Astronomy & Celestial Mechanics
the sky, computed
Galaxies

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.

Assumes Dust polarisation, Polarimetry and Extinction.

16 min read 5 figures Light is the only messengerMeasuring the unreachableSmall perturbations, large consequences

Interstellar dust does two things with the Galaxy’s magnetic field, and they are measured with completely different instruments. It polarises starlight passing through it, which is measured with optical polarimeters on telescopes pointed at individual stars. And it polarises its own thermal emission at submillimetre wavelengths, which is measured by satellites and balloons mapping the whole sky. The direction in each case is set by the field — starlight is polarised along it, the dust’s glow across it — and that much has been understood since the 1950s.

What has not been settled for nearly as long is which grains do the work. Interstellar dust is a mixture: silicate grains, made of the rock-forming elements, and carbonaceous grains, made of carbon in various forms. Both absorb starlight, both are heated by it, and both glow. Whether both are aligned with the field — and therefore both polarise — was, for a long time, answered “no”. The standard models of the 2000s aligned the silicates and left the carbon grains spinning at random, because the evidence of the time suggested that carbon grains, which are often thought to be more nearly spherical or less paramagnetic, would align poorly.

That answer makes a prediction, and the prediction has been tested.

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.
Fig. 1 The polarisation fraction of dust emission relative to its value at 353 GHz, against frequency. One population at one temperature gives a fraction that does not change. If the carbon grains are unaligned and a few kelvin warmer than the silicates, they take a growing share of the emission toward high frequency and dilute the polarisation, so the fraction falls — to 0.90 of its 353 GHz value at 1200 GHz for a 3 K difference, to 0.85 for 5 K. The shaded band is flat to ten per cent from 100 to 1200 GHz, the agreement the satellite and balloon measurements across this range show with no change.

Starlight polarised along the field

The extinction side of the story is older and comes first. Starlight passing through a dusty cloud is dimmed and reddened, and if the grains in the cloud are elongated and aligned, it is dimmed more for light whose electric field lies along the grains’ long axes than across them. The grains align with their long axes across the magnetic field, so the light that survives is polarised along the field.

A peak at 0.55 µm, and therefore a grain size. Interstellar polarisation against wavelength — the Serkowski law, p(λ) = p_max exp[−K ln²(λ_max/λ)] with K = 1.66 λ_max. The heavy curve peaks at 0.550 µm, measured off the drawing rather than read back from the parameter, and falls to half its peak at 1.314 µm on the red side, against the closed form λ_max exp√(ln2/K) = 1.315. That peak wavelength is the measurement. It is set by the size of the grains doing the aligning — bigger grains, longer λ_max — and it is tied to the shape of the extinction curve along the same sight line by R_V ≈ 5.5 λ_max, which gives 3.03 here against the diffuse-medium value of 3.1. The two faint curves are populations peaking at 0.35 µm and 0.75 µm: the same amount of polarisation, distributed differently, and a different dust. Nothing in a photometric measurement of the same star distinguishes them.
Fig. 2 The wavelength dependence of interstellar polarisation in extinction — the Serkowski curve — peaking near half a micron and falling on both sides. The peak sits where the wavelength is comparable to the size of the aligned grains, so its position measures their size, and its height per unit of reddening measures how well they are aligned. The maximum measured in the clearest sight lines is about thirteen per cent per magnitude of reddening.

The curve’s shape says something about which grains polarise. Its peak near half a micron means the aligned grains are those of a tenth of a micron or so in radius — the larger grains of the size distribution. Very small grains, a few nanometres across, contribute to extinction in the ultraviolet but not to polarisation, which falls toward short wavelengths. That alone shows that not all grains are aligned. It does not say which materials the aligned ones are made of, because silicate and carbon grains of the same size and shape would produce nearly the same curve.

Silicate leaves a fingerprint, and carbon does not. The silicate grains have a strong absorption band near ten microns, and that band is polarised in sight lines toward embedded infrared sources: the silicates are aligned. The carbonaceous grains have a weaker feature near three and a half microns, and searches for polarisation in it have found none, to limits of a few times less than the silicate band’s. That was the evidence for aligned silicates and unaligned carbon. It is genuinely evidence, but it is limited: the three-and-a-half-micron feature arises in only some forms of carbon, and its absence of polarisation does not say that the carbon in other forms is unaligned.

