Magnetars

A magnetar is a young, isolated neutron star whose entire observable life is dictated by an ultrastrong magnetic field rather than by rotational kinetic energy. Ordinary radio pulsars are spin-powered: the reservoir they draw on is $\tfrac12 I\Omega^2$ , and the field ( $B\sim10^{12}\,\mathrm{G}$ ) is merely the coupling that lets the star radiate its rotation away. Magnetars invert this hierarchy. With inferred surface dipole fields of $10^{14}$ – $10^{15}\,\mathrm{G}$ , and interior fields plausibly an order of magnitude larger, the magnetic energy $E_B\sim(B^2/8\pi)V$ reaches $10^{47}$ – $10^{48}\,\mathrm{erg}$ — a hundred times the rotational store of a slowly spinning ( $P\sim5\,\mathrm{s}$ ) star. It is this magnetic bank account, tapped by crustal fracturing, ambipolar diffusion, and dissipation of magnetospheric currents, that funds both the persistent X-rays and the spectacular bursts. Two historically separate classes turned out to be one population. Soft Gamma Repeaters (SGRs) announced themselves through short hard bursts and, once each in a generation, through giant flares — the 1979 March 5 event from SGR 0526−66 and the 2004 December 27 flare of SGR 1806−20, the latter releasing $\sim2\times10^{46}\,\mathrm{erg}$ in a fraction of a second. Anomalous X-ray Pulsars (AXPs) are persistent, pulsed X-ray sources whose luminosity, $\sim10^{35}\,\mathrm{erg\,s^{-1}}$ , exceeds their spin-down power by a factor of tens and cannot be fed by a companion, because none is seen. Both share long periods clustered at $2$ – $12\,\mathrm{s}$ , large $\dot P$ , young characteristic ages ( $\lesssim10^4\,\mathrm{yr}$ ), and frequent supernova-remnant associations. Because $B$ approaches and exceeds the QED critical field $B_Q=m_e^2c^3/(e\hbar)\approx4.4\times10^{13}\,\mathrm{G}$ , magnetars are the only macroscopic laboratories for strong-field quantum electrodynamics. Electron motion across the field is quantized into Landau levels of spacing comparable to $m_ec^2$ , the vacuum turns birefringent, photon splitting $\gamma\to\gamma\gamma$ opens up, and scattering opacities collapse — tying compact-object astrophysics directly to fundamental physics.

Key takeaways

Magnetars are neutron stars carrying the strongest magnetic fields known, $B\sim10^{14}$ – $10^{15}\,\mathrm{G}$ , well above the QED critical field $B_Q\approx4.4\times10^{13}\,\mathrm{G}$ .
Their emission is powered not by rotation but by the decay and dissipation of the internal magnetic field, released through crustal fracturing and magnetospheric currents.
They are seen as Soft Gamma Repeaters and Anomalous X-ray Pulsars, sharing long periods $P\sim2$ – $12\,\mathrm{s}$ and rapid spin-down $\dot P\sim10^{-11}\,\mathrm{s\,s^{-1}}$ .
Giant flares release up to $\sim10^{46}\,\mathrm{erg}$ in seconds, briefly outshining every other Galactic gamma-ray source.
The field is read two independent ways: magnetic-dipole spin-down gives $B\propto\sqrt{P\dot P}$ , and proton-cyclotron absorption lines fix the local surface field directly.
Above $B_Q$ the QED vacuum stops behaving classically — Landau quantization, photon splitting, and vacuum birefringence all become physically important.
Key idea: in a magnetar the magnetic energy exceeds the rotational energy, so field decay — not spin-down — is the engine; the tell that a slow, hard X-ray pulsar is magnetically powered is that $L_X\gg\dot E_{\rm rot}=I\Omega\dot\Omega$ .

The core insight

In a magnetar the magnetic energy exceeds the rotational energy, so field decay — not spin-down — is the engine; the diagnostic that a slow, hard X-ray pulsar is magnetically powered is that $L_X\gg\dot E_{\rm rot}=I\Omega\dot\Omega$ .

