova; what remains is the neutron star. Its numbers are hard to picture. Combining radius measurements from NASA's NICER X-ray telescope with gravitational-wave data and nuclear theory gives a radius of about 12.0 km for a star of 1.4 solar masses, with a 95 per cent range of about 11.3 to 12.6 km :cite[rutherford2024]. That puts the mean density near $4 \times 10^{17}$ kg/m³: a teaspoon would weigh about two billion tonnes. Surface gravity is about $10^{12}$ m/s², a hundred billion times Earth's, and the escape speed is about 60 per cent of the speed of light. The outer kilometre or so is a solid crust of neutron-rich nuclei in a lattice; below it, nuclei dissolve into a fluid of neutrons with a few per cent of protons and electrons. What happens in the centre, at several times nuclear density, is one of the open questions of physics, and a neutron star's mass and radius are the main way to test the answers. ### How heavy can one be? Heavier neutron stars are slightly smaller, and above some maximum mass nothing can stop collapse to a [[Black hole]]. That ceiling is not yet pinned down. The pulsar PSR J0740+6620 weighs 2.08 ± 0.07 solar masses, measured from the delay its radio pulses suffer passing its companion :cite[fonseca2021]. The "black widow" pulsar PSR J0952-0607, whose companion it is slowly evaporating, weighs 2.35 ± 0.17 solar masses, which places the ceiling above about 2.2 solar masses at one standard deviation :cite[romani2022]. The combined NICER and gravitational-wave analysis predicts a maximum of about 2.1 to 2.2 solar masses, with uncertainties near 0.2 :cite[rutherford2024]. ### Bent light A neutron star of 1.4 solar masses and 12 km radius is only 2.9 times its own Schwarzschild radius, so gravity bends its light strongly. A distant observer sees about 76 per cent of its surface at once, and the star looks larger than it is :cite[beloborodov2002]. That bending is what lets NICER measure radii: the way X-rays from hot spots near the magnetic poles brighten and fade as the star turns depends on how compact it is :cite[riley2019] :cite[miller2019]. ::figure{src="File:Neutron_star_hot_caps_sim.png" size=wide alt="A pale blue disc on a black sky of stretched star streaks, with two small bright patches on its left and right edges." caption="Sim reference render: a 1.4 solar-mass neutron star, 12 km in radius, seen side-on. In flat space its two hot polar caps would sit on the far edges, out of sight; bent light brings both into view at the rim. The background stars are smeared by lensing."} ### Heat A newborn neutron star is hotter than a billion kelvin inside. It cools first by emitting neutrinos from its core and later, after about 100,000 years, mainly by radiating from its surface. The Vela pulsar, about 20,000 years old, has a surface near 660,000 K; stars around a million years old are below 300,000 K :cite[potekhin2020]. At these temperatures the surface glows in X-rays and ultraviolet, and what little visible light it emits is a pale blue. ## Pulsars In 1967 Jocelyn Bell, a graduate student at Cambridge working with Antony Hewish, found a radio source that pulsed every 1.34 seconds with clockwork regularity :cite[hewish1968]. It was a spinning neutron star. A neutron star's magnetic axis is usually tilted from its spin axis, and beams of radio waves stream out above the magnetic poles; each time a beam sweeps across Earth we see a pulse. The beams are radio waves, invisible to the eye. A pulsar slows as it spins, radiating away its rotational energy through its magnetic field and a wind of particles :cite[goldreich1969]. Measure the period $P$ and how fast it lengthens, $\dot{P}$, and three standard estimates follow: $$ B \approx 3.2 \times 10^{19}\,\sqrt{P\dot{P}}\ \mathrm{G}, \qquad \tau_\mathrm{c} = \frac{P}{2\dot{P}}, \qquad \dot{E} = \frac{4\pi^2 I \dot{P}}{P^3}, $$ the magnetic field at the equator (in gauss, with $P$ in seconds), the **characteristic age**, and the **spin-down power**, with the moment of inertia $I$ usually taken as $10^{45}$ g cm². The field estimate assumes a spinning magnet in a vacuum, and the age assumes the star was born spinning much faster than now; both are estimates. The Crab pulsar shows how well they work. It spins every 33.39 milliseconds and slows by $4.21 \times 10^{-13}$ seconds each second :cite[atnf]. That gives a field of $3.8 \times 10^{12}$ gauss, a characteristic age of about 1,260 years (the true age, from the supernova Chinese astronomers recorded in 1054, is 972 years) and a spin-down power of about $4.5 \times 10^{38}$ erg/s, more than 100,000 times the Sun's luminosity. That power keeps the Crab Nebula glowing. Pulsar periods span an extraordinary range. The fastest known, PSR J1748-2446ad, turns 716 times a second :cite[hessels2006]. The slowest radio pulsar confirmed as a neutron star, PSR J0901-4046, takes 76 seconds :cite[caleb2022], and radio sources that repeat every 18 minutes or more have been found whose nature, neutron star or white dwarf, is still debated :cite[hurleywalker2022]. ### Clocks in orbit In 1974 Russell Hulse and Joseph Taylor found a pulsar in a 7.75-hour orbit around another neutron star :cite[hulse1975]. Over four decades of timing, its orbit has shrunk exactly as general relativity predicts for a system losing energy to gravitational waves: the measured decay is 0.9983 ± 0.0016 times the prediction, and the two stars weigh 1.438 and 1.390 solar masses :cite[weisberg2016]. In 2017 the LIGO and Virgo detectors caught two neutron stars merging, GW170817, the first such event seen in both gravitational waves and light :cite[abbott2017]. ## Millisecond pulsars Pulsars spinning every few milliseconds are old neutron stars "recycled" by a companion star. Gas flowing onto the neutron star carries angular momentum that spins it up to hundreds of turns a second, while its field decays to $10^8$ or $10^9$ gauss :cite[alpar1982]. The first, PSR B1937+21, was found in 1982 spinning every 1.56 ms :cite[backer1982]. With weak fields they slow very little, so they tick for billions of years with a steadiness rivalling atomic clocks. Pulsar timing arrays watch dozens of them for tiny, correlated shifts in arrival times; in 2023 the NANOGrav collaboration reported evidence of a background of gravitational waves with periods of years, probably from pairs of supermassive black holes :cite[nanograv2023]. PSR J0437-4715, 157 parsecs away, is the nearest and brightest millisecond pulsar. NICER and radio timing give it 1.418 ± 0.037 solar masses and a radius of 11.4 km (+1.0 / -0.6 km) :cite[choudhury2024]. ## Magnetars **Magnetars** are young neutron stars with fields of $10^{14}$ to $10^{15}$ gauss, a hundred to a thousand times those of ordinary pulsars and up to a thousand trillion times the field at Earth's surface :cite[duncan1992]. They shine mostly by the decay of that field, which stresses the crust until it cracks, and they spin slowly, once every few seconds. About thirty are known :cite[kaspi2017] :cite[olausen2014]. On 27 December 2004 the magnetar SGR 1806-20 released the brightest flash ever recorded from outside the Solar System. The discovery paper, assuming a distance of 15 kiloparsecs, calculated that in its first fifth of a second the flare emitted as much energy as the Sun radiates in a quarter of a million years :cite[hurley2005]. Later measurements put the star at about 8.7 kiloparsecs :cite[bibby2008], which lowers that energy by a factor of three. In 2020 another magnetar, SGR 1935+2154, emitted a millisecond radio burst of the kind seen from distant galaxies as fast radio bursts, tying at least some of those bursts to magnetars :cite[chime2020]. ## X-ray pulsars A neutron star in a close binary can pull gas from its companion. If its field is strong, the field channels the gas down