The glow, at two temperatures

The emission side is newer. Interstellar grains heated by the starlight of the Galaxy reach equilibrium temperatures of fifteen to twenty-five kelvin and radiate at far-infrared and submillimetre wavelengths. The emission of each grain is its absorption efficiency at those wavelengths times a blackbody at its temperature, which gives each population a modified blackbody spectrum.

A grain’s temperature depends on what it is made of. Carbonaceous grains absorb visible and ultraviolet starlight more strongly per unit mass than silicates, and they radiate at long wavelengths with comparable efficiency, so under the same starlight they come to equilibrium a few kelvin warmer. Two populations of grains that share a cloud therefore glow with two slightly different spectra.

Two dusts that glow at slightly different temperatures. The far-infrared and millimetre emission of interstellar dust modelled as two populations — silicate grains at 17.5 K (aligned with the field) and carbonaceous grains at 20.5 K (not aligned) — each a blackbody modified by an emissivity rising as frequency to the 1.6, normalised to the total at 353 GHz on logarithmic axes. Carbon supplies 35 per cent of the emission at 353 GHz and, being warmer, 59 per cent at 3000 GHz. The two curves are nearly parallel across the microwave bands and separate toward the peak, which is where a difference in temperature shows.
Fig. 3 The dust emission modelled as two populations — silicates at 17.5 K, aligned with the field, and carbonaceous grains at 20.5 K, not aligned — each a blackbody modified by an emissivity rising as frequency to the 1.6, normalised to the total at 353 GHz. Carbon supplies 35 per cent of the emission at 353 GHz and, being warmer, 59 per cent at 3000 GHz. The curves are nearly parallel at microwave frequencies and separate toward the peak, which is where a difference in temperature shows.

That is the mechanism behind the first figure. If only the silicates are aligned, only their emission is polarised, and the polarisation fraction of the total is the silicate fraction of the total times the silicates’ own polarisation. As the frequency rises toward the emission peak, the warmer carbon supplies a growing share of the light, the silicate share falls, and the polarisation fraction falls with it. A three-kelvin difference costs ten per cent of the fraction between 353 and 1200 gigahertz; a five-kelvin difference costs fifteen.

One population cannot do that. If silicate and carbon are mixed in the same grains, at the same temperature and the same alignment, then every photon emitted comes from an aligned grain with the same efficiency, and the polarisation fraction is the same at every frequency. A flat fraction across the whole emission spectrum is therefore the signature of one population.

A thermometer that cannot read one grain

The argument depends on dust temperatures, so it is worth asking how a dust temperature is measured at all, since no one has ever put a thermometer in contact with an interstellar grain.

It is read from the spectrum. A modified blackbody has three parameters — an amplitude, a temperature and an emissivity index — and fitting them to the emission measured at several frequencies gives all three. The same logic reads a star’s temperature from its colour, with the important difference that a star’s spectrum is close to a true blackbody and a cloud’s is not. The emissivity index tilts the spectrum in nearly the same way a change of temperature does over a limited range of frequencies, so the two are anti-correlated in any fit: a slightly cooler cloud with a steeper emissivity looks almost the same as a warmer one with a shallower emissivity. The degeneracy is broken only by measuring on both sides of the emission peak, which for dust at twenty kelvin lies near two thousand gigahertz, about a hundred and fifty microns.

The temperature is also an energy balance, and that gives a check. A grain’s temperature is set by how much starlight it absorbs against how efficiently it radiates, and the energy it radiates in the far infrared is exactly the energy taken out of the starlight in the ultraviolet and visible. Compare the dust emission integrated over frequency with the extinction toward stars behind the same cloud and the absorbed and radiated energies must agree. That comparison is what weighs the dust that reddening cannot see, and its success for the total emission is part of the evidence that the same grains dominate both.

For two populations there are two temperatures in every sight line, and a fit of a single modified blackbody to their sum returns a temperature between the two and an emissivity index that is shallower than either, because the sum is broader than each. A difference of a few kelvin between silicate and carbon grains would show up as a small excess of emission on the high-frequency side — one more place for the second population to hide. The polarisation fraction is a cleaner test because it compares the polarised spectrum with the total spectrum directly: two populations at two temperatures cannot make them agree at every frequency, however their parameters are chosen.

