Concept

Alfven speed — where it appears

The speed at which a disturbance travels along a magnetic field line, equal to the field strength divided by the square root of the mass density. It is the magnetic counterpart of a sound speed, and comparing the two gives the plasma beta.

Named by 3 essays across 3 fields — 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 field strength read off the scatter of directions. The Davis–Chandrasekhar–Fermi estimate: field strength against the dispersion of polarisation angles across a cloud, at a density of 10⁴ molecules per cubic centimetre and a turbulent velocity of 0.9 kilometres a second. The polarisation directions themselves contain no field strength — an aligned grain reports which way the field points and nothing about how hard it is pulling. The strength is in the disorder. Turbulence of a given energy bends a stiff field less than a weak one, so the angular scatter is the ratio of the turbulent velocity to the Alfvén speed, and inverting it gives the field: 220 µG at a 9-degree dispersion. The relation is exactly inverse, so the estimate is most trustworthy where the field is most ordered and worst where it matters most. The factor of 0.5 in front is not theory — it is what simulations of a known field, analysed this way, turn out to need, and the honest statement is that this method is calibrated rather than derived.

A direction measured by something with no strength in it

An interstellar grain spins with its long axis across the magnetic field, so starlight through a cloud is polarised along the field and the cloud's own emission across it. The observable contains no field strength whatever — and the strength is recovered anyway, from how much the directions disagree.

galaxies · Dust polarisation

An electroweak field decays toward one line, and helicity decides where it meets it. The comoving strength of a magnetic field against its coherence length, both on logarithmic scales. A field made at the electroweak transition, at 100 GeV, starts on a hundredth of the Hubble length then (1 AU today) with a tenth of the radiation's energy density (1 × 10⁻⁶ G), and decays as its turbulence is processed until the largest eddy is the one an Alfvén wave can cross by recombination — the straight line, 10⁻⁸ G at 1 Mpc. With no net helicity it falls as λ^−5/2 and stops at 0.038 pc and 4 × 10⁻¹⁶ G. Maximally helical, it falls only as λ^−½ and stops at 4.7 kpc and 5 × 10⁻¹¹ G. The shaded floor is what the missing gamma-ray halos exclude: a field coherent over more than a megaparsec must exceed 9 × 10⁻¹⁷ G, and the bound rises as the inverse square root of the coherence length below the leptons' cooling length of 0.6 Mpc. The non-helical field ends 3.0 decades below it; the helical one 4.6 decades above it. Above 10⁻⁹ G at a megaparsec the microwave background excludes the field.

A twist that decides where the field ends

A magnetic field made in the first trillionth of a second starts strong and absurdly small, and its turbulence spends the next three hundred thousand years trading strength for size. How far it gets depends on one conserved quantity — how twisted its field lines are — and for a field made at the electroweak transition, that twist is the difference between failing the void bound by three decades and clearing it by five.

cosmology · Primordial fields

Named alongside it

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

Turbulence Accretion Alpha viscosity Angular momentum Blazar Coherence length Davis chandrasekhar fermi Dead zone Dust polarisation Extinction Grain alignment Interstellar dust

All concepts