Astronomy & Celestial Mechanics
the sky, computed
Concept

Magnetic critical mass — where it appears

The largest mass a given magnetic flux can support against its own gravity, about 0.13 times the flux over the square root of the gravitational constant. Unlike a Jeans mass it cannot be exceeded by compression, because squeezing raises both energies equally.

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

One dimensionless number decides whether a cloud may collapse. Field strength against hydrogen column density, with three loci of constant mass-to-flux ratio. The ratio of mass to magnetic flux is conserved under flux freezing, so it cannot be changed by anything that happens during a collapse — which is what makes it a criterion rather than a description. Its critical value is the pure constant 1/(2π√G), and dividing by that gives the dimensionless λ drawn here: below λ = 1 the field can hold the cloud up for ever, however cold it gets, because gravity and the magnetic force scale the same way with radius; above it no field strength suffices. Each locus is a straight line of slope exactly one, because at fixed λ the required field is exactly proportional to the column. Zeeman measurements of dense cores put them a little above the line and their envelopes a little below it, which is the arrangement a slow leak of flux out of the centre would produce and is the observational case for ambipolar diffusion.

A threshold with no free parameter in it

Divide a cloud's mass by the magnetic flux threading it. Gravity and the magnetic force both fall as the inverse square of the radius, so the ratio cannot change during a collapse — and the critical value that separates a cloud which must collapse from one that never can is one over two pi root G, a pure constant.

stars · Star formation The one number a cloud cannot change by squeezing. The mass-to-flux ratio in units of its critical value, against column density, for clouds threaded by fields of 3, 10, 30, 100 microgauss. λ below one is subcritical, and the field alone holds the cloud up, and no amount of compression changes that, because squeezing raises the magnetic and the gravitational energy at the same rate and leaves their ratio exactly where it was. λ above one is supercritical and the field is irrelevant to whether the cloud collapses. Each line has slope exactly one because λ is proportional to the column density at fixed field, and each crosses the boundary at 3.9·10²⁰ cm⁻² for 3 µG, 1.3·10²¹ cm⁻² for 10 µG, 3.9·10²¹ cm⁻² for 30 µG, 1.3·10²² cm⁻² for 100 µG. The Jeans mass is a threshold a cloud can cross by contracting; this one is a label it is born with, and the only way past it is to let the field leak out.

Support that cannot be squeezed away

A cloud held up by pressure can always be defeated by compressing it, because gravity gains faster than heat does. A cloud held up by a magnetic field cannot — squeezing raises both energies at exactly the same rate, so the ratio a cloud is born with is the one it keeps, and the only way out is to let the field leak.

galaxies · Molecular clouds

Named alongside it

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

Ambipolar diffusionFlux freezingJeans massMass-to-flux ratioZeeman effectCore-collapseCosmic-ray ionisationFree-fall timeIonisation fractionMolecular cloudMolecular cloudsStar formation

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