How flat it is

The Planck satellite measured the polarised and total dust emission across the whole sky at frequencies from 100 to 353 gigahertz, and found the two spectra almost identical: fitted with modified blackbodies, the polarised emission has an emissivity index of about 1.53 and the total about 1.48, with temperatures that agree. The polarisation fraction varies with frequency, over that range, by no more than a few per cent.

The balloon-borne polarimeter BLASTPol measured molecular clouds at 250, 350 and 500 microns — 1200, 860 and 600 gigahertz — on the rising side of the emission peak, where a temperature difference between populations would show most strongly. It found the polarisation fraction nearly the same at all three wavelengths, to about ten per cent.

How much warmer the unaligned grains may be. The polarisation fraction at 1200 GHz relative to 353 GHz against how much warmer the unaligned carbon grains are than the aligned silicates, for carbon supplying 20, 35, 50 per cent of the 353 GHz emission. A drop of more than ten per cent (below the dashed line) is excluded by the measured flatness. The allowed temperature difference is about 5.8, 3.2, 2.2 K respectively. Grains of different materials heated by the same starlight equilibrate at temperatures set by how they absorb and emit, and two-population models typically make the carbon a few kelvin warmer — at or beyond these limits.
Fig. 4 The polarisation fraction at 1200 GHz relative to 353 GHz against how much warmer the unaligned carbon grains are than the aligned silicates, for carbon supplying 20, 35 and 50 per cent of the 353 GHz emission. A drop of more than ten per cent (below the dashed line) is excluded by the measured flatness. The allowed temperature difference is about 6, 3 and 2 kelvin respectively — and two-population models typically make the carbon a few kelvin warmer, at or beyond these limits.

The constraint is not absolute, and it is worth stating what it allows. The carbon could be unaligned if it supplies a small share of the emission and is only slightly warmer. It could be partly aligned. Or the two measurements, made in different regions of the sky — Planck’s at high Galactic latitude, BLASTPol’s toward dense clouds — could each be flat for different reasons. But the simplest reading is the one recent dust models adopted: a single dominant population of grains in which silicate and carbonaceous material are mixed, aligned together, and heated to one temperature. Brandon Hensley and Bruce Draine called it astrodust.

A ratio that measures two things at once

The emission and extinction measurements can be combined in a second way, and this one was historically the first warning that the two-population models had something wrong.

Along sight lines to stars behind diffuse clouds, Planck measured the polarised submillimetre emission of the clouds, and optical polarimeters measured the polarisation of the starlight passing through them. The ratio of the two — polarised emission per unit of starlight polarisation — came out at about 5.4 megajanskys per steradian, and the ratio of the two polarisation fractions, emission over extinction, at about 4.3. Those numbers depend on how efficiently aligned grains polarise in emission compared with how efficiently they polarise in extinction, and the two-population models of the time predicted ratios well below what was measured.

What composition can do to the emission-to-extinction ratio. How much the ratio of polarisation in emission to polarisation in extinction changes, relative to a population in which every grain is aligned, against the share of the visual extinction carried by the carbon grains, for carbon unaligned, half-aligned and fully aligned, with carbon supplying 35 per cent of the submillimetre emission. Unaligned carbon dilutes the emitted polarisation by its share of the emission and the starlight polarisation by its share of the extinction, and the ratio moves by the quotient of the two — up to a factor of 2.2 when carbon carries most of the extinction, not at all when its two shares are equal, and below one when it carries less extinction than emission. The grains' elongation moves the same ratio by comparable factors, so a measured ratio constrains a combination of shape and composition and settles neither; the change of the polarisation fraction with frequency, which shape does not affect, is what separates them.
Fig. 5 How much the emission-to-extinction polarisation ratio changes, relative to a population in which every grain is aligned, against the share of the visual extinction carried by the carbon grains — for carbon unaligned, half-aligned and fully aligned, with carbon supplying 35 per cent of the submillimetre emission. Unaligned carbon dilutes the emitted polarisation by its share of the emission and the starlight polarisation by its share of the extinction, so the ratio moves by their quotient: up to a factor of two when carbon carries most of the extinction, not at all when its two shares are equal. Elongation moves the same ratio by comparable factors.

