10¹¹ tesla: a litre of this magnetic field weighs 44,000 tonnes

Here's a number with a strange claim attached: 10¹¹ tesla, and a field that weighs more than lead.

10¹¹ is a 1 followed by eleven zeros: a hundred billion. The tesla is the unit of magnetic field; a fridge magnet gives a few thousandths to a few hundredths of one.

A hundred billion tesla is the field at the surface of a magnetar, a small, dead, spinning star. These are the strongest magnetic fields known in any star.

And "weighs" means something real here. A field holds energy, and Einstein showed that energy has mass. Near a magnetar, a litre of field carries more mass than a litre of lead. Far more.

Guess first

So a teaspoon of that field, near a magnetar: what would it weigh?

The answer

About 220 tonnes (this page's arithmetic). A teaspoon of the star itself would weigh billions of tonnes.

Along the way: what such a field would do to your bank card, to atoms and to empty space, and which parts are measured, which are worked out and which are only predicted.

Chapter 1

A field heavier than lead

Start with a field you know. Earth's, the one that swings a compass needle, is 25 to 65 millionths of a tesla.

A magnetar is a kind of neutron star: more than the Sun's mass crushed into a ball some 22 to 26 kilometres across. At its surface the field is about a hundred billion tesla.

A field stores energy, and the stronger the field, the more it stores: double the field and you get four times the energy.

Now the twist. Energy has mass: that's what Einstein's most famous equation says, for the energy in a field as for any other. Turn the field's energy into the mass it's worth and you get about 44,000 tonnes in every litre (this page's arithmetic).

A litre of lead has a mass of 11.3 kilograms. So near a magnetar, a litre of magnetic field carries about four million times the mass of a litre of lead. A teaspoon of it: about 220 tonnes. (A teaspoon of the star itself would weigh billions of tonnes, as Nº 0 mentions.)

Two warnings. Nobody has held a meter up to a magnetar: its field is worked out from how fast the star's spin slows down (chapter 5). And the field doesn't outweigh the star. The star itself is still about ten million times denser, on average (this page's arithmetic).

Most magnetars read 10 billion to 100 billion tesla.

Chapter 2

From fridge magnet to magnetar

The fields in this story span about twenty-four powers of ten, from the faint field of your brain to a magnetar.

On Earth

Earth's field: 25 to 65 microtesla, or millionths of a tesla (as in Nº 14). A fridge magnet: a few to a few tens of millitesla, or thousandths. A hotel key card's stripe can be rewritten by about 30 millitesla, a bank card's by about ten times that. An MRI scanner, the hospital machine that takes pictures inside the body: 1.5 to 3 tesla. A 16 tesla magnet once made a living frog float. 🐸

Magnets and coils

Magnets and coils have reached about 45 tesla held steady, about 100 tesla in pulses, 1,200 tesla in a 2018 shot in Tokyo that destroyed the equipment, and reportedly about 2,800 tesla with explosives. A magnetar is tens of millions of times stronger (this page's arithmetic).

Laser-heated plasmas

Laser-heated plasmas (gas so hot that electrons are torn off its atoms) have reached about 70,000 tesla, a value worked out from the laser light, for trillionths of a second: a magnetar is still about a million times stronger (this page's arithmetic again).

In space

The most magnetic white dwarfs, the Earth-sized leftovers of stars like the Sun, reach about 100,000 tesla; ordinary pulsars (neutron stars that flash once a turn, like a lighthouse), about 100 million; magnetars, 10 billion to 100 billion.

Here's the surprise: the field's weight grows much faster than its strength.

Every tenfold step in field is a hundredfold step in weight. A magnetar's field is about ten trillion times a fridge magnet's; its weight, about a hundred trillion trillion times.

So as the field climbs, its weight passes real materials one by one: air's at about 500,000 tesla, water's at about 15 million, lead's at about 50 million (this page's arithmetic), well within the range of ordinary pulsars. A magnetar's field is even denser than a white dwarf's matter, on average, though far less dense than an atomic nucleus.

Two marks on the ladder come up later. At about 235,000 tesla, the atomic unit of field, a field starts to reshape atoms (chapter 10). At about 4.4 billion tesla, the critical field, empty space itself starts to respond strongly (chapter 12).

Drag the field up, or press Climb the ladder, and watch the litre of field against the litre of lead 👇

Chapter 3

Energy has weight

It takes work
Why does a field hold energy? Because building one takes work. Switch on the current in a coil and the growing field pushes back; the work done against that push is stored in the field.
It pushes
That stored energy is also a push. A field presses outwards across its lines and pulls inwards along them, like a bundle of stretched elastic. At a hundred billion tesla the push is about 4 × 10²² atmospheres, where one atmosphere is the push of the air around us: a 4 followed by 22 zeros (this page's arithmetic).
It has mass
And the energy has mass. In 1905 Einstein found that a body giving off energy loses mass (Nº 5 follows that idea into the proton). A field is no exception: a box with a field inside is, in principle, harder to push than the same box empty, and it pulls on things around it a little more.

That's all "weighs" means here. The field isn't made of mass, and it isn't a substance you could pour into a jar. It has energy, and energy has weight. You could only weigh a field by weighing whatever holds it.

All the field outside one magnetar carries about the mass of five Moons (this page's arithmetic). That's still only a ten-millionth of the star.

What we know, and how

Nothing about a magnetar's field so far is measured directly: its strength is worked out from how the star slows down, and its weight, push and five Moons are this page's arithmetic. The fields on Earth up to the 1,200 tesla record are measured; the 2,800 tesla is reported; the laser value is worked out from the light.

Chapter 4

The magnet stars

A neutron star is what's left when the core of a big star collapses. Most of the ones we know are pulsars, with fields of about 100 million tesla.

In 1992 Robert Duncan and Christopher Thompson suggested that some are born with far more: in the first seconds after the collapse, the churning newborn star could wind its field up to 10 billion or even 100 billion tesla. They called such stars magnetars.
It answered a puzzle: a few sources, the soft gamma repeaters, kept firing short bursts of gamma rays, light far more energetic than the light our eyes see. In 1995 the pair showed how a magnetar could do it: the field strains the star's crust until it cracks, and the field outside snaps into a new shape, letting energy go. That's still the main picture, though nobody knows exactly how a burst works.
The decisive clue came in 1998. Chryssa Kouveliotou and her colleagues found X-ray pulses from SGR 1806−20 every 7.47 seconds, the gap growing a little each year. For a spinning magnet, that meant a field of about 80 billion tesla and an age of about 1,500 years: young, for a star.

Magnetars show up as soft gamma repeaters, or as "anomalous X-ray pulsars", slow spinners too bright in X-rays for their spin to pay for. Either way, magnetism powers them.

About thirty are known, as of October 2026. The main catalogue, last updated in November 2020, lists 30, six of them candidates, and a few have been found since; the newest is so far reported only in a preprint, a paper not yet checked by other scientists.

Like other neutron stars, each packs more than the Sun's mass into a ball the size of a city. 🏙️

Chapter 5

Weighing a field by its spin

How do you measure a field thousands of light-years away? Its light carries no simple reading of it. What can be measured, very precisely, is the star's spin. X-ray pulses arrive once a turn, like a lighthouse beam, and their timing tells how long a turn takes and how fast that time is growing.

Here's the trick. A spinning magnet sends energy out into space, and the stronger its field, the faster it loses spin. Know how fast a star turns and how fast it's slowing, and you can work out its field. Every magnetar's overall field in this story was found that way: worked out, not read off a meter.

The sum assumes an idealised star, with a bar-magnet field and a 10 kilometre radius. For SGR 1806−20, the catalogue's numbers give about 200 billion tesla, the strongest in its list.

But that star's slowing isn't steady. In the catalogue it slows about six times faster than in 1998, and one team found its braking changing by up to about four times. Depending on the years you use, its field reads anywhere from about 80 billion to 200 billion tesla (this page's arithmetic).

One number for a whole star hides a lot, too. SGR 0418+5729 slows so gently that its field reads only about 600 million tesla. Yet its X-rays show a dark line, a gap at one X-ray energy where something soaks them up, and the gap shifts as the star turns. One team reads it as the mark of patches near the surface with 20 billion to more than 100 billion tesla. Deep inside, theory predicts stronger fields still.

One number hides a lot

SGR 1806−20, from its slowing about 80–200 billion tesla, by the years used (this page's arithmetic)

SGR 0418+5729, from its slowing about 600 million tesla

SGR 0418+5729, surface patches 20 billion to over 100 billion, on one team's reading

So, sorted

Measuredthe spins and their slowing
Worked outthe fields, with a model
Predictedthe fields deep inside

Chapter 6

Halfway to the Moon

Guess first

A magnetar of a hundred billion tesla, turning every 7.55 seconds, sits where the Moon is. Your cards?

The answer

They'd be fine: its field at Earth would be about 2 to 4 millitesla, too weak to wipe any card (this page's arithmetic).

You may have read that a magnetar at the Moon's distance would wipe the cards in your wallet. The sums say otherwise.