Where this lives today

Magnetars sit at the crossroads of several active frontiers. The 2020 detection of a fast radio burst from the Galactic magnetar SGR 1935+2154 — coincident with an X-ray burst — was the first direct evidence that at least some FRBs, the millisecond radio flashes seen across the observable Universe, come from magnetars, turning an extragalactic mystery into a nearby, testable one. At the other end of the energy scale, the "millisecond magnetar" central-engine model proposes that a newborn magnetar spinning at $P\sim1\,\mathrm{ms}$ injects $\sim10^{52}\,\mathrm{erg}$ into its supernova ejecta over days, powering superluminous supernovae and long gamma-ray bursts; NICER, Fermi, and Swift, with radio timing at facilities like FAST, monitor the Galactic population for the bursts and glitches that test it. Meanwhile LIGO–Virgo–KAGRA search for continuous gravitational waves from the ellipticity a $\gtrsim10^{16}\,\mathrm{G}$ internal toroidal field imposes, and for the oscillation modes seen as quasi-periodic oscillations in giant-flare tails — asteroseismology that probes the dense-matter equation of state directly. The open problems remain deep: the true internal field strength and topology, the nature of low-field magnetars, and whether ordinary pulsars and magnetars form a single evolutionary sequence.

The physical picture

Picture the neutron-star crust as a rigid conducting shell threaded by field lines anchored deep in the fluid interior. A slowly evolving internal field twists and shears that shell the way a wrench turns a bolt. The crust holds elastically until the accumulated magnetic stress passes its yield strength; then it cracks — a starquake — dumping magnetic and elastic energy into the magnetosphere as a burst, exactly as tectonic stress released in an earthquake. Between bursts the same twisted field drives currents that resonantly scatter surface photons into the hard X-ray tail. The first figure fixes the two facts that make a magnetar a magnetar: an interior field of order $10^{16}\,\mathrm{G}$ , and a magnetic reservoir that dwarfs everything rotation could supply.

Figure

A magnetar cutaway. A dynamo-amplified interior field B_int ∼ 10¹⁶ G threads a rigid crust and emerges as a twisted dipole of surface strength B_surf ∼ 10¹⁵ G. The magnetic reservoir E_B ∼ B²R³/6 ∼ 2×10⁴⁷ erg is about a hundred times the rotational store ½IΩ² ∼ 10⁴⁵ erg of a P = 5 s star, so field decay, not spin-down, powers the emission

The critical field $B_Q$ is where the electron cyclotron energy equals the electron rest energy. Above it the QED vacuum stops behaving classically: two polarization modes travel at different speeds (vacuum birefringence), a single photon can split into two, and the smooth-blackbody picture of the surface is replaced by strongly anisotropic, polarization-dependent opacities. The second figure is the diagram a magnetar astronomer actually reaches for — the period–period-derivative plane — where the same spin-down physics that dates ordinary pulsars reads off a field, and magnetars separate cleanly from the crowd by sitting above the critical line.

Figure

The P–Ṗ diagram, the working diagnostic. Diagonal lines are loci of constant surface dipole field from B = 3.2×10¹⁹ √(P Ṗ) G. Magnetars occupy long periods P ∼ 2–12 s and large Ṗ ∼ 10⁻¹¹, above the critical line B_Q = 4.4×10¹³ G, while ordinary pulsars cluster near 10¹² G. SGR 1806−20 sits at B ≈ 2×10¹⁵ G

The core equations

The whole subject turns on one comparison — magnetic versus rotational energy — expressed through a handful of estimators. Each is an order-of-magnitude relation built on the canonical neutron star ( $I=10^{45}\,\mathrm{g\,cm^2}$ , $R=10\,\mathrm{km}$ , $M=1.4\,M_\odot$ ), and each is used as a diagnostic that a given source is, or is not, magnetically powered. The first sets the scale for every QED effect: the field at which the electron cyclotron energy equals its rest energy.

B_Q=\frac{m_e^2c^3}{e\hbar}\approx4.41\times10^{13}\,\mathrm{G} \qquad (1)

where: $m_e$ — electron mass; $e$ — elementary charge; $\hbar$ — reduced Planck constant; $c$ — speed of light. Reading: fields at or above $B_Q$ Landau-quantize the electrons and make the vacuum a nonlinear optical medium; magnetar fields exceed it by factors of a few to twenty. The workhorse estimator turns two measured timing quantities into a field, by equating magnetic-dipole radiation to the loss of rotational energy.

B\approx3.2\times10^{19}\sqrt{P\,\dot P}\ \mathrm{G} \qquad (2)

where: $P$ — spin period in seconds; $\dot P$ — dimensionless period derivative; $B$ — characteristic surface dipole field. Reading: for a magnetar with $P\sim8\,\mathrm{s}$ and $\dot P\sim10^{-11}$ this gives $B\sim10^{15}\,\mathrm{G}$ , an order of magnitude above $B_Q$ . The same braking law dates the star, but only as an upper bound.