The figure shows why that ratio, on its own, could not settle the question. Composition moves it, through the difference between the unaligned material’s share of the extinction and its share of the emission. Grain shape moves it too: a more elongated grain polarises more strongly in emission relative to extinction than a less elongated one, by factors that depend on how the elongation and the optical properties combine at each wavelength. A measured ratio is therefore one equation in at least two unknowns. The models that fitted it after the measurement did so by adjusting shape — making the grains more elongated — and by adjusting their optical properties at long wavelengths, and both adjustments were allowed.

The frequency dependence of the fraction is different in kind. A grain’s shape does not change with frequency, so shape cannot make the polarisation fraction rise or fall across the emission spectrum. Only a mixture of populations with different temperatures and different alignments can. The flat fraction is the measurement that separates composition from shape, which is why it was decisive where the ratio was not.

The surprising consequence for the extinction curve

If the carbon is in the same grains as the silicates, the carbon participates in polarising starlight as well as in emitting polarised light. That has a consequence for the extinction side that had not been anticipated.

The interstellar extinction curve has a strong bump near 2175 ångströms, attributed to small carbonaceous grains — graphite or polycyclic aromatic material a few nanometres across. If the carbon in the large grains were the same material as in the small ones, and the large grains were aligned, the bump might be expected to appear in polarisation too. In almost all sight lines it does not. That is consistent with astrodust only if the carbon responsible for the bump is in the small grains, which are not aligned, while the carbon in the large, aligned grains is in a different form that produces no bump. The single-population picture is thus a picture of two size ranges: large composite grains, aligned and polarising, and very small carbonaceous grains, unaligned, producing the ultraviolet bump and the mid-infrared emission features.

That is not the same as the old two-population picture. The division is by size, not by material, and the large grains — which dominate the mass and the submillimetre emission — are one population.

What alignment requires

None of this says why the grains align, and the answer matters for whether the single population is plausible.

The leading explanation is radiative torques. An irregular grain illuminated by an anisotropic radiation field is spun up by the radiation — irregular shapes scatter left- and right-handed light differently — and the spinning grain, if it has any magnetic susceptibility at all, precesses around the field and settles with its long axis perpendicular to it. The mechanism requires that the grain be larger than about a tenth of the wavelength of the illuminating light, which is why large grains align and small ones do not, and it requires that the radiation field be anisotropic, which is why alignment fails deep inside dense clouds where the starlight has been absorbed.

Radiative-torque alignment does not care much what a grain is made of. Its efficiency depends on the grain’s size, shape and irregularity, and only weakly on its composition. A composite grain of silicate and carbon would be aligned about as well as a pure silicate one of the same size. The older argument for unaligned carbon was partly that carbon grains would be poorly aligned by the paramagnetic relaxation mechanism that was once thought responsible; if alignment is radiative, that argument loses most of its force, and a single aligned population becomes the expected outcome rather than a surprise.

What the measurements cannot see

The polarisation fraction is a ratio along a sight line. Every measurement averages over all the dust along the line, with whatever variation in field direction and alignment it contains. A fraction that is flat with frequency is flat for the sum; two populations that differ in temperature from cloud to cloud could average to a nearly flat sum if the differences were arranged in particular ways. The argument rests on the simplest arrangement being the true one.

The far-infrared emission at higher frequencies is less well measured. The decisive range for a temperature difference is near and above the emission peak, around 2000 to 3000 gigahertz, and polarimetry there has been done only for bright, dense regions. The diffuse interstellar medium, where Planck measured, has not been mapped in polarisation above 353 gigahertz.

The emission-to-extinction comparison uses a few hundred stars. Each star gives one point, and the sight lines are selected to have little dust beyond the star — so the comparison is made in diffuse, high-latitude gas, which may not represent the dust in the Galactic plane or in dense clouds.

The figures here are a sketch. The two-population model uses one temperature per population, one emissivity index for both, and a polarisation fraction for each that does not depend on frequency. Real grains have size distributions with a range of temperatures, and their polarised emissivity can vary with frequency for reasons of optics alone. The temperature limits read from the third figure are illustrative of the size of the effect rather than a fit to any particular measurement.