Near the star the field weakens very fast: ten times farther, a thousand times weaker. That rule stops at an invisible boundary where a field line turning with the star would have to move at the speed of light. For a star turning every 7.55 seconds, like SGR 1806−20, it sits about 360,000 kilometres out, just short of the Moon. Beyond it, the spin winds the field into a spiral carried out on a wind of particles, and the field fades far more slowly.

Put a magnetar with the round hundred billion tesla and that spin at the Moon's distance, and its field at Earth would be about 2 to 4 millitesla: forty to eighty times Earth's field, and too weak to wipe any card (this page's arithmetic).

Hotel key card

A hotel key card, which about 30 millitesla can rewrite, would be at risk only somewhat closer than halfway to the Moon (this page's arithmetic).

Bank card

A bank card, which typically needs about 0.28 tesla, would be at risk only inside about a fifth of the way (this page's arithmetic, for typical stripes).

The spin matters: the same field turning every 2.07 seconds, as one real magnetar does, would give about 14 to 27 millitesla at the Moon, up to near the hotel-card level (this page's estimate).

Find your own distance: slide yourself along, change the star, or press a Go to button 👇

48tesla

One Earth-width from the star, the field would be about 48 tesla: sixteen times a 3 tesla hospital scanner (this page's arithmetic).

Chapter 7

27 December 2004

A twisted field can snap into a shape with less energy and let the difference go, like a twisted elastic band. On 27 December 2004, SGR 1806−20 let go.

One of the teams that studied its giant flare called it "the brightest extra-solar transient event ever recorded": the brightest sudden flash ever recorded from beyond the Solar System.

0.2seconds

For a fifth of a second its gamma rays brought energy to Earth faster than the full Moon's light does.

Nobody saw it: our eyes can't see gamma rays, and the air stopped them high up. A glow followed for about 380 seconds, pulsing every 7.55 seconds as the star turned.

What was measured is how much energy arrived here. Turning that into the star's total needs its distance, which is argued over. The discovery papers assumed about 49,000 light-years. A 2008 study of the star's cluster says about 28,000 (anywhere from about 23,000 to 34,000). A 2011 study of X-ray echoes off dust says 31,000 to 61,000, which leaves out 28,000. So the star is somewhere between about 23,000 and 61,000 light-years away, and no one distance is settled.

Twice as far means four times the energy.

One 2005 team compared the flash to a quarter of a million years of the Sun's output. The two 2005 papers' measurements lead to somewhat different energies, so each distance gives two answers.

If the star is 28,000 light-years away, the flash matched what the Sun gives out in about 56,000 to 100,000 years; if it is 49,000, about 170,000 to 310,000. Across the whole range of distances, it is anywhere from about 38,000 to 470,000 years (this page's arithmetic).

The biggest flares on our Sun are roughly a hundred trillion times smaller (this page's arithmetic), and the superflares Sun-like stars throw about once a century each (Nº 12) are far smaller too. The two other giant flares from our neighbourhood, in 1979 and 1998, were far weaker, at the distances assumed then.

Set the distance yourself, then press Replay the flare. Chapter 8 follows the flash into our sky 👇

Chapter 8

A flash that reached our sky

High above us, sunlight knocks electrons off a few of the air's molecules. That charged layer, the ionosphere, bounces long radio waves, so radio signals travelling under it show how many free electrons it holds.

The 2004 flash struck the daytime half of Earth. A team led by Umran Inan found its mark in radio signals sent from Hawaii and picked up in Antarctica. About 60 kilometres up, the free electrons jumped about a hundredfold; about 30 kilometres up, a thousandfold or more. It took more than an hour to settle.

It had happened before. In the 1998 flare from another magnetar, the ionosphere flickered every 5.16 seconds, in time with the spin of a star across the Galaxy.

None of this was dangerous. All the energy that reached Earth came to about 40 tonnes of TNT, spread over the whole daytime half of the planet in a fifth of a second (this page's arithmetic). Harmless, but enough to measure, from tens of thousands of light-years away.

One team argues that the flare also made heavy elements. Anirudh Patel and colleagues found a gamma-ray glow, peaking about ten minutes after the flash, that matches fresh heavy atoms decaying. On their reading, such flares make at least roughly 1 to 10% of the Galaxy's heavy elements of the kind built when atomic nuclei swallow neutrons very fast. Where gold comes from is still argued over (Nº 7).

Chapter 9

A radio burst from next door

Fast radio bursts are flashes of radio waves, about a thousandth of a second long, from other galaxies. For years nobody knew what made them.

On 28 April 2020, a magnetar in our own Galaxy, SGR 1935+2154, made one, or something very like one. Two radio projects caught it, CHIME and STARE2. It was about 4,000 times more energetic than any earlier radio burst of its kind from our Galaxy, yet about 30 times less energetic than the faintest one then known from another galaxy. It came with a burst of X-rays.

So at least some fast radio bursts can come from magnetars. Not necessarily all.

Its distance is uncertain too: about 20,000 to 40,000 light-years. As far as we can find, as of October 2026, it is still the only magnetar seen to make a radio burst that energetic. The same star made more X-ray bursts with radio partners in 2022.

What we know, and how

The spins, the flares, the 2004 flash at Earth, its effect on our sky and the 2020 radio burst are measured. The fields, distances, flare energies and the heavy-element idea are worked out with models. The card distances are this page's estimates.

Chapter 10

Atoms squeezed into needles

What does a field like this do to matter? An electron in a magnetic field circles round the field lines, as electrons do in the ring of a particle collider, a giant machine for smashing particles together (Nº 9). Quantum physics allows only certain circles, and the stronger the field, the tighter the smallest one.

At about 235,000 tesla, a field physicists call the atomic unit, the smallest circle is as small as an ordinary hydrogen atom. Below that, the nucleus decides an atom's shape. Above it, the field does.

Far above it, the electron is squeezed sideways into a thin tube round the field line, while along the line the nucleus still holds it loosely. The atom becomes a needle. At magnetar strength a hydrogen atom is, roughly, a needle tens of times longer than it is wide, and far thinner than the same atom with no field (this page's arithmetic, rough).

64× harder

The needle is also harder to break. Pulling hydrogen's electron away takes 64 times the usual energy at magnetar strength.

The change comes gradually, and at first squeezing isn't the reason. At about 100,000 tesla, the strongest white-dwarf fields, the atom is already about a third harder to break apart, but its shape has barely changed. Why? Mostly because an electron set free in a field can't stop circling, so freeing it costs the energy of that circling too. Squeezing takes over from about 10 million tesla.

Turn up the field on one hydrogen atom, or press Squeeze 👇

Chapter 11

Chains, and why no lab can do it

Needle atoms change chemistry. In theory, they link end to end into long chains along the field, and the chains pack side by side into a solid. On a magnetar, below about a million degrees, the surface itself may be liquid or solid rather than a gas.

This is theory: nobody has seen a needle atom or a chain. Fits to the X-rays of two magnetars suggest a liquid or solid patch on the surface. They don't show one.

Could a lab try? Not with ordinary atoms.

Magnets and coils

The strongest magnets and coils are about a hundred times too weak even to start reshaping them (this page's arithmetic).

Laser-heated plasmas

Laser-heated plasmas get about a third of the way (this page's arithmetic), but they're far too hot to hold whole atoms.

Rydberg atoms

So physicists make the atom bigger instead. Kick an electron far up the atom's ladder of energy levels and the atom swells, and its electron is held far more weakly. These giant, highly excited atoms are called Rydberg atoms. With the electron on the 40th rung, a magnet of 6 tesla already beats the nucleus's grip (this page's arithmetic). Lab magnets have rearranged the light from atoms like these since 1969.

None of these is a needle. But each lets a few tesla play a magnetar's part. 🔬

Chapter 12

Empty space as a crystal

Fields this strong act on empty space too. In quantum physics, empty space, which physicists call the vacuum, isn't quite empty: pairs of electrons and their antimatter partners, positrons, flicker in and out of existence, and a strong field tugs on them.

In 1936 Werner Heisenberg and Hans Euler worked out that light can then, very weakly, feel a magnetic field. The effect becomes large only near about 4.4 billion tesla, the critical field (Nº 5 meets its electric cousin).

Light's polarisation is the direction it wiggles in, across its path: polarising sunglasses pass one direction and block the other. In a strong field, light wiggling along the field and light wiggling across it travel at slightly different speeds, as it does in calcite, the crystal that shows a double image. So empty space acts a little like a crystal, though there's no crystal there, only those flickering pairs, and the effect is far weaker.

In the lab it's still too small to measure: the PVLAS experiment spent 25 years shining laser light through strong magnets, and ended with an uncertainty about seven times the effect. No laboratory has measured the difference in speeds.

So the hope is the sky. In theory, light leaving each spot of a magnetar's surface starts out with its polarisation set by the field there, and since the field points different ways on different spots, the directions partly cancel. The vacuum effect keeps each X-ray's polarisation turning with the field until the light is far from the star; then it freezes, so light from the whole surface ends up lined up.

There's a catch. A small hot spot seen from the side can look lined up on its own, so how lined up the light is can't settle it alone. Seen almost end-on, its light mostly cancels again without the effect. Switch the vacuum on and off, and try a small hot spot from different angles 👇

In this cartoon, a small spot round the magnetic pole, seen well off to the side, is 95% lined up even without the effect; seen almost end-on, under 1%.