onto the magnetic poles, where it lands at a good fraction of the speed of light and heats spots of the surface to tens of millions of kelvin. The X-rays pulse as the star turns. The first such **accreting X-ray pulsars**, Centaurus X-3 and Hercules X-1, were found by the Uhuru satellite in 1971 and 1972 :cite[giacconi1971] :cite[tananbaum1972]. When the inflow is heavy, the gas piles into a column above each pole, held up by its own radiation :cite[basko1976]. Absorption lines in these X-ray spectra, caused by electrons spiralling in the magnetic field, give the most direct measurement of a neutron star's field. The first, found in Hercules X-1 in 1976, implies several $10^{12}$ gauss at the pole; about 35 accreting pulsars now show such lines :cite[staubert2019]. ## Quiet neutron stars Most neutron stars in the Galaxy are old, cold and silent, their beams long faded or pointed away from us. A few isolated ones are close enough to see by the glow of their surfaces. The nearest known, RX J1856.5-3754, is 123 parsecs away :cite[walter2010]: one of the "Magnificent Seven", slowly spinning neutron stars seen only by their thermal X-rays. Others, the central compact objects, sit as hot, faint X-ray sources inside young supernova remnants. ## Notable neutron stars | Name | Kind | Period | Field (G) | Distance | Note | |---|---|---|---|---|---| | Crab Pulsar (PSR B0531+21) | pulsar | 33.39 ms | 3.8e12 | 2.0 kpc | remnant of the 1054 supernova :cite[atnf] | | Vela Pulsar (PSR B0833-45) | pulsar | 89.33 ms | 3.4e12 | 280 pc | surface near 660,000 K :cite[atnf] :cite[potekhin2020] | | Geminga (PSR J0633+1746) | pulsar | 237.1 ms | 1.6e12 | about 190 to 250 pc | pulses in gamma rays, radio quiet toward Earth :cite[atnf] | | RX J1856.5-3754 | thermal isolated | 7.055 s | 1.5e13 | 123 pc | nearest known :cite[walter2010] | | PSR J0437-4715 | millisecond | 5.757 ms | 5.8e8 | 157 pc | 1.418 solar masses, 11.4 km :cite[choudhury2024] | | PSR B1913+16 | binary pulsar | 59.03 ms | 2.3e10 | several kpc | first binary pulsar :cite[weisberg2016] | | PSR J0740+6620 | millisecond | 2.89 ms | | 1.14 kpc | 2.08 solar masses :cite[fonseca2021] | | PSR J0952-0607 | millisecond (black widow) | 1.41 ms | 6e7 | | 2.35 solar masses :cite[romani2022] | | PSR J1748-2446ad | millisecond | 1.40 ms | | Terzan 5 cluster | fastest known, 716 Hz :cite[hessels2006] | | PSR J0901-4046 | pulsar | 76 s | | | slowest confirmed radio neutron star :cite[caleb2022] | | SGR 1806-20 | magnetar | 7.55 s | about 2e15 | 8.7 kpc | 2004 giant flare :cite[olausen2014] :cite[bibby2008] | | Hercules X-1 | accreting pulsar | 1.24 s | several e12 | about 7 kpc | 1.7-day orbit; first cyclotron line :cite[staubert2019] | :::callout{type=sim title="In Pax Abyssi"} **Built, awaiting the lead's verdict.** Seven neutron stars can be flown to: the Crab, Vela, Geminga, RX J1856.5-3754, PSR J0437-4715, Hercules X-1 and SGR 1806-20. Each is drawn as a 12 km sphere in the same light-bending pass as the black holes, so the star looks larger than it is and shows more than half its surface. Its temperature comes from a cooling table drawn through the observed stars :cite[potekhin2020]; pulsars carry hot polar caps of the size the Goldreich-Julian model gives, magnetars are hot all over, and Hercules X-1 has its accretion disk and companion. No visible beams are drawn, because the real beams are radio. Where a mass is not measured the star takes 1.27 solar masses, the peak of the birth-mass distribution; for now every stop sets the magnetic axis 60 degrees from the spin axis. The galaxy map shows every pulsar in the ATNF catalogue plus 375 other known neutron stars. Not yet built: pulsar wind nebulae, radiation hazards near a neutron star, and neutron stars as galaxy-map destinations. ::: ## See also - [[Black hole]] - [[White dwarf]] - [[Supergiant]] - [[Milky Way]] - [[Star catalogue]] - [[Stellar classification]]