Astronomy & Celestial Mechanics
the sky, computed
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Dust polarisation — the series

One essay so far on this idea, and more questions about it than one essay answers.
  1. 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.

    part 1 · galaxies

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