\tau_c=\frac{P}{2\dot P} \qquad (3)

where: $\tau_c$ — characteristic (spin-down) age. Reading: $\tau_c$ assumes the star was born spinning far faster than today and that $B$ is constant; both fail for magnetars, so $\tau_c$ overestimates the true age. The reservoir the whole model rests on is simply the field energy density times the stellar volume.

E_B\sim\frac{B^2}{8\pi}\cdot\frac{4}{3}\pi R^3=\frac{B^2R^3}{6} \qquad (4)

where: $B$ — volume-averaged interior field; $R$ — stellar radius. Reading: at $B=10^{15}\,\mathrm{G}$ this is $\sim2\times10^{47}\,\mathrm{erg}$ , roughly a hundred times the $\tfrac12 I\Omega^2\sim10^{45}\,\mathrm{erg}$ of a five-second rotator. The energy that rotation can actually supply — the quantity magnetars overshoot — is the spin-down luminosity.

|\dot E_{\rm rot}|=I\Omega|\dot\Omega|=4\pi^2 I\frac{\dot P}{P^3} \qquad (5)

where: $I$ — moment of inertia $\sim10^{45}\,\mathrm{g\,cm^2}$ ; $\Omega=2\pi/P$ . Reading: for a typical AXP this is $\sim10^{33}\,\mathrm{erg\,s^{-1}}$ , well below the observed $L_X\sim10^{35}$ — the defining energetic signature. The field is also read locally, without any spin model, from cyclotron absorption. Protons, being heavier, resonate in the observable keV band precisely when $B$ is super-critical.

E_{\rm cyc,p}=\frac{\hbar eB}{m_p c}=0.63\left(\frac{B}{10^{14}\,\mathrm{G}}\right)\mathrm{keV} \qquad (6)

where: $m_p$ — proton mass; $E_{\rm cyc,p}$ — fundamental proton cyclotron energy. Reading: a $\sim1\,\mathrm{keV}$ feature (as in SGR 0418+5729) pins the surface field to $\sim10^{14}\,\mathrm{G}$ independently of the dipole estimate. Finally, the field makes the star radiate far above its nominal Eddington limit by choking the scattering cross section below the cyclotron frequency.

\sigma_\parallel\approx\left(\frac{\omega}{\omega_c}\right)^2\sigma_T,\qquad \omega\ll\omega_c \qquad (7)

where: $\omega$ — photon angular frequency; $\omega_c=eB/m_ec$ — electron cyclotron frequency; $\sigma_\parallel$ — cross section for the mode with $\mathbf E\parallel\mathbf B$ . Reading: with $\sigma\ll\sigma_T$ the radiation force per particle collapses, so a magnetically confined fireball stays bound even while radiating a thousand times $L_{\rm Edd}$ .

Derivation AThe dipole field from spin-down

The goal is to turn two directly measured timing quantities, the period $P$ and its derivative $\dot P$ , into an estimate of the surface magnetic field, by asserting that a spinning magnetized star loses rotational energy exactly as fast as a rotating magnetic dipole radiates it. This is the single most-used equation in magnetar astronomy, and getting its numerical coefficient right requires being explicit about how the surface field is defined in terms of the dipole moment — the step where textbooks quietly differ by a factor of two.

Step 1. A magnetic dipole moment $m$ whose component perpendicular to the spin axis is $m_\perp$ radiates, by the Larmor formula for a source oscillating at $\Omega$ , a power $\dot E=\tfrac{2}{3c^3}m_\perp^2\Omega^4$ . Write the surface field through $m_\perp=BR^3$ , the convention in which $B$ is the characteristic equatorial field of the dipole. Why: fixing the relation between $m$ and $B$ up front is what nails the coefficient; the alternative choice $m_\perp=BR^3/2$ describes the polar field and yields $6.4\times10^{19}$ instead.

Step 2. Equate this radiated power to the rate at which the star sheds rotational energy, $-I\Omega\dot\Omega=\tfrac{2}{3c^3}B^2R^6\Omega^4$ , so the rotational reservoir is being spent entirely on dipole radiation. Why: this is the physical content of the model — spin-down is powered by the rotating field, so the observed braking directly measures the field strength.