The first claim, in 2016, came from the visible light of RX J1856.5−3754, a lone neutron star of about a billion tesla, not a magnetar. It was only about three times its uncertainty, and was argued over.

Since 2022, NASA's IXPE satellite has found magnetars among the most polarised X-ray sources in the sky, up to about 80%: they look as if the effect is happening.

In 2026 two teams published studies of the same IXPE observation of one magnetar, 1E 1547.0−5408. Both think its X-rays come from one small hot spot; they disagree about the angle we see it from, and about how much the data alone can show.

Published first

One, publishing first, said that for the angle it fitted, the high polarisation "cannot be regarded as compelling evidence".

In Nature

The other, in the journal Nature, said the effect "can naturally explain" what they saw, and still calls it unconfirmed, though a university press release said one of its astronomers "may have just confirmed" it.

Where it stands, as of October 2026, in this page's judgement: the evidence from magnetars is growing but not yet conclusive.

Chapter 13

What the weight means

Back to the litre: near a magnetar it carries about 44,000 tonnes, four million times a litre of lead. Every step is named: a field worked out from a slowing spin, an energy that grows four times when the field doubles, and Einstein's rule that energy has mass.

Here's how the story sorts out.

Measured
magnetars' spins and their slowing; their bursts and three nearby giant flares; the 2004 flash at Earth and what it did to our sky; the 2020 radio burst; X-rays lined up by up to about 80%.
Worked out with a model
the fields and their stronger patches; the laser-plasma field; distances; flare energies; liquid or solid surface patches; the vacuum effect around magnetars (argued over).
Predicted, not yet seen
needle atoms and chains; the vacuum effect measured in a lab; the strongest fields deep inside.

And five things this page doesn't say.

That the field is made of mass: its weight is the mass its energy is worth.
That it's denser than the star: the star is about ten million times denser, on average.
That anyone measured it with a meter.
That it could wipe your cards from the Moon.
Or that the vacuum effect is proven.

Usually the weight of a field is far too small to notice. Around a dead star, it outweighs lead four million times over. Let's add it all up.

Weighbridge ticket · Nº 25A magnetar, itemised

Magnetar fieldworked out from its spinabout 10¹¹ tesla

A litre of that fieldthis page's arithmetic44,000 tonnes

Versus a litre of lead11.3 kilograms× 4 million

A teaspoon of field5 millilitres220 tonnes

All the field outside one starthis page's arithmetic≈ 5 Moons

The star, on averagethis page's arithmetic10 million × denser

Hotel key card at riska magnetar turning every 7.55 secondswithin ~40–50% of the way to the Moon

Bank card at risksame starwithin ~⅕ of the way

The 2004 flashgamma raysa fifth of a second

…in years of the Sun's outputdepends on the distance38,000–470,000

Hydrogen, at 10¹¹ teslato break apart64 × harder

Strongest magnets and coils on Earthindoors; reported with explosives1,200 / ~2,800 tesla

Magnetars knownOctober 2026about 30

Heavier than lead? Than the star?litre for litre, on averageyes / no

energy has weight ✦ fields reshape atoms ✦ the vacuum's case is still open

Somewhere across the Galaxy, a small dead star turns once every few seconds.

Around it lies a field so strong that you could almost weigh it, litre by litre, against lead.

Once, it snapped, and a fifth of a second of its light reached our sky.

Near its surface, atoms should be drawn out into needles.

And the empty space around it might be acting like a crystal.

A litre of magnetar field weighs more than a litre of lead: four million times more.

Part IA field you could weigh

Chapter 1A hundred billion tesla

A fridge magnet gives a few to a few tens of millitesla at its face, and Earth's field is 25 to 65 microtesla. At the surface of a magnetar, a neutron star with more than the Sun's mass packed into a ball some 22 to 26 km across, the field is about 10¹¹ T: a hundred billion tesla, or 10¹⁵ gauss in the units astronomers use. A field stores energy, and the amount per cubic metre grows as the square of the field:

u = B²/2μ₀ ≈ 4.0 × 10²⁷ J m⁻³ at B = 10¹¹ Tμ₀ = 1.25663706127 × 10⁻⁶ N A⁻², the magnetic constant (CODATA 2022). Doubling the field quadruples the energy. This page's arithmetic.

Energy has mass: that is what E = mc² says, for the energy of a field as for any other. Dividing by c² gives the mass the field's energy is equivalent to, per cubic metre:¹

ρ = u/c² = B²/(2μ₀c²) ≈ 4.4 × 10¹⁰ kg m⁻³With B in tesla, ρ = B²/(2.2588 × 10¹¹) kg m⁻³; c = 299,792,458 m/s. The field at 10¹¹ T gives 4.43 × 10¹⁰. This page's arithmetic.

That is the field's mass-equivalent density: 44 million tonnes in each cubic metre, about 44,000 tonnes in a litre, and about 220 tonnes in a 5 mL teaspoon. A litre of lead has a mass of 11.3 kg,² so near a magnetar a litre of magnetic field carries about four million times the mass of a litre of lead (3.9 × 10⁶; this page's arithmetic).

It does not mean that the field is made of mass, or is a substance you could pour into a jar: it has energy, and energy has inertia and gravitates (Chapter 3). Nor does the field outweigh the star. A neutron star of 1.4 solar masses and 12 km radius averages about 3.8 × 10¹⁷ kg m⁻³, and nuclear matter is about 2.7 × 10¹⁷ kg m⁻³, so the field near a magnetar, for all its 44,000 tonnes a litre, is still about ten million times less dense than the star, on average (8.7 million times for that star, and 6.1 million times less dense than nuclear matter; this page's arithmetic).

The McGill magnetar catalogue gives most magnetars dipole fields (the shape of a bar magnet's field) of 10¹⁰ to 10¹¹ T, and the strongest, SGR 1806−20's, about 2 × 10¹¹ T.³ None was read off an instrument: each is inferred from how fast the star's spin slows (Chapter 5).

These are the strongest magnetic fields known in any star, and the strongest that last on any large scale. A proton's own field exceeds 10¹¹ T within about two femtometres of it (this page's arithmetic): it lasts, but not on any large scale. And lead or gold nuclei grazing one another in a collider make far stronger fields, of order 10¹⁴ T at the Relativistic Heavy Ion Collider and about 10¹⁶ T at the peak of the Large Hadron Collider's lead collisions, for peaks lasting less than 10⁻²³ s. The MoEDAL collaboration called the LHC's "the strongest known magnetic fields in the current Universe";⁴ in 2024 the STAR collaboration reported evidence of such a field's effect on the particles the collisions make.⁵ The fields themselves are calculations, not measurements.

Chapter 2From a fridge magnet to a magnetar

Magnetic fields span about thirty powers of ten. The brain's field, picked up outside the head by magnetoencephalography, is about 10⁻¹³ to 10⁻¹² T;⁶ Earth's is 25 to 65 microtesla,⁷ as in Nº 14. A small, thick neodymium magnet gives about half a tesla at its face, a thin one less. A card's magnetic stripe can be rewritten by a field above its coercivity, the reverse field that cancels its magnetisation: about 30 mT (300 oersted) for low-coercivity stripes (hotel keys, older cards) and 0.28–0.40 T (2,750–4,000 oersted) for high-coercivity ones (bank cards). These are typical values for the two ISO/IEC 7811 classes, not the standards' limits.⁸ Sunspots hold about 0.3 T, up to about 0.6–0.8 T in places.⁹

MRI scanners run at 1.5 to 3 T, some at 7 T; France's Iseult imaged human brains at 11.7 T in 2024.¹⁰ A 16 T magnet has levitated a living frog, whose water the field weakly repels.¹¹ The records for fields made with magnets and coils are about 45 T steady (45.5 T in a test coil),¹² about 100 T in pulses the magnet survives,¹³ 1,200 T inside an imploding metal liner, in a shot that destroyed it, in Tokyo in 2018,¹⁴ and reportedly about 2,800 T from explosive flux compression in Russia.¹⁵ A magnetar is tens of millions of times stronger. Laser-heated plasmas have reached about 70,000 T, inferred from the polarisation of the laser's harmonics, for trillionths of a second;¹⁶ a magnetar is still about a million times stronger (both ratios this page's arithmetic).

In space, the most strongly magnetised white dwarfs, the Earth-sized cores that stars like the Sun leave behind, reach about 10⁵ T,¹⁷ radio pulsars typically 10⁸ T,¹⁸ magnetars 10¹⁰ to 10¹¹ T.³ Between them sit two thresholds: the atomic unit of field, 2.35 × 10⁵ T, where fields start to reshape atoms (Chapter 10), and the quantum critical field, 4.4 × 10⁹ T, the natural scale for the vacuum's response (Chapter 12). At the top are the collider fields, whose peaks last less than 10⁻²³ s; on Kirill Tuchin's calculation a weaker field then lingers while the collision's hot plasma of quarks and gluons lasts.^4,19

The energy grows faster than the field. A magnetar's field is about 10¹³ times a fridge magnet's, so its energy density is about 10²⁶ times larger: every tenfold step in field is a hundredfold step in mass. As it climbs, the field's mass-equivalent matches the densities of real materials one after another: air's at about 5 × 10⁵ T, water's at 1.5 × 10⁷ T, lead's at 5 × 10⁷ T (a field well within the range of ordinary radio pulsars), the average of white-dwarf matter (Sirius B's mean, about 2.7 × 10⁹ kg m⁻³ from its measured mass and radius¹⁷) at 2.5 × 10¹⁰ T, and nuclear matter's only at 2.5 × 10¹⁴ T (this page's arithmetic). Figure 1 weighs the field at each rung.

