Astronomy & Celestial Mechanics
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Dust polarisation — the series

4 essays on one idea, from the one that introduces it to the one that assumes the rest.
  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
  2. Polarised dust, synchrotron and the signal between them. The amplitude of B-mode polarisation at angular multipole 80, in microkelvin of CMB temperature on a logarithmic scale, against frequency from 20 to 450 GHz, for a patch of sky as clean as the cleanest large field observed. Dust is a modified blackbody with emissivity index 1.53 at 19.6 K, normalised to 4.6 µK² at 353 GHz; synchrotron falls as frequency to the power −3.1 in antenna temperature, normalised to an illustrative 1 µK² at 23 GHz. The horizontal lines are a primordial signal with tensor-to-scalar ratio 0.01, about 0.048 µK, and the lensing B-modes, about 0.071 µK. The foregrounds together are faintest at 81 GHz, at 0.038 µK, 0.8 times the signal. At 150 GHz the dust alone is 0.105 µK, the amplitude a tensor ratio of 0.046 would produce; at 353 GHz it is 2.23 µK, 47 times the signal. No frequency has the signal above the foreground.

    A foreground drawn by the field it traces

    The grains that polarise starlight along the Galaxy's magnetic field glow, at millimetre wavelengths, with light polarised across it — and that glow is brighter than the primordial signal cosmologists are looking for at every frequency above eighty gigahertz and in every patch of sky. Its pattern on the sky is set by how loosely the interstellar filaments follow the field, and removing it rests on a bet that the clouds along each line of sight share one temperature.

    part 2 · galaxies
  3. A polarisation fraction that should change with frequency. The polarisation fraction of dust emission relative to its value at 353 GHz, against frequency on a logarithmic axis. A single population at a single temperature gives a fraction that does not change at all. If the carbon grains are unaligned and warmer than the silicates, they take a growing share of the emission toward high frequency and dilute the polarisation: at 1200 GHz the fraction falls to 0.90 of its 353 GHz value for a 3 K difference and 0.85 for 5 K. Half-aligned carbon halves the effect. The shaded band is flat to within ten per cent between 100 and 1200 GHz, the precision with which the satellite and balloon measurements across this range agree with no change.

    The grains that glow and the grains that align

    Interstellar dust polarises starlight and polarises its own glow, and for decades the standard account gave the two jobs to different grains — aligned silicates, unaligned carbon. Two populations at two temperatures predict a polarisation fraction that falls toward high frequency; what satellites and balloons measured was a fraction that does not change. That flatness, which no grain shape can fake, says the grains that glow are the grains that align.

    part 3 · galaxies
  4. How a cloud's glow loses its polarisation as it thickens. The polarisation fraction of dust emission against the column density through a cloud, both on logarithmic scales, for four clouds built from cells of 10²¹ hydrogen atoms per square centimetre, each polarising its glow by 20%. A single uniform field with every grain aligned keeps 20% at every column. A field tangled from cell to cell by 40 degrees about a mean direction loses polarisation at first and then levels off at 7.5%, the share its mean direction carries: between 10²² and 10²³ its slope is −0.05. A field with no mean direction at all adds its cells as a pure random walk and falls with a slope of −0.55. Grains that align only in the outer 3 × 10²¹ cm⁻² on each side, where starlight still reaches, contribute nothing from the interior, and the fraction falls with a slope of −1.00.

    A falling polarisation and the angle that says why

    The glow of dust in a molecular cloud is less polarised the thicker the cloud, almost everywhere it has been measured. Two explanations fit that fall equally well — a magnetic field tangled along the line of sight, or grains in the dark interior that have stopped lining up with it — and between them they can produce any slope a cloud has shown. What separates them is not how much polarisation is lost but whether the direction of what remains wanders.

    part 4 · galaxies

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