Step 3. Substitute $\Omega=2\pi/P$ and $\dot\Omega=-2\pi\dot P/P^2$ . The powers of $2\pi$ collect to give $P\dot P=\dfrac{8\pi^2 B^2 R^6}{3Ic^3}$ , a clean relation between the measurable product $P\dot P$ and $B^2$ . Why: casting the result in terms of $P\dot P$ is what makes it observational — both factors come straight from timing a pulse train.

Step 4. Solve for the field and insert the canonical $I=10^{45}\,\mathrm{g\,cm^2}$ , $R=10^6\,\mathrm{cm}$ , $c=3\times10^{10}\,\mathrm{cm\,s^{-1}}$ : $B=\left(\dfrac{3Ic^3}{8\pi^2R^6}P\dot P\right)^{1/2}\approx3.2\times10^{19}\sqrt{P\dot P}\ \mathrm{G}$ . Why: this is the estimator that, applied across the P–Ṗ diagram, separates magnetars from ordinary pulsars — the same arithmetic that gives $10^{12}\,\mathrm{G}$ for the Crab gives $10^{15}\,\mathrm{G}$ for an SGR. *Note: inserting the canonical values $I=10^{45}\,\mathrm{g\,cm^2}$ , $R=10^6\,\mathrm{cm}$ , $c=3\times10^{10}\,\mathrm{cm\,s^{-1}}$ gives $\sqrt{3Ic^3/8\pi^2R^6}=3.20\times10^{19}$ , confirming the numerical coefficient in equation (2).*

Go deeper · Derivation B · 1 minThe magnetic reservoir and how slowly it drains

Derivation BThe magnetic reservoir and how slowly it drains

The goal is to show quantitatively that the magnetic field of a magnetar stores more than enough energy to power its persistent luminosity over its lifetime, and that this energy is released on exactly the right timescale — thousands to hundreds of thousands of years — by Ohmic and Hall diffusion of the field through the finitely conducting crust. Together these two estimates are what make "field decay" a viable engine rather than a slogan.

Step 1. The stored energy is the field energy density integrated over the star, $E_B\sim\dfrac{B^2}{8\pi}\dfrac{4\pi R^3}{3}=\dfrac{B^2R^3}{6}$ ; at $B=10^{15}\,\mathrm{G}$ and $R=10\,\mathrm{km}$ this is $\approx1.7\times10^{47}\,\mathrm{erg}$ . Why: this is the size of the tank — two orders of magnitude above rotation, and comparable to the binding energy fluctuations the crust can hold.

Step 2. The field diffuses through the crust according to the resistive induction equation $\partial\mathbf B/\partial t=(c^2/4\pi\sigma)\nabla^2\mathbf B$ , whose dimensional decay time over a lengthscale $L$ is $\tau_{\rm Ohm}\sim 4\pi\sigma L^2/c^2$ . Why: the crust is a good but not perfect conductor, so the frozen-in field slips and dissipates rather than lasting forever.

Step 3. Insert crustal conductivity $\sigma\sim10^{24}$ – $10^{25}\,\mathrm{s^{-1}}$ and $L\sim1\,\mathrm{km}$ to get $\tau_{\rm Ohm}\sim10^3$ – $10^5\,\mathrm{yr}$ , comparable to inferred magnetar ages; Hall drift in the crust and ambipolar diffusion in the core can act faster still. Why: the decay time landing on the observed age range is the key consistency check — the reservoir empties neither instantly nor never, but over a magnetar lifetime.

Step 4. The heating rate follows as $L_{\rm heat}\sim E_B/\tau_{\rm decay}\sim(2\times10^{47})/(10^4\,\mathrm{yr})\approx6\times10^{35}\,\mathrm{erg\,s^{-1}}$ , comfortably exceeding the observed $L_X\sim10^{35}$ . Why: this closes the argument — field decay supplies more power than the star radiates, so it is an ample, not marginal, energy source. *Note: evaluating equation (4) directly gives $B^2R^3/6=1.67\times10^{47}\,\mathrm{erg}$ at $B=10^{15}\,\mathrm{G}$ , and the resulting timescales and heating rates are consistent with magnetothermal evolution models.*

Go deeper · Derivation C · 1 minWhen magnetic stress fractures the crust

Derivation CWhen magnetic stress fractures the crust

The goal is to establish the threshold field above which the Maxwell stress of the internal field exceeds the elastic yield strength of the neutron-star crust, so the crust fails, injects a twist into the magnetosphere, and triggers an SGR burst. This is what explains the observed dividing line: only stars with fields above a few times $10^{14}\,\mathrm{G}$ produce bursts, and that number falls straight out of comparing magnetic pressure to the crust's shear strength.