Figure 1⚖️ Try it

Weigh a litre of field

Drag the field up

Field strength

On Earth

In space

Mass-equivalent (litre)A litre of it weighs

× density of leadTimes heavier than lead

Energy density u

Magnetic pressurePush, in atmospheres (air = 1)

B/B₀

What this field doesAt this strength

Between the densities ofAs heavy as

Mass-equivalent density of a magnetic field, ρ = B²/(2μ₀c²) = B²/(2.2588 × 10¹¹) kg m⁻³ with B in tesla (CODATA 2022), against a litre of lead (11,340 kg m⁻³). Rungs as in Chapter 2: the laser-plasma rung is inferred; magnetars are the McGill catalogue's equatorial dipoles from spin-down; collider fields are calculations whose peaks last less than 10⁻²³ s, their density this page's arithmetic in the collision's frame. This page's arithmetic.Drag the slider or tap a name to choose a field, then see what a litre (or a teaspoon) of it would weigh, as if you could weigh it, compared with the same amount of lead. Every tenfold step up in field makes its weight a hundred times heavier. At about 50 million tesla, well within the range of ordinary pulsars, the litre of field comes to outweigh the litre of lead.

On SGR 1806−20's catalogue field, 2 × 10¹¹ T, a litre carries about 180,000 tonnes, some sixteen million times a litre of lead; on its 1998 spin-down field, 8 × 10¹⁰ T, about 28,000 tonnes, some 2.5 million times (this page's arithmetic; Chapter 5 explains the difference).

Chapter 3Energy that has weight

Why does a field hold energy? Building one takes work: switch on the current in a coil and the growing field pushes back on the current, and the work done against that push sits in the field until the current is switched off. The same quantity, u = B²/2μ₀, is a pressure: a field pushes outwards across its lines and pulls inwards along them, like a bundle of stretched elastic. At 10¹¹ T:

p_B = B²/2μ₀ ≈ 4 × 10²⁷ Pa ≈ 4 × 10²² atmospheres3.98 × 10²⁷ Pa, or 3.9 × 10²² standard atmospheres of 101,325 Pa. This page's arithmetic.

Field stresses of this kind are what, in the magnetar model, crack the star's crust (Chapter 4). The energy also has inertia, and it gravitates. In 1905 Einstein asked whether a body's inertia depends on its energy content, and found that a body giving off energy E loses mass E/c²¹ (Nº 5 follows the idea into the proton). The rule makes no exception for a field: a box holding one is, in principle, harder to accelerate than the same box empty, by u/c² per cubic metre of field, and it gravitates more.

A footnote for relativists. In general relativity the whole stress–energy gravitates. With a pressure B²/2μ₀ across the lines and an equal tension along them, a local "active" density, (u + Σp)/c², comes to 2u/c²; for a whole static star the field's energy still counts once. This page uses the plain u/c².

The picture of a litre of field on a balance against a litre of lead breaks in one clear place: you could only weigh the field by weighing whatever holds it.

The star's thin outer skin is far less dense than its average, and on Dong Lai's rough model a condensed iron surface at 10¹¹ T would be about 1.8 × 10¹⁰ kg m⁻³,²⁰ about as dense as the field's own mass-equivalent (this page's arithmetic from Lai's formula, an approximate model).

How much does a magnetar's whole outside field weigh? As a dipole outside a star of radius R with equatorial surface field B_eq:

E_ext = (4π/3) R³B_eq²/μ₀ ≈ 3.3 × 10⁴⁰ JFor R = 10 km and B_eq = 10¹¹ T, a vacuum dipole outside r = R. E_ext/c² = 3.7 × 10²³ kg, about five times the Moon's 7.35 × 10²² kg. This page's arithmetic.

So the field outside one magnetar has the mass-energy of about five Moons, a ten-millionth of the star's 2.8 × 10³⁰ kg; for SGR 1806−20, about 3 to 20 Moons, depending on which years' spin-down sets its field. A 12 km star with the same spin-down would hold 1.7 times less energy outside it (this page's arithmetic).

Measured, inferred, predicted. Nothing about a magnetar's field in Part I is measured directly: its strength is inferred from spin-down, and its weight, pressure and Moon masses are this page's arithmetic. Of Chapter 2's rungs, Earth's field, MRI scanners, the 45, 100 and 1,200 T records and sunspot fields are measured; the explosive 2,800 T is reported; the laser-plasma rung is inferred; the collider rungs are calculated.

Part IIThe stars that hold them

Chapter 4Proposed in 1992

A neutron star is the collapsed core of a massive star. Most known ones are radio pulsars, with fields typically about 10⁸ T. In 1992 Robert Duncan and Christopher Thompson proposed that some are born with far more: a dynamo in the churning newborn star, working in the first seconds after the collapse, could wind its field up to dipole strengths of 10¹⁰ to 10¹¹ T (10¹⁴ to 10¹⁵ G). They called such stars magnetars.²¹

The idea answered a puzzle: a handful of sources, the soft gamma repeaters, fired short bursts of "soft", lower-energy gamma rays again and again. In 1995 Thompson and Duncan showed how a magnetar could make them: the field stresses the crust until it cracks, and the field outside snaps into a new shape, releasing energy.²²

The decisive observation came in 1998: Chryssa Kouveliotou and colleagues found X-ray pulses from SGR 1806−20 every 7.47 s, lengthening by 2.6 × 10⁻³ s per year, which for a spinning dipole implied a field of about 8 × 10¹⁰ T and an age of about 1,500 years.²³

Magnetars show themselves as soft gamma repeaters and as anomalous X-ray pulsars, slow spinners too bright in X-rays for their spin to pay for. That crust-cracking picture of their bursts is still the mainstream model in Victoria Kaspi and Andrei Beloborodov's 2017 review,²⁴ though nobody knows exactly how a burst works.

About thirty are known, as of October 2026. The McGill catalogue, last updated in November 2020, lists 30, six of them candidates.³ A few have been found since: SGR J1830−0645 in October 2020,²⁵ Swift J1555.2−5402 in June 2021,²⁶ and EP J2237, found by the Einstein Probe in June 2026 and reported in a preprint, with a field of about 1.3 × 10¹⁰ T on the catalogue's convention (this page's arithmetic, from the paper's polar value).²⁷ A September 2026 preprint also speaks of "only about 30 known sources", and reports seven candidates, not yet confirmed.²⁸

The catalogue's formula, and this page, assume a 10 km radius; NASA's NICER telescope puts the best-measured radii, of millisecond pulsars rather than magnetars, at about 11 to 13 km.²⁹

Chapter 5Weighing a field by its spin

A magnetar is thousands of light-years away and a couple of dozen kilometres across, and its light carries no simple reading of its field. What can be measured precisely is its rotation: X-ray pulses arrive once a turn, and their timing gives the spin period P and how fast it lengthens, Ṗ. A magnet spinning about a tilted axis radiates away rotational energy at a rate that grows with the square of its field; set that equal to the fall in spin energy and the field follows from P and Ṗ. The McGill catalogue writes it as:³

B = 3.2 × 10¹⁹ (PṖ)^½ G = 3.2 × 10¹⁵ (PṖ)^½ TP in seconds, Ṗ in seconds per second. It assumes a vacuum dipole with moment of inertia I = 10⁴⁵ g cm² and gives the equatorial surface field for a radius of 10 km. The field at a dipole's magnetic poles is twice as strong, so papers that quote the polar field use 6.4 × 10¹⁹; this page uses the equatorial convention throughout.

For SGR 1806−20 the catalogue gives P = 7.54773 s and Ṗ = 49.5 × 10⁻¹¹, and the formula returns 1.96 × 10¹⁵ G, or 2.0 × 10¹¹ T, the strongest dipole in the catalogue.³ Kouveliotou's 1998 numbers, 7.47 s and 2.6 × 10⁻³ s per year (Ṗ = 8.24 × 10⁻¹¹), give 7.9 × 10¹⁴ G, about 8 × 10¹⁰ T, and a characteristic age P/2Ṗ (the age the spin-down alone implies) of about 1,500 years.²³ The same star, two answers.

Its slowing is not steady: the catalogue's Ṗ is about six times the 1998 value. Peter Woods and colleagues found "large changes in the spin-down torque up to a factor of ~4" in SGR 1806−20 and SGR 1900+14.³⁰ Since the inferred field goes as Ṗ^½, the star's dipole has read anywhere from about 0.8 to 2 × 10¹¹ T, depending on the years used (this page's arithmetic).

