Dust makes everything look further away

The space between the stars is not empty, and the part of it that matters here is a very small part by mass: about one per cent of the interstellar medium, in grains a fraction of a micron across. That one per cent absorbs and scatters starlight, and for a century after photometry became quantitative it was assumed not to exist.

The assumption was catastrophic and the reason it survived is that it fails quietly. Dust does not blur an image or leave an obvious signature. It makes a star fainter, and a star that is fainter than it should be is indistinguishable from a star that is further away.

The error is a factor, not a fraction #

Extinction enters where a distance is taken from a brightness. The distance modulus relates apparent magnitude, absolute magnitude and distance:

$$m - M = 5\log_{10} d - 5 + A,$$

with $A$ the extinction in magnitudes along that sight line. Ignore $A$ and the inferred distance is too large by a factor of $10^{A/5}$.

That is a factor of 1.58 for one magnitude, 2.5 for two, 6.3 for four. It is not a small correction that averages out, because it is one-signed: dust never makes a star brighter.

The measurement that established it #

Robert Trumpler’s 1930 paper is the standing example of how to detect a systematic that has no direct signature, and the method is worth spelling out because it uses nothing but a comparison of two distances that ought to agree.

He had a catalogue of open star clusters. For each he could estimate a distance in two independent ways.

The first was photometric: identify the main sequence, use the apparent magnitudes of its stars against their known absolute magnitudes, and read off the modulus. The second was geometric: measure the cluster’s angular diameter, and — assuming clusters are all roughly the same physical size — convert that into a distance.

The two disagreed, and they disagreed systematically. Taking the photometric distances at face value made the more distant clusters come out physically larger, with the linear diameter growing steadily with distance. There is no plausible reason for a cluster’s size to depend on how far away from the Sun it happens to be. What there is a plausible reason for is a photometric distance that is too large by an amount that grows with distance — which is exactly the shape of the curve above.

Trumpler concluded that light is absorbed in the plane of the Milky Way at about 0.7 magnitudes per kiloparsec in the photographic band, and the modern value along a typical low-latitude sight line is of the same order. The evidence was a correlation between two quantities neither of which was the dust. The cost of the omission before Trumpler was the shape of the galaxy. Kapteyn’s model of 1922, built from star counts, put the Sun near the centre of a stellar system some ten kiloparsecs across — because in every direction along the plane the counts fell off, and the falling-off was read as an