Step 1. The field exerts a Maxwell shear stress on the crustal lattice of order $\Sigma_{\rm mag}\sim B^2/4\pi$ . Why: this is the driving force — the interior field, evolving under Hall drift, transmits stress to the rigid crust it is frozen into.

Step 2. The crust resists elastically up to a maximum shear stress $\Sigma_{\rm max}\sim\mu\,\theta_{\max}$ , where $\mu\sim10^{30}\,\mathrm{erg\,cm^{-3}}$ is the shear modulus near the crust base and $\theta_{\max}\sim0.1$ is the yield strain from molecular-dynamics simulations. Why: a Coulomb lattice of nuclei has a real, computable breaking strain, which sets how much stress the crust can bank before it snaps.

Step 3. Failure requires $\Sigma_{\rm mag}\gtrsim\mu\theta_{\max}$ , i.e. $B_{\rm crit}\sim(4\pi\mu\theta_{\max})^{1/2}\sim\text{few}\times10^{14}\,\mathrm{G}$ — squarely the magnetar range. Why: this predicts, with no free parameters beyond laboratory-grade material constants, exactly the field above which bursting turns on, matching where SGRs sit on the P–Ṗ diagram.

Step 4. A local fracture over a patch of volume $\Delta V$ releases $\sim\Sigma_{\rm mag}\Delta V$ ; a global failure with large-scale magnetospheric reconnection taps the full reservoir and powers a giant flare up to $\sim10^{46}\,\mathrm{erg}$ . Why: the same criterion scales from the common small bursts to the once-a-generation giant flares, unifying the burst zoo under one mechanism. *Note: molecular-dynamics simulations give a yield strain $\theta_{\max}\sim0.1$ , and the resulting critical field $B_{\rm crit}\sim\text{few}\times10^{14}\,\mathrm{G}$ is consistent with the observed onset of bursting activity in magnetars.*

Limiting cases

The regimes are organized by how $B$ compares to the critical field $B_Q$ and by which energy reservoir dominates.

Case	Result	Meaning
Ordinary pulsar	$B\sim10^{12}\,\mathrm{G}\ll B_Q,\ \|\dot E_{\rm rot}\|>L_X$	Rotation powers the emission; QED vacuum effects negligible; periods short.
Magnetar (super-critical)	$B\sim10^{14}\text{–}10^{15}\,\mathrm{G}>B_Q,\ L_X\gg\|\dot E_{\rm rot}\|$	Field decay powers emission; Landau quantization, photon splitting, vacuum birefringence all active.
Giant flare	$E_{\rm flare}\sim10^{44}\text{–}10^{46}\,\mathrm{erg}$	Global crustal failure and reconnection; a trapped fireball yields a pulsating tail modulated at $P$ .
Extreme-field interior	$B\gg B_Q\ (\gtrsim10^{16}\,\mathrm{G})$	Magnetic pressure nears degeneracy pressure and deforms the star into an ellipsoid — a continuous gravitational-wave source.

Common trapThe characteristic age and dipole field are model estimates, not measurements

Do not read $\tau_c=P/2\dot P$ as the star's true age, nor $B\propto\sqrt{P\dot P}$ as its true field. Both assume pure magnetic-dipole braking ( $n=3$ ) with a constant field and a birth spin much faster than today. Magnetars violate all three: they are born spinning slowly (so $\tau_c$ overestimates the age), their spin-down is enhanced and variable because twisted magnetospheric currents add torque, and the field itself decays. The dipole formula, moreover, returns only the large-scale polar-cap field — the internal and multipolar components, which cyclotron lines sometimes reveal to be stronger, are invisible to it. Treat both numbers as order-of-magnitude locators on the P–Ṗ diagram, not as precision quantities.

Worked examples

1 · Is an anomalous X-ray pulsar rotation-powered? (confidence builder)

A representative AXP has $P=8\,\mathrm{s}$ , $\dot P=4\times10^{-11}\,\mathrm{s\,s^{-1}}$ , moment of inertia $I=10^{45}\,\mathrm{g\,cm^2}$ , and observed $L_X\approx10^{35}\,\mathrm{erg\,s^{-1}}$ . Decide what powers it.