The model ignores torques from escaping particles and a twisted outer field, and returns one idealised dipole for the whole star. Locally the field can be much stronger. SGR 0418+5729 slows so gently that its dipole field reads only 6 × 10⁸ T (an upper limit of 7.5 × 10⁸ T in 2010),^3,31 yet its X-ray spectrum shows an absorption line whose energy changes as the star turns. Andrea Tiengo and colleagues read it as a proton cyclotron line, X-rays absorbed by protons circling in the field, which would need 2 × 10¹⁰ to more than 10¹¹ T in patches near the surface.³² Deeper inside, fields of 10¹¹ to 10¹² T are predicted by theory, not measured.²⁴

Quantity	Status	How it is known
Spin periods and their slowing	measured	timing of X-ray pulses
Dipole fields	inferred	vacuum-dipole spin-down model; varies with the years used
Local surface fields	inferred	an absorption line read as a proton cyclotron feature
Interior fields of 10¹¹–10¹² T	predicted	theory

Chapter 14 completes the table.

Chapter 6Halfway to the Moon

An often-repeated claim is that a magnetar at the Moon's distance would wipe every credit card on Earth. The arithmetic does not support it. Close to the star the field is a dipole, which weakens as the cube of the distance:

B(r) = B_s(R/r)³ on the equator, 2B_s(R/r)³ on the magnetic axisB_s: the equatorial surface field; R = 10 km. Ten times farther, a thousand times weaker.

That rule stops at the light cylinder, the distance at which a field line turning with the star would have to move at the speed of light:

R_LC = cP/2π ≈ 360,000 km for P = 7.55 sField lines reaching beyond it open out into a wind of charged particles.

Beyond it the star's turning winds the field into a spiral that falls much more slowly. Peter Goldreich and William Julian's 1969 model of a pulsar's magnetosphere, the region round the star that its field controls, set out the picture. Curtis Michel's 1973 split-monopole solution (field lines running straight out, reversing direction across the equator) and Anatoly Spitkovsky's 2006 simulations give the shape this page uses.³³ On the equator the wound-up field falls as 1/r; along the spin axis the winding vanishes and the open field falls as 1/r²:

B_eq(r) ≈ B_eq(R_LC) R_LC/r, B_axis(r) ≈ 2B_s(R/R_LC)³(R_LC/r)² for r > R_LCThis page's simplified model of an aligned rotator, a star whose magnetic axis lies along its spin axis. The switch at r = R_LC is an idealisation: the light cylinder surrounds the spin axis, so a path along the axis never crosses it.

Take a magnetar with the round 10¹¹ T field, spinning every 7.55 s like SGR 1806−20. At the Moon's distance, 384,400 km, just outside the light cylinder, the field is about 2 mT on the equator and 4 mT along the axis (2.0 and 3.8 mT; this page's arithmetic): forty to eighty times Earth's field, and too weak to wipe any stripe. A hotel key card (typically about 30 mT) would be at risk only somewhat closer than halfway to the Moon, within 149,000 km on the equator to 188,000 km along the axis; a bank card (typically 0.28 T) only inside about a fifth of the Moon's distance, within 71,000 to 90,000 km (equator to axis; this page's arithmetic, with the typical stripe values of Chapter 2⁸).

The field at the Moon depends on the spin: a faster magnetar has a smaller light cylinder and a stronger wind, and the same 10¹¹ T spinning every 2.07 s, as 1E 1547.0−5408 does (Chapter 13), gives about 27 mT at the Moon on the equator and 14 mT along the axis (this page's estimate, idealised wind). A 2000 Astronomy Picture of the Day said "half the distance to the Moon",³⁴ which fits the low-coercivity stripes of hotel keys and older cards. Figure 2 lets you find your own distance.

Figure 2💳 Try it

How close could you stand?

Find your card's limit

Your distance from the star

Which magnetar

Surface field (equator)

Spin period

Go to

Field hereField where you are

× Earth's fieldTimes Earth's field

Hotel key card (30 mT, typical)

Bank card (0.28–0.40 T, typical)

Light cylinder cP/2π

Field law hereHow it falls

Field of a magnetar of equatorial surface field B_s and spin period P at distance r, this page's simplified model: a vacuum dipole inside the light cylinder R_LC = cP/2π (B ∝ r⁻³, twice as strong on the axis), and beyond it an idealised split-monopole wind (Michel 1973; Spitkovsky 2006), whose toroidal field falls as r⁻¹ on the equator and vanishes on the axis, where the open field falls as r⁻². Presets: McGill catalogue fields (equatorial, R = 10 km) and Stewart et al. 2026. This page's estimate.Slide yourself closer to or farther from a magnetar and read the field where you stand. Press a Go to button to jump to where a hotel key card, a bank card or an MRI-strength field begins, or to the Moon. Close to the star the field falls very fast; beyond the dashed line the star's wind carries it out much farther.

One Earth-width from the star, 12,756 km (twice Earth's equatorial radius),³⁵ the field is about 48 T, sixteen times a hospital scanner's 3 T (this page's arithmetic). At the other end, the field would weaken to Earth's own 50 µT only about 15 million km out on the equator, some forty times the Moon's distance, because beyond the light cylinder it falls only as one over the distance; along the spin axis Earth's level comes at about 3 million km (this page's estimate, aligned rotator).

Chapter 727 December 2004

A twisted field can snap into a shape of lower energy and let the difference go, as a twisted elastic band does, though the field's energy is spread through the space round the star rather than held in a band. On 27 December 2004 SGR 1806−20 let go. David Palmer and colleagues called its giant flare "the brightest extra-solar transient event ever recorded": for 0.2 s its gamma rays delivered energy to Earth faster than the full Moon's light does, about 5 erg cm⁻² s⁻¹ against the Moon's 3.³⁶ Nobody saw it: gamma rays are invisible, and were stopped high in the atmosphere. A 380 s tail followed, pulsing with the star's 7.55 s spin.³⁷

What was measured is the energy per unit area, the fluence: (1.36 ± 0.35) erg cm⁻² above 30 keV in the spike. Over a sphere around the star, that is

E = 4πd²F ≈ 3.7 × 10⁴⁶ erg × (d/15 kpc)²Assuming the flare shone equally in all directions; 3.7 × 10³⁹ J at the 15 kpc assumed in 2005. This page's arithmetic from Hurley et al.'s fluence; Palmer et al.'s published energy for that distance is 2 × 10⁴⁶ erg.

Kevin Hurley and colleagues wrote that "in the first 0.2 s, the flare released as much energy as the Sun radiates in a quarter of a million years". With the Sun's nominal luminosity, 3.828 × 10²⁶ W,³⁵ the two 15 kpc energies give about 170,000 to 310,000 years (this page's arithmetic).

The catch is the distance, still argued over. The discovery papers assumed a nominal 15 kpc, about 49,000 light-years. In 2008 J. L. Bibby and colleagues put the star's host cluster at 8.7 (+1.8/−1.5) kpc, about 28,000 light-years, cutting the energy threefold; the McGill catalogue adopts their value.³⁸ In 2011 Gilad Svirski, Ehud Nakar and Eran Ofek used X-ray echoes of a 2006 burst off dust clouds to set "a lower limit of 9.4 kpc and an upper limit of 18.6 kpc (90% confidence)", 31,000 to 61,000 light-years, which excludes Bibby's central value.³⁹ Taken together, the estimates put SGR 1806−20 somewhere between about 23,000 and 61,000 light-years away, from the low end of Bibby's range to Svirski's upper limit, and no one distance is settled.

Since the energy scales as the distance squared, the honest range runs from about 38,000 Sun-years (years of the Sun's output) at 7.2 kpc on Palmer et al.'s energy to about 470,000 at the 18.6 kpc upper limit on Hurley et al.'s fluence; at Bibby's central 8.7 kpc it is about 56,000 to 100,000 on the two energies (this page's arithmetic).

For scale, the largest solar flares release upwards of 10³² erg,⁴⁰ and superflares above 10³⁴ erg happen roughly once a century on each Sun-like star (Nº 12).⁴¹ The 2004 spike was roughly 10¹⁴ times the largest solar flares (this page's arithmetic). The only two other giant flares from our neighbourhood were far weaker at the distances then assumed: at least 6 × 10⁴⁴ erg from SGR 0526−66 in the Large Magellanic Cloud on 5 March 1979, and about 2 × 10⁴⁴ erg from SGR 1900+14 on 27 August 1998.³⁷ A burst of gamma rays from the galaxy NGC 253 in 2020, GRB 200415A, about 1.3 × 10⁴⁶ erg, was probably a giant flare too (the classification is disputed).⁴² Figure 3 replays the flare at the distance you choose; Chapter 8 follows it into our sky.

