Astronomy & Celestial Mechanics
the sky, computed
Concept

Magnetar — where it appears

A neutron star whose inferred dipole field exceeds ten to the fourteenth gauss and whose X-ray output far exceeds what its spin-down can supply. The energy is generally attributed to the decay of the field itself, which is the only reservoir of the right size.

Named by 3 essays across one field — each of them below, with the objects they name alongside it.

Two measured numbers, and everything else on the page derived from them. 25 pulsars in the plane of period against period derivative, at their catalogued values. Only the two axes are measurements; the three families of contour are models. Constant surface field runs at slope −1 because B ∝ √(PṖ), constant characteristic age at slope +1 because τ = P/2Ṗ, and the two families cross the population at right angles — which is why a single dot fixes both. The Crab sits at 3.8·10¹² G and 1257 years, and its true age is 972; the millisecond pulsars at the lower left have fields ten thousand times weaker and characteristic ages of billions of years, because they were spun back up by a companion long after they died. The line at the lower right is the death line, B/P² below which the model says no pair production and therefore no radio emission — and J2144−3933 is drawn below it, an 8.5-second pulsar that is radiating anyway.

A neutron star born turning too slowly

Collapse an iron core a few thousand kilometres across down to twelve, and conservation of angular momentum multiplies its rotation rate by about eighteen thousand. A model with no transport in it delivers a newborn pulsar at the break-up limit; the ones that are observed turn twenty times slower, which is a measurement of the core before it fell.

stars · Supernovae A formula everyone uses, and the number no pulsar has. Above: the braking index measured for the 4 pulsars whose spin-down has been followed long enough to give a second derivative, against the value a magnetic dipole rotating in vacuum requires. That value is exactly 3, and it is what every catalogued field strength and every characteristic age assumes. Not one measurement reaches it: they run from 1.4 to 2.839, and all of them fall short in the same direction, which is the signature of a systematic rather than of noise. Below: what that costs. The age a spin-down history gives is the period divided by (n − 1) times its derivative, so the ratio to the quoted characteristic age is 2/(n − 1) — 5.00 for Vela. The numbers are not thereby useless: an exponent recovered from the data is exactly the kind of correction a measurement can absorb. What has gone is the claim that the field strength printed beside a pulsar is a measurement of a field. It is a measurement of a spin-down rate, read through a model the same pulsar refutes.

The exponent no pulsar has

Every field strength in the pulsar catalogue comes from one formula, which assumes the star is a magnetic dipole rotating in a vacuum and therefore that its spin-down obeys an exponent of exactly three. Where that exponent has been measured it is 2.51, 2.84, 1.4 — never three, and always short.

stars · Pulsars Field strength against radius, from the Sun to a magnetar. Surface magnetic field against radius, both on logarithmic scales, radius in solar radii and field in gauss, for five kinds of star: the Sun's dipole, Ap and Bp stars, magnetic white dwarfs, radio pulsars, magnetars. The diagonal lines are constant magnetic flux, πR²B = 10²³, 10²⁵, 10²⁷ gauss square centimetres, along which a star shrinking with its field frozen in would slide. The Ap and Bp stars, the magnetic white dwarfs and the magnetars all fall close to the upper lines: a field of a few kilogauss on a star of three solar radii, squeezed to the size of a white dwarf, becomes a hundred million gauss, and squeezed to twelve kilometres becomes a hundred trillion. The Sun's dipole and the ordinary pulsars carry a hundred to a thousand times less flux.

The same flux in three sizes

A few per cent of hot main-sequence stars carry kilogauss fields that do not change over decades. So do a similar share of white dwarfs, at a million times the strength, and of young neutron stars, at a hundred billion times it. Multiply each field by its star's area and the three classes carry nearly the same magnetic flux — what a field frozen into a star would keep as the star shrank by a factor of a hundred thousand. A collapse makes a field enormous, but it cannot make it important.

stars · Flux freezing

Named alongside it

The objects these essays reach for when they reach for this one.

Braking indexCharacteristic ageMoment of inertiaNeutron starAngular momentumAngular momentum transportAp starsAsteroseismologyBirth periodCollapsarCore collapseFlux freezing

All concepts