Step 1. Compute the spin-down luminosity from equation (5): $|\dot E_{\rm rot}|=4\pi^2 I\,\dot P/P^3=4\pi^2(10^{45})(4\times10^{-11})/8^3\approx\mathbf{3.1\times10^{33}\ erg\,s^{-1}}$ . This is the maximum power rotation can deliver.

Step 2. Compare to the observed X-rays: $L_X/|\dot E_{\rm rot}|\approx10^{35}/3.1\times10^{33}\approx\mathbf{32}$ . The star radiates thirty times more energy than its rotation supplies — impossible for a rotation-powered pulsar, which would need efficiency above 100%.

Step 3. Exclude accretion. No binary companion is detected and no orbital Doppler modulation appears, ruling out a donor; isolated accretion from the interstellar medium falls orders of magnitude short of $10^{35}\,\mathrm{erg\,s^{-1}}$ . Rotation and accretion are both eliminated.

Step 4. Infer the field from equation (2): $B\approx3.2\times10^{19}\sqrt{P\dot P}=3.2\times10^{19}\sqrt{8\times4\times10^{-11}}\approx\mathbf{5.7\times10^{14}\ G}$ . A super-critical field whose slow decay easily supplies $L_X$ over the source lifetime — the magnetar interpretation. The source is magnetically powered: $L_X\approx32\,|\dot E_{\rm rot}|$ and $B\approx6\times10^{14}\,\mathrm{G}>B_Q$ .

2 · Reading the field off a cyclotron line

The critical field is $B_Q=4.4\times10^{13}\,\mathrm{G}$ . A magnetar shows a proton-cyclotron absorption feature at $E=1.0\,\mathrm{keV}$ . What surface field does it imply, and is it super-critical? Compare with the field that would put the fundamental electron cyclotron line in the same band.

Step 1. Invert equation (6): $B=\dfrac{E}{0.63\,\mathrm{keV}}\times10^{14}\,\mathrm{G}=\dfrac{1.0}{0.63}\times10^{14}\approx\mathbf{1.6\times10^{14}\ G}$ . This is a direct, spin-model-independent reading of the field where the line forms.

Step 2. Compare to $B_Q$ : $1.6\times10^{14}/4.4\times10^{13}\approx\mathbf{3.6}$ , so the surface field is several times critical — comfortably in the magnetar regime, and broadly consistent with the dipole estimate from spin-down for such sources.

Step 3. For contrast, the electron is $m_p/m_e\approx1836$ times lighter, so its fundamental cyclotron energy is $1836\times$ higher at the same field. To place the electron line at $1\,\mathrm{keV}$ would need $B\approx1.6\times10^{14}/1836\approx\mathbf{8.7\times10^{10}\ G}$ — an ordinary-pulsar field. A keV proton line means $B\sim10^{14}\,\mathrm{G}$ (super-critical); the same photon energy from electrons would need only $\sim10^{11}\,\mathrm{G}$ .

Physics of the portrait

The magnetar went from a back-of-envelope speculation to an established class of star in a single working lifetime, driven by a theoretical prediction that a rare flare then confirmed.

Origins · 1 minDuncan and Thompson and how this was discovered

Duncan and Thompson

magnetar theory 1992–1996 · strong-field neutron-star astrophysics

The idea that some neutron stars are governed by their magnetic fields rather than their spin was worked out by Robert C. Duncan and Christopher Thompson in a 1992 paper that also coined the word "magnetar". Their insight was that the first seconds of a proto-neutron star's life — hot, convective, and possibly rotating near break-up — are exactly the conditions for a helical dynamo, which can amplify a seed field to equipartition values of order $10^{16}\,\mathrm{G}$ in the interior. Building on a suggestion by Bohdan Paczyński, they argued that such a field, frozen into a rigid crust, would stress and fracture it, dumping energy into the magnetosphere as the soft-gamma-repeater bursts that had puzzled astronomers since the 1979 March 5 giant flare. In two 1995–1996 papers Thompson and Duncan developed the full machinery: the trapped-fireball model of giant flares, the resonant magnetospheric scattering that hardens the persistent spectrum, and the crustquake trigger. The decisive test came in 1998, when Chryssa Kouveliotou and collaborators measured the spin and spin-down of SGR 1806−20 and found $B\sim10^{15}\,\mathrm{G}$ exactly as predicted, unifying SGRs and anomalous X-ray pulsars into one population. The picture has since only broadened — low-field magnetars with $B<B_Q$ but magnetar-like bursts, and in 2020 a fast radio burst from the Galactic magnetar SGR 1935+2154 — but it remains the framework Duncan and Thompson set down.