Figure 3⚡ Try it

Replay 27 December 2004

Set the distance, then replay

Distance to SGR 1806−20

Spike energy

Sun-yearsThe Sun would need

DistanceHow far

× largest solar flareTimes the Sun's biggest flares

Reached Earth (from the measured fluence)What reached Earth

The giant flare of SGR 1806−20 on 27 December 2004. Spike energies: Palmer et al.'s isotropic 2 × 10⁴⁶ erg and this page's 4πd²F from Hurley et al.'s fluence, 3.7 × 10⁴⁶ erg, both at the 15 kpc assumed in 2005, rescaled as d². Sun-years use L_☉ = 3.828 × 10²⁶ W (IAU 2015). Energy at Earth: the measured fluence over πR_⊕², whatever the distance. Markers, on a log scale: the flares of Chapter 7, the 1979 and 1998 ones at the distances then assumed. Light curve schematic, except the 0.2 s spike and the 380 s tail's 7.55 s pulses. Ionosphere: Inan et al. 2007. This page's arithmetic.Nobody agrees exactly how far away this star is, so set the distance yourself: the farther it is, the brighter it must really have been. Each distance gives two numbers, because the two 2005 papers' measurements lead to somewhat different energies. Then press Replay to watch the fifth-of-a-second flash, the long pulsing glow after it, and the extra free electrons it made in Earth's upper air (drawn as a glow, though nobody could see it; the next chapter tells that part).

Chapter 8A flash that reached our sky

High in the atmosphere, sunlight keeps a small fraction of the air's molecules ionised. That layer, the ionosphere, reflects long radio waves, so very-low-frequency (VLF) radio signals travelling under it gauge how many free electrons it holds. The flare struck the daytime half of Earth, and Umran Inan and colleagues found its mark in VLF signals from Hawaii received in Antarctica: electron densities rose "by a factor of ∼100" at about 60 km and by 1,000 or more at about 30 km, and the disturbance lasted more than an hour.⁴³

It had happened before. The 1998 flare from SGR 1900+14 "produced enhanced ionization at ionospheric altitudes of 30 to 90 km", and the radio signals "exhibited the 5.16 s periodicity of the giant flare": the ionosphere flickered with the spin of a star across the Galaxy.⁴⁴

None of this was dangerous. The energy that reached Earth is the measured fluence over Earth's disc, whatever the distance:

E_⊕ = F × πR_⊕² ≈ 1.36 × 10⁻³ J m⁻² × 1.28 × 10¹⁴ m² ≈ 1.7 × 10¹¹ JR_⊕ = 6,378 km; 1 t of TNT = 4.184 × 10⁹ J. This page's arithmetic.

About 40 tonnes of TNT over the whole dayside in a fifth of a second: harmless to life, yet enough to measure, from a star tens of thousands of light-years away.

At the star, the flare released anything from under 1% to a few tens of per cent of the energy stored in the field outside it, depending on the distance and on which years' spin-down sets the field (this page's estimate, for 8.7 to 18.6 kpc: about 0.5–4% on the catalogue's field, 3–27% on the 1998 field). Palmer and colleagues put the exterior field energy at about ten times the flare's.³⁶

One team argues that the flare also made heavy elements: Anirudh Patel and colleagues found a gamma-ray glow, peaking about ten minutes after the spike, that matches the decay of about a millionth of a solar mass of fresh r-process nuclei, built by rapid neutron capture; on their reading, giant flares supply at least roughly 1–10% of the Galaxy's r-process elements.⁴⁵ Where gold comes from is still argued over (Nº 7).

From another galaxy such a flare would look like a short gamma-ray burst, and some have been caught: GRB 200415A from NGC 253, about 11 million light-years away, probably one (Chapter 7);⁴² and GRB 231115A, on 15 November 2023, from the direction of M82, "with high confidence" a magnetar giant flare, in the words of Sandro Mereghetti and colleagues.⁴⁶

Chapter 9A radio burst from next door

Fast radio bursts (FRBs) are millisecond radio flashes from other galaxies, long of unknown origin. On 28 April 2020 a magnetar in our own Galaxy, SGR 1935+2154, made one, or something very like one, catalogued as FRB 200428 after its date. The CHIME telescope caught a two-part burst carrying about 3 × 10³⁴ erg at 400–800 MHz, three orders of magnitude brighter than any earlier radio burst from a magnetar.⁴⁷ The STARE2 radio stations found it about 4,000 times more energetic than any earlier Galactic radio burst of similar duration, yet about 30 times less energetic than the faintest extragalactic burst then known.⁴⁸ So at least some fast radio bursts can come from magnetars; not necessarily all.

The distance is again uncertain. Both papers quote 6.6 to 12.5 kpc, about 20,000 to 40,000 light-years, from nearby gas clouds, the radio delay of the burst's lower frequencies and the surrounding supernova remnant; one remnant study allows it to be as near as 4.5 kpc (4.5–9.0 kpc).⁴⁹ The energies assume about 10 kpc (32,600 light-years).

As far as we can find, SGR 1935+2154 is still the only magnetar seen to make a burst this energetic, as of October 2026: a 2026 paper in the Astrophysical Journal says "to date, only one radio burst as energetic as FRBs has been detected from a Galactic magnetar".⁵⁰ FRB 200428 itself arrived with an X-ray burst.⁴⁸ Further X-ray bursts with radio counterparts came from the same star in late 2022, and two were analysed in 2026 papers: one on 14 October 2022, "the second FRB-associated magnetar X-ray burst" to its discoverers on the GECAM gamma-ray mission,⁵⁰ and one on 20 November 2022.⁵¹ Separately, Kenzie Nimmo and colleagues used the scintillation, the twinkling imposed by gas along the way, of FRB 20221022A, a burst from another galaxy, to show that its emission region is at most about 30,000 km across, which they read as emission from within or just beyond its source's magnetosphere:⁵² one burst from one source, not a proof for all.

Measured, inferred, predicted. In Part II the spin periods and their slowing, the giant flares, the 2004 fluence and its ionospheric effect, and FRB 200428 are measured; the dipole fields, distances, flare energies and the heavy-element reading are inferred with named models; the interior fields of Chapter 5 are predicted; the card distances and the flare's share of the field's energy are this page's estimates.

Part IIIWhat the field does to matter, and to nothing

Chapter 10Atoms squeezed into needles

An electron in a magnetic field circles the field lines (as in Nº 9's collider ring). Quantum mechanics allows only certain circles, each with a fixed energy: the Landau levels. The smallest has a radius of order the magnetic length:

ρ̂ = (ħ/eB)^½ = 25.7 nm × (B/1 T)^−½, b = B/B₀, B₀ = 2.35 × 10⁵ TAt B₀, the atomic unit of field, ρ̂ equals the Bohr radius a₀ = 52.9 pm, the size scale of an ordinary hydrogen atom.

Below B₀ the nucleus decides an atom's shape; above it the field does.²⁰ Far above it, the electron is confined sideways to a tube whose radius is of order ρ̂, while along the field the nucleus holds it loosely over roughly a₀/ln b: a needle. At 10¹¹ T (b = 4.3 × 10⁵, ρ̂ = 81 fm) a hydrogen atom is roughly a quarter of a picometre wide and several picometres long, a needle tens of times longer than it is wide; with no field it is about 100 pm across (this page's arithmetic, rough; the needle is a cloud of probability, not a rod).

The needle is also harder to break. Hydrogen's ionisation energy rises from 13.6 eV with no field to about 160 eV at 10⁸ T and about 870 eV at 10¹¹ T, 64 times its usual value (Lai's table, "generally accurate to within 10%").²⁰ The change is gradual, and at first squeezing is not the cause. At 10⁵ T, the strongest white-dwarf fields, the energy is already about 18 eV, a third higher, on Alexander Potekhin's fit as Lai prints it.⁵³ An electron freed in a field cannot stop circling: it keeps the field's minimum circling energy, 5.8 eV at 10⁵ T, so freeing it costs that much more. The field's push on the bound electron's orbit works the other way, raising its energy by 1.2 eV: 13.6 + 5.8 − 1.2 = 18.2 eV (this page's arithmetic). The magnetic length there is still 1.5 Bohr radii, so the shape has barely changed; squeezing takes over from about 10⁷ T. Figure 4 turns up the field on one hydrogen atom.

Figure 4🧵 Try it

Squeeze an atom

Turn up the field

Field strength

Ionisation energy

× zero-field 13.6 eVTimes harder than normal

Shape

Across × along (roughly, 2σ)Size, roughly

Magnetic length ρ̂

Hydrogen's ground state in a field B, with b = B/B₀ (B₀ = 2.3505 × 10⁵ T). Ionisation energy measured from the lowest Landau level: the Potekhin (1998) fit printed as Lai (2001) eq. 3.8 up to b = 10⁴, then Lai's Table I interpolated in log B (within about 10%). Shape: this page's drawing convention, per-axis rms sizes σ_⊥ = a₀(1 + b²)^−¼ and σ_∥ = the larger of a₀[1 + ln²(1 + b)]^−½ and σ_⊥, tending to the magnetic length and the rough a₀/ln b; sizes are 2σ. Shape words follow b: the drawing understates moderate stretches. This page's arithmetic and drawing.Turn up the field and watch a hydrogen atom change. At first the atom's shape barely changes, though it already starts getting harder to break apart; above about 235,000 tesla the field starts to win, and at magnetar strength the atom is a thin needle along the field, far harder to break apart. The marks under the slider show the strongest fields made with magnets and coils, and in laser-heated plasmas.

