Astronomy & Celestial Mechanics
the sky, computed
Concept

Dead zone — where it appears

A layer near the midplane of a protoplanetary disc where the gas is too weakly ionised to couple to a magnetic field, so magnetic turbulence cannot operate there. Gas must accrete through it by other means, such as winds from the disc surfaces, or pile up until something else takes over.

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

A vanishing field that changes the answer completely. The growth rate of the magnetorotational instability against wavenumber, both in units the orbital frequency sets: the vertical axis is the growth rate divided by Ω, the horizontal is the wavenumber multiplied by the Alfvén speed and divided by Ω. The maximum is exactly three quarters of the orbital frequency and it does not depend on the field strength at all — it occurs at kv_A = √15Ω/4, so a weaker field simply moves the fastest-growing wavelength to a longer one. The curve vanishes above kv_A = √3Ω, which is the only thing the field decides: modes shorter than that are stabilised by magnetic tension. An unmagnetised Keplerian disc is Rayleigh-stable and would never accrete; a disc with a field a millionth of the strength needed to matter dynamically grows a mode that doubles in about a fifth of an orbit. The limit is discontinuous, which is the reason this was found late and by algebra rather than early and by observation.

The weakest field changes the answer

A Keplerian disc is stable by every hydrodynamic test there is. Add a magnetic field of any strength whatever — a millionth of what would matter dynamically — and it becomes violently unstable, at a growth rate of three quarters of an orbit per radian that does not depend on the field at all.

gravitation · Magnetorotational instability A bead on a rotating wire: when gas is flung off a disc. The effective potential — gravity plus the centrifugal potential in the frame rotating with the footpoint — for gas sliding along a rigid magnetic field line that leaves a Keplerian disc at 20°, 30°, 40° from the vertical, in units of GM over the footpoint radius, against distance along the line in units of that radius. The field line corotates with the disc where it is anchored, like a wire whipped round, and gas on it behaves like a bead. Close to vertical the potential rises away from the disc and the gas is bound to its footpoint. Inclined by more than 30° it falls, and gas is flung outward along the line with nothing but the rotation to drive it. The 30° threshold is exact for a Keplerian disc — the second derivative of the potential at the footpoint changes sign there — and it was the result that made magnetised disc winds a mechanism rather than a speculation.

A disc that throws its spin upward

A disc does not need turbulence to accrete. A magnetic field threading it can fling gas off its surface along field lines tilted more than thirty degrees from the vertical, and each gram flung out leaves with several times the angular momentum it had — so a wind carrying a few per cent of the inflow can drive the rest onto the star. Because it pulls on the disc's faces rather than across its edge, a wind outpulls the turbulence as soon as the field's pressure is a few ten-thousandths of the gas's.

gravitation · Magnetorotational instability

Named alongside it

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

Magnetorotational instabilityPlasma betaAccretionAlfven radiusAlfven speedAlpha viscosityAngular momentumAngular momentum transportDisc windIonisationJetLever arm

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