History

1979

— the March 5 giant flare from SGR 0526−66 reveals a new class of soft gamma repeater

1992

— Duncan and Thompson propose the magnetar and its dynamo-amplified ∼10¹⁵ G field

1995

— Thompson and Duncan work out the burst, fireball, and persistent-emission mechanisms

1998

— Kouveliotou and collaborators measure spin-down of SGR 1806−20, confirming B ∼ 10¹⁵ G

2004

— the December 27 giant flare of SGR 1806−20 releases ∼2×10⁴⁶ erg

2020

— SGR 1935+2154 emits a fast radio burst, linking magnetars to the FRB phenomenon

Going further

Texts. Carroll & Ostlie, An Introduction to Modern Astrophysics, 2nd ed., Ch. 16 (neutron stars, pulsars, magnetars) · Shapiro & Teukolsky, Black Holes, White Dwarfs and Neutron Stars, Ch. 10 (pulsar electrodynamics) · Lorimer & Kramer, Handbook of Pulsar Astronomy, Ch. 3 (the P–Ṗ diagram) · Kaspi & Beloborodov, ARA&A 55, 261 (2017), "Magnetars" · Harding & Lai, Rep. Prog. Phys. 69, 2631 (2006), "Physics of strongly magnetized neutron stars". Key numerical anchors for the equations above: (1) $B_Q=m_e^2c^3/e\hbar=4.41\times10^{13}\,\mathrm{G}$ ; (2) the dipole coefficient $3.2\times10^{19}$ follows from $B=\sqrt{3Ic^3/8\pi^2R^6}\,\sqrt{P\dot P}$ with $I=10^{45}\,\mathrm{g\,cm^2}$ , $R=10\,\mathrm{km}$ — note the $8\pi^2$ convention uses $m_\perp=BR^3$ (equatorial field); the polar-field convention $m_\perp=BR^3/2$ gives $6.4\times10^{19}$ instead; (3) AXP spin-down power $|\dot E_{\rm rot}|=4\pi^2I\dot P/P^3\approx3\times10^{33}\,\mathrm{erg\,s^{-1}}$ for $P=8\,\mathrm{s}$ , $\dot P=4\times10^{-11}$ ; (4) magnetic reservoir $E_B=B^2R^3/6\approx1.7\times10^{47}\,\mathrm{erg}$ at $10^{15}\,\mathrm{G}$ ; (5) proton cyclotron energy $E_{\rm cyc,p}=\hbar eB/m_pc=0.63\,\mathrm{keV}$ at $10^{14}\,\mathrm{G}$ ; (6) Eddington luminosity $1.8\times10^{38}\,\mathrm{erg\,s^{-1}}$ for $1.4\,M_\odot$ . Observational anchors: SGR 1806−20 giant flare $\sim2\times10^{46}\,\mathrm{erg}$ ; magnetar periods $2$ – $12\,\mathrm{s}$ .

Builds on: Neutron Stars · Pulsars · Pulsar Magnetospheres and Spin-Down · Neutron Star Structure and Interior · Equation of State of Dense Matter. Leads to: Pulsar Glitches and Neutron Star Superfluidity · Tolman–Oppenheimer–Volkoff Equation.

Ask the tutor: Ask me to walk through the P–Ṗ diagram for any pulsar or magnetar and show whether spin-down or field decay is running the show.

What actually distinguishes a magnetar from an ordinary pulsar?

The energy source, and it shows up in the numbers. An ordinary pulsar is spin-powered: its X-ray and radio output is paid for out of rotational kinetic energy, so its luminosity is at most $|\dot E_{\rm rot}|=I\Omega\dot\Omega$ . A magnetar radiates far more than that — its persistent $L_X\sim10^{35}\,\mathrm{erg\,s^{-1}}$ is tens of times its spin-down power — so rotation cannot be the source. The books are balanced instead by the magnetic reservoir $E_B\sim B^2R^3/6\sim10^{47}\,\mathrm{erg}$ , released by field decay and crustal fracturing. Everything else — the long $2$ – $12\,\mathrm{s}$ periods, the bursts, the super-critical fields — follows from that one inversion of the energy hierarchy.

If magnetars are so luminous, why are only a few dozen known?

Because they are young and short-lived as a phenomenon. The strong field that makes a magnetar bright also decays on a timescale of $10^3$ – $10^5\,\mathrm{yr}$ ; once it fades, the star drops off the P–Ṗ diagram's upper right and blends into the pulsar population. So at any moment only the handful born recently in our Galaxy are active, and about thirty are catalogued. Many were found only because they burst — a source can sit quiet for years and then announce itself with an SGR outburst, which is why survey instruments like Fermi and Swift, watching the whole sky for transients, keep adding new ones.

How do we measure a field of 10¹⁵ G that we can never make on Earth?

Two independent ways that agree. The first is timing: measure the period $P$ and its slowing $\dot P$ , and if the star spins down as a rotating magnetic dipole, $B\approx3.2\times10^{19}\sqrt{P\dot P}\,\mathrm{G}$ follows straight from energy balance. The second is spectroscopy: a super-critical field puts the fundamental proton cyclotron resonance in the observable keV X-ray band, at $E_{\rm cyc,p}=0.63(B/10^{14}\,\mathrm{G})\,\mathrm{keV}$ , so an absorption line reads the field off directly, with no spin model at all. When the two methods agree — as they do for sources like SGR 0418+5729 — the super-critical field is on firm ground.

What is the QED critical field, and why does it matter for magnetars?

$B_Q=m_e^2c^3/e\hbar\approx4.4\times10^{13}\,\mathrm{G}$ is the field at which the electron cyclotron energy $\hbar eB/m_ec$ equals the electron rest energy $m_ec^2$ . Below it, magnetism is a small perturbation on atomic and plasma physics; at and above it, the physics changes qualitatively. Electron transverse motion is frozen into discrete Landau levels, the vacuum becomes birefringent so the two photon polarizations travel differently, a single photon can split into two, and scattering cross sections are strongly suppressed and polarization-dependent. Magnetar fields exceed $B_Q$ by factors of a few to twenty, which is why these stars are the only place strong-field QED is realized in a macroscopic astrophysical setting rather than in a fleeting collision.

Do magnetars produce fast radio bursts?

At least some do. In April 2020 the Galactic magnetar SGR 1935+2154 emitted an extraordinarily bright, millisecond-duration radio burst — FRB 200428 — simultaneously with an X-ray burst, the first time a fast radio burst was traced to a specific object. Its energy was lower than the cosmological FRBs seen from distant galaxies, but it bridged the gap and established magnetars as at least one FRB source class. The favoured mechanisms involve magnetospheric activity or shocks driven by the same field that powers the X-ray bursts, so FRBs have become a new observational window on magnetar magnetospheres, complementary to the X-ray and gamma-ray view.

Why is the characteristic age P/2Ṗ unreliable for a magnetar?

Because the two assumptions behind it both fail. The formula $\tau_c=P/2\dot P$ comes from integrating pure dipole braking backward under the assumption that the star was born spinning far faster than it is now. Magnetars are instead born spinning relatively slowly, so much of the extrapolated slowdown never happened, and $\tau_c$ comes out too large. On top of that, a magnetar's braking is enhanced and variable because twisted magnetospheric currents add torque, and the field that sets the braking is itself decaying — so the braking index is not the assumed $n=3$ . Independent ages from associated supernova remnants are typically younger than $\tau_c$ , confirming the bias.

What keeps a magnetar's persistent X-rays glowing between bursts?

Steady release of magnetic energy, through two channels. Deep inside, the decaying field deposits heat in the crust and core by Ohmic dissipation, Hall drift, and ambipolar diffusion, keeping the surface hotter than passive cooling alone would allow — this is the thermal, roughly blackbody part of the spectrum. In the magnetosphere, the same twist that stresses the crust drives currents whose electrons resonantly scatter those thermal photons up to higher energies, producing the hard non-thermal tail that distinguishes magnetars from cooling neutron stars. Both channels draw on the reservoir $E_B\sim10^{47}\,\mathrm{erg}$ , which the field-decay timescale releases at $\sim10^{35}$ – $10^{36}\,\mathrm{erg\,s^{-1}}$ — enough to sustain the observed $L_X$ for the star's active lifetime.