Slide it from 10⁵ T to magnetar strength: the binding climbs from about 1.3 to 64 times its usual value, and the cloud, barely changed at first, ends as a needle.

Chapter 11Chains, solids and the laboratory's reach

Needles change chemistry. In Lai's review the elongated atoms bond end to end into molecular chains along the field, chains bind side by side into a solid, and in fields far above 10¹⁰ T, below about a million kelvin, a neutron star's surface may be a condensed liquid or solid rather than a gas.²⁰ This is theory; nobody has seen a needle atom or a chain. But fits to the X-ray polarisation of two magnetars, 1RXS J170849.0−400910 and EP J2237, measured by the IXPE satellite (Chapter 13), now pair a condensed-surface region with a hotter patch covered by an atmosphere:^54,27 they suggest a condensed patch; they do not show one.

No laboratory can do this to an ordinary, unexcited atom. Magnets and coils, at 1,000 to 3,000 T for microseconds, are about a hundred times too weak even to start reshaping atoms and thousands of times too weak to make needles, which need 10⁷ T and up (this page's arithmetic).^14,15 Laser-heated plasmas get about a third of the way to the atomic unit (b ≈ 0.3; this page's arithmetic), but in matter too hot to hold intact atoms, for trillionths of a second;¹⁶ collider fields peak for less than 10⁻²³ s, with no atoms in them.

Physicists reach the regime by enlarging the atom instead. An atom whose electron is excited to a high level n, a Rydberg atom, is about n² times larger and far more weakly bound, so the field at which magnetism rivals the nucleus falls roughly as B₀/n³: at n = 40, 6 T is already past it (scaled field bn³ ≈ 1.6; this page's arithmetic). Laboratory magnets have rearranged the spectra of highly excited barium (W. R. S. Garton and F. S. Tomkins, 1969) and hydrogen (A. Holle and colleagues, 1988).⁵⁵ None of these is a needle, but each lets a few tesla play a magnetar's part.

Chapter 12Light against light

Fields this strong act on empty space too. In quantum electrodynamics (QED), the quantum theory of light and electrons, empty space is not inert: short-lived virtual pairs of electrons and positrons, the electron's antimatter partner, flicker in and out of existence, and a strong field tugs on them. In 1936 Werner Heisenberg and Hans Euler worked out the consequence: the vacuum's response to a field is not quite in proportion to it, so light can, very weakly, feel other light and feel a magnetic field.⁵⁶ The natural scale is the field at which an electron's circling energy equals its rest energy, 511 keV:

B_Q = m_e²c²/(eħ) = 4.414 × 10⁹ TThe quantum critical field, the magnetic counterpart of the electric field at which, in Julian Schwinger's 1951 calculation, the vacuum gives up pairs (Nº 5).

Schwinger's paper set the scale;⁵⁷ by 1971 several authors, among them Zofia Białynicka-Birula and Iwo Białynicki-Birula and, in what became the classic paper, Stephen Adler, had worked out what a magnetic field does to light crossing it.⁵⁸ Light is a travelling wave of electric and magnetic fields, and its polarisation is the direction in which the electric field swings, at right angles to its travel; polarising sunglasses pass one direction and block the other. Light polarised along the field, as the field looks from the ray, and light polarised at right angles to it travel at slightly different speeds: the vacuum becomes birefringent. For fields well below B_Q, and light crossing the field at an angle θ, the two refractive indices n, which say how much the vacuum slows each kind of light (it travels at c/n), are:⁵⁹

n_∥ − 1 = (7α/90π)(B/B_Q)² sin²θ, n_⊥ − 1 = (4α/90π)(B/B_Q)² sin²θ, Δn = (α/30π)(B/B_Q)² sin²θα ≈ 1/137 is the fine-structure constant. At θ = 90°, Δn = 3.97 × 10⁻²⁴ × (B/1 T)². This page's arithmetic.

The effect is tiny until the field nears B_Q: Δn is a few parts in 10¹⁴ at 10⁵ T, 4 × 10⁻⁸ at a pulsar's 10⁸ T, 4 × 10⁻⁶ at 10⁹ T (this page's arithmetic from the formula). Above B_Q the weak-field formula fails (at 10¹¹ T it would give 0.04, five times too much). Fits valid at any field (Alexander Potekhin and colleagues, as given by Alice Harding and Dong Lai) give 8.6 × 10⁻⁵ at B_Q, 3.8 × 10⁻⁴ at 10¹⁰ T and 7.9 × 10⁻³ at 10¹¹ T: the effect keeps growing, more slowly, and at magnetar strength the two speeds differ by nearly 1% (this page's arithmetic from the fits).⁵⁹

Photon splitting, one photon becoming two, is a separate prediction for the same fields, made in the same years, and not birefringence; it has not been observed in a magnetic field (in the electric fields of atomic nuclei it was seen in 2002).⁵⁸

No laboratory has measured the difference in speeds. The PVLAS experiment spent 25 years sending laser light through strong magnets, latterly two 2.5 T permanent magnets; its final result at 2.5 T, Δn = (12 ± 17) × 10⁻²³ against QED's 2.5 × 10⁻²³, has an uncertainty about seven times the effect.⁶⁰ The same nonlinearity has been seen another way: at the LHC the fields of passing lead nuclei act as clouds of photons, and ATLAS saw those photons scatter off one another (evidence in 2017; a discovery-grade observation in 2019).⁶¹ That is light scattering off light, not birefringence. In 2021 the STAR collaboration found that electron–positron pairs made from colliding photons at the Relativistic Heavy Ion Collider depend on the photons' polarisation, with "implications for vacuum birefringence"; Brookhaven's press release called it a first Earth-based observation of the effect. It measures how pairs are made, not a difference in speeds, so this page does not count it as a measurement.⁶¹

Chapter 13Empty space as a crystal

Calcite, a crystal, shows a double image because it too carries the two polarisations at different speeds, and "the vacuum as a crystal" is a fair picture with a clear break: there is no lattice, only virtual pairs, and calcite's double image is far stronger than anything the vacuum does to visible light near a magnetar.

A magnetar might show the effect through the polarisation of its X-rays. In the models, each patch of the surface sends out X-rays whose polarisation is set by the local field (mostly at right angles to it, in the "extraordinary" mode), and since the field points different ways on different patches, their polarisations should partly cancel. Vacuum birefringence changes that, in theory: close to the star each X-ray's polarisation turns to follow the field as it climbs out, until it freezes at the polarisation-limiting radius:⁶²

r_pl ≈ 4.8 (B_P/10¹¹ G)^2/5 (E/1 keV)^1/5 RTaverna et al. 2015, with B_P the polar field and E the photon energy. For an equatorial 10¹¹ T, about 250 stellar radii at 1 keV and 290 at 2 keV (this page's arithmetic). Published estimates span a few tens to a few hundred stellar radii.

That far out, the field looks almost the same from every visible patch, so the frozen polarisations line up and the star looks highly polarised. The argument has a catch. A high degree of polarisation, the share of the light whose polarisation lines up, favours birefringence only when, without the effect, the field directions across the emitting region would point different ways and cancel. Over a small region the field is nearly uniform, so a small hot spot seen well away from the magnetic axis keeps its own polarisation even without the effect, and the degree alone cannot decide. Seen nearly along the axis, even a small spot's field directions fan out around the line of sight and cancel without it. In this page's toy model, a spot 10° in radius round the magnetic pole, seen from 60° off the axis, is 95% polarised without the effect; seen from 10° off the axis it is 21%, and from 1.5°, under 1%.

Figure 5💎 Try it

How the vacuum lines up the light

Switch the vacuum on

Surface field (equator)

Light

Angle between our view and the magnetic axis

Where the light comes from

Polarisation at the surface

Compare with

Δn at the surface (equator)

Polarisation-limiting radius

Degree, vacuum off (toy)Without the effect (in this cartoon)

Degree, vacuum on (toy)With the effect (in this cartoon)

Star view: this page's toy model of why vacuum birefringence raises a neutron star's observed X-ray polarisation (after Heyl and Shaviv). Each ray leaves the surface polarised along the local projected dipole field (degree p₀; real emission is mostly across it, which gives the same degree). With the vacuum off, the polarisation is fixed at the surface and patches with different field directions cancel; with it on, it follows the field out to the polarisation-limiting radius r_pl ≈ 4.8 (B_P/10¹¹ G)^0.4 (E/1 keV)^0.2 R (Taverna et al. 2015), where the field looks almost the same from every visible patch. Straight rays, uniform brightness, a sharp freeze, an aligned dipole: a cartoon, not a fit to any star. Measured degrees sit beside the bar, not on it: the toy omits the emission physics. Side view (wide screens): one ray's polarisation, turning with the field until it freezes at r_pl. Chart: Δn = n_∥ − n_⊥ across the field: weak-field Heisenberg–Euler below 10⁻³ B_Q, the fits of Potekhin et al. 2004 (as given by Harding and Lai 2006) above.In theory, a star's light starts out with its polarisation set by the magnetic field at each spot on its surface. Without the vacuum effect, the spots point every which way and mostly cancel. With it, the light keeps turning with the field until it is far from the star, and then it all lines up. This is a cartoon that leaves out how a real star gives off its light, so its numbers aren't predictions for any real star. Try a small hot spot too (only that patch is drawn, enlarged): seen from the side, even the plain version looks lined up, but seen almost end-on it cancels again, so the angle we see a star from matters as much as where its light comes from.

The first claim from a star came in 2016, in visible light: Roberto Mignani and colleagues measured 16.43 ± 5.26% polarisation from RX J1856.5−3754, an isolated neutron star of about 10⁹ T, not a magnetar, "large enough to support the presence of vacuum birefringence".⁶³ The result was only about three times its uncertainty, and it was argued over: L. M. Capparelli, Luciano Maiani and colleagues replied that a polarised surface could produce it alone, and the original team disputed that.⁶⁴

Since 2022 NASA's Imaging X-ray Polarimetry Explorer, IXPE, has found magnetars among the most polarised X-ray sources. For 4U 0142+61, (15.0 ± 1.0)% at 2–4 keV and (35.2 ± 7.1)% at 5.5–8 keV, with the polarisation angle swinging by 90° in between; its team's submitted manuscript said the results "lend further support" to vacuum birefringence; the published paper's abstract does not repeat the phrase, and reads them with a model of surface emission scattered in the magnetosphere.⁶⁵ For 1RXS J170849.0−400910, about 35% overall, rising from about 20% at 2–3 keV to about 80% at 6–8 keV, though that team said the comparatively small size of the emitting regions "does not allow to reach a robust conclusion" about vacuum birefringence.⁵⁴

In 2026 two teams published full analyses of the same IXPE observation (about 500,000 seconds, 26 March to 5 April 2025) of the magnetar 1E 1547.0−5408, one of the few that also send out radio pulses:

Taverna et al., ApJ, April 2026

Degree: 47.7 ± 2.9%, averaged over 2–6 keV
Emission: "a single, fairly small hot spot"
Geometry: magnetic axis and line of sight both misaligned with the spin axis
Verdict: the high polarisation "cannot be regarded as compelling evidence" for vacuum birefringence, though the angle's swing and the degree's change with energy "hint once more" at QED effects

Stewart et al., Nature, August 2026

Degree: about 46% averaged over 2–8 keV (arXiv manuscript); 65% at 2 keV alone, nearly 80% at some phases
Emission: one small hot spot (about 13 km² in their arXiv manuscript), best fitted as an offset wedge near the magnetic pole
Geometry: hot-spot model: a near-aligned star seen about 1.5° from its axis in their arXiv manuscript, roughly as their radio data suggest (their fit to the angle's swing gives a misaligned one); models without the effect fit much worse
Verdict: vacuum birefringence "can naturally explain" the signal; still "a long-standing but unconfirmed prediction"

Roberto Taverna's team published first, and the Nature paper cites it.⁶⁶ Rachael Stewart's team, who added NICER X-ray and Parkes radio data, call their result "a marked advance in probing" the prediction and say their geometry depends on the model. Their own fit of the rotating-vector model, which follows how the polarisation angle swings as the star turns, gives a misaligned star, as Taverna's team's does.⁶⁷ So both teams put the X-rays in one small hot spot and read the angle's swing as a hint of the effect.

They differ on the geometry and on how far the data go, and Figure 5 shows why the geometry matters. Stewart's team's hot-spot fit in their arXiv manuscript has us looking within about 1.5° of the magnetic axis. From there, in this page's toy, a small spot centred on the pole is under 1% polarised without the effect, and a wedge shaped like their best-fit spot about 30–50%, against about 99% with it; on that geometry, they found, models without the effect fit much worse. Taverna's team fitted a misaligned star and judged that, for it, the high degree is not compelling evidence. A third 2026 paper, by Biao-Peng Li and colleagues, fitted only the angle's swing and found that it alone does not prefer the near-aligned radio geometry, though it does not rule it out.⁶⁸ A university press release said one of its astronomers "may have just confirmed" the effect;⁶⁹ the Nature paper still calls it "unconfirmed".

Where it stands, in this page's judgement as of October 2026: the magnetar evidence for vacuum birefringence is growing but not yet conclusive, and depends on models of the emitting region and the viewing geometry. No laboratory has yet measured the difference in speeds itself.

Chapter 14What the weight means

Back to the litre: near a magnetar, by E = mc², it carries about 44,000 tonnes, four million times a litre of lead. The number is arithmetic on an inference, every step named: a field read from a spin-down, an energy that grows as its square, Einstein's conversion. Everything on this page sorts into three groups:

Status	What
Measured or observed	Spin periods of most of the thirty or so magnetars, and spin-down rates of about two dozen; bursts and three local giant flares; the 2004 flare's fluence and ionospheric effect; FRB 200428; X-ray polarisation up to about 80%; SGR 0418+5729's variable absorption line
Inferred with a model	Dipole fields (from spin-down); laser-plasma fields (from harmonics); local fields (from cyclotron lines); collider fields (calculated); distances (SGR 1806−20's contested); flare energies; condensed surfaces (from polarisation fits); vacuum birefringence in magnetospheres (from polarisation, contested)
Predicted, not yet seen	Needle atoms and molecular chains; photon splitting in a magnetic field; vacuum birefringence measured in a laboratory (a 2021 collider claim aside, Chapter 12); interior fields of 10¹¹–10¹² T

And five things this page does not say about the field:

Made of mass: Its weight is the mass E = mc² assigns to its energy (Chapters 1 and 3).
Denser than the star: It is about ten million times less dense than the star, on average (Chapter 1; the thin outer skin, Chapter 3).
Measured with a magnetometer: It is inferred from spin-down under a vacuum-dipole model (Chapter 5).
Able to wipe cards from the Moon: For a 10¹¹ T star spinning every 7.55 s it is 2–4 mT there; a hotel key card is at risk somewhat closer than halfway, a bank card only inside about a fifth of the way (Chapter 6).
Proof of vacuum birefringence: The evidence is growing but not yet conclusive, in this page's judgement (Chapter 13).

Where things stand, as of 25 October 2026: about thirty magnetars are known, the newest in a preprint; SGR 1935+2154 is the only one seen to make a burst as energetic as a fast radio burst, as far as we can find; SGR 1806−20's distance is disputed; two refereed 2026 analyses of one X-ray observation read the case for vacuum birefringence with different confidence, while the best laboratory search has not reached the predicted size.

A field is energy spread through space, and energy has inertia and pulls on everything around it. Usually that weight is unnoticeable; around a dead star, it outweighs lead four million times over. Energy has weight, and here you can almost weigh it.

Glossary

Tesla, gauss: The SI unit of magnetic field, and the older unit in which astronomers quote magnetar fields: 1 T = 10⁴ G.
Magnetic energy density, magnetic pressure: The energy a field stores per cubic metre, B²/2μ₀. The same quantity is the pressure the field exerts across its lines.
Mass-equivalent density: The energy density divided by c²: the mass that E = mc² assigns to a field's energy, per cubic metre.
Neutron star, pulsar, magnetar: A collapsed stellar core with more than the Sun's mass, some 22–26 km across. A pulsar is one seen to pulse once a turn; a magnetar, a young one powered by its field, seen as a soft gamma repeater or an anomalous X-ray pulsar.
Spin-down, P and Ṗ: The slowing of a star's rotation: P is the spin period, Ṗ how much it lengthens each second.
Dipole field; local fields: A bar magnet's field shape, falling as 1/r³, twice as strong at the poles as at the equator. Local fields are those of small patches near the surface, which can be much stronger than the dipole value.
Magnetosphere, light cylinder, pulsar wind: The magnetosphere is the region round a star that its field controls. The light cylinder is the distance cP/2π at which a field line turning with the star would move at light speed; beyond it the lines open into a wind and weaken more slowly.
Kiloparsec, erg, electronvolt: 1 kpc = 3,261.56 light-years; 1 erg = 10⁻⁷ J; 1 eV, the energy an electron gains across one volt, is 1.602 × 10⁻¹⁹ J.
Atomic unit of field, B₀: 2.35 × 10⁵ T, where the magnetic length (ħ/eB)^½ equals the Bohr radius, 52.9 pm. Above it the field, not the nucleus, sets an atom's shape.
Landau level: One of the fixed energies of an electron circling in a magnetic field. Even the lowest has a minimum circling energy.
Ionisation (binding) energy: The energy needed to free an atom's electron: 13.6 eV for hydrogen in no field.
Quantum critical field, B_Q: 4.414 × 10⁹ T, where an electron's circling energy equals its rest energy, 511 keV.
Polarisation, degree of polarisation; IXPE: Polarisation is the direction in which light's electric field swings, at right angles to its travel; the degree is the fraction of the light whose polarisation is lined up. IXPE, NASA's Imaging X-ray Polarimetry Explorer, measures it in X-rays of 2–8 keV.
Vacuum birefringence: The prediction of quantum electrodynamics (QED) that a strong field makes empty space carry the two polarisations of light at slightly different speeds, through virtual electron–positron pairs.
Polarisation-limiting radius: In theory, the distance out to which the vacuum keeps each X-ray's polarisation following the field; beyond it the polarisation freezes.

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