Astronomy & Celestial Mechanics
the sky, computed
Concept

Corotation radius — where it appears

The orbital radius at which a circular orbit keeps pace with a spinning body's rotation. A magnetised star can accrete only from inside it; matter caught by the field beyond it is flung outward instead, and the star spins down.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

Also named here as magnetospheric radius — the same set of essays touches all of them, so they are one junction rather than several.

Where the disc stops, and the spin that follows from it. Two radii against accretion rate, for a neutron star with a 10⁸-gauss field. The falling curve is the magnetospheric radius, where the field's stress on the disc matches the rate at which the flow carries angular momentum inward; it goes as the accretion rate to the minus two sevenths, which is a weak enough dependence that the factor of 1000 in supply drawn here moves the boundary by a factor of 7.2. The horizontal lines are corotation radii for three spin periods — the radius at which the disc orbits as fast as the star turns. Above corotation the field is spinning the gas faster than it wants to go and flings it out; below, the gas is faster and spins the star up. So the crossing is an attractor, and a star accreting steadily walks to the period where the two coincide. That period goes as the field to the six sevenths and the rate to the minus three sevenths — which is why a neutron star that has swallowed a tenth of a solar mass from a companion comes out at a few milliseconds, and why the millisecond pulsars have fields ten thousand times weaker than the young ones.

The period a star is pulled towards

A magnetised neutron star does not let a disc reach it. The disc stops where the field's stress wins, and if that radius lies inside the corotation radius the star is spun up while outside it the star is spun down — so there is one period at which nothing changes, and an accreting star walks to it.

gravitation · Accretion A field that makes electrons transparent. The electron-scattering cross-section for photons polarised across a strong magnetic field, as a share of the free-electron value, against photon energy, for fields of 10¹², 10¹³, 10¹⁴ gauss, on logarithmic axes. Below the electron cyclotron energy — 12, 116, 1160 keV for these fields — an electron bound to the field can barely respond to a wave whose electric field is perpendicular to it, and the cross-section falls as the square of the ratio of energies. At the 10 keV of these sources' X-rays, a 10¹⁴ gauss field reduces it 13,456-fold. The Eddington limit is written with the free-electron cross-section; in such a field it is the wrong number.

A limit written for free electrons

The Eddington limit says a star cannot shine brighter than the point where its light pushes its own gas away, and the push is calculated for free electrons scattering light. In a magnetic field of a hundred trillion gauss an electron is not free. It is bound to the field, it can barely respond to light polarised across it, and the limit calculated for it is the wrong number by a factor of hundreds — which is one of two ways a neutron star can shine five hundred times brighter than it is supposed to.

stars · Eddington limit

Named alongside it

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

Magnetospheric radiusAccretionAccretion columnAlfven radiusAngular momentumCyclotron resonanceEddington limitElectron scatteringMagnetarsMagnetorotational instabilityMillisecond pulsarNeutron stars

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