One population, one temperature, one field

The shift from two dust populations to one has practical consequences for the measurement that motivates much of this work: the search for primordial gravitational waves in the polarisation of the microwave background, against a foreground of polarised dust emission that is brighter than the signal everywhere above about eighty gigahertz.

The foreground must be measured at high frequencies, where it dominates, and extrapolated to the frequencies where the signal is sought. The extrapolation uses the dust’s polarised spectrum. If the polarised and total spectra differ — as they would with two populations — the extrapolation needs separate parameters for each, more degrees of freedom, and larger errors after subtraction. If they are the same, the polarised spectrum is the total spectrum, which is measured with much greater precision, and the extrapolation inherits that precision. The flatness of the polarisation fraction is, in that sense, a gift to the cosmologists: it removes a whole dimension of uncertainty from the foreground model.

It does not remove all of it. The temperature of the dust varies along each line of sight, from cloud to cloud, and a sum of modified blackbodies at different temperatures is not a single modified blackbody. That decorrelation — the dust’s spectrum differing slightly between directions and between frequencies — is now the limiting uncertainty in the foreground, and it is the subject that the next generation of high-frequency polarisation maps is designed to measure.

A measurement that compared two telescopes

The deeper lesson of the argument is about method. For decades the question “which grains are aligned” was approached from one side at a time — the shape of the optical polarisation curve, the polarisation of a single infrared absorption band, the polarisation of the submillimetre emission — and each side gave an answer consistent with the assumptions of its era. The decisive evidence came from comparing the two sides: emission against extinction along the same sight lines, and the emission’s polarisation across frequencies that sample different parts of the population’s temperature distribution.

Both comparisons needed instruments built for other purposes. Planck was designed to measure the microwave background; its dust maps were the foreground it had to remove. The optical polarimetry of the stars came from surveys designed to map the field’s direction. The instrumental polarisation of each, calibrated for its own purpose, set the precision with which the comparison could be made.

Still open: whether the large grains are one population everywhere

The flatness of the polarisation fraction is measured best in the diffuse, high-latitude interstellar medium and in a few bright clouds. Whether the same holds in the Galactic plane, in dense molecular cores where grains grow by accreting ice mantles and coagulating, and in other galaxies is not known. In dense cores alignment is expected to weaken as the starlight that drives it is absorbed — the polarisation fraction falls with column density in most clouds — and whether it weakens equally for every grain or selectively for some is the next test of the single-population picture.

The decisive measurements are polarimetry near the emission peak, at a hundred to three hundred microns, of diffuse regions as well as dense ones, and polarimetry of the carbon absorption features at higher sensitivity than before. Both are planned for instruments on the next generation of balloons and proposed far-infrared space missions. If the fraction stays flat wherever it is measured, the grains that glow are the grains that align, and the interstellar medium’s large dust is a single substance that the Galaxy’s field orders everywhere it can reach.

Where this goes next

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. 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. How much light a fixed mass of dust scatters, as its largest grains grow. The scattering cross-section per unit mass of dust, on a logarithmic scale relative to the largest value drawn, against the size of the largest grains in a power-law distribution n(a) ∝ a^−3.5 from 0.005 µm, at wavelengths of 1.25, 2.2, 3.6 µm. With the largest grains at a quarter of a micron — the size the interstellar extinction curve implies — the dust scatters 3.6 µm light 33 times less efficiently than it does once they reach a micron: grains much smaller than the wavelength scatter as the fourth power of their size over the wavelength and are all but invisible. At 3.6 µm the scattering per mass peaks when the largest grains are 3.5 µm, and falls beyond, as the mass moves into grains too large to scatter efficiently per gram. A dense core that glows at 3.6 µm in scattered starlight is therefore a core whose grains have grown to a micron or more. A glow that weighs the grains reddening cannot see The interstellar extinction curve reads the sizes of dust grains from how much more they dim blue light than red, and it goes blind at the top end: grains larger than about a micron dim every visible colour alike. Those are the grains that hold most of the mass, and the ones from which planets begin. Dense cloud cores glowing faintly at 3.6 microns in scattered starlight are the first direct sign of them — because only grains grown to a micron or more scatter that light at all.

The objects this essay names

Each one links to every other essay that touches it.

AstrodustDust polarisationExtinctionGrain alignmentInterstellar dustModified blackbodyPolarisation fractionRadiative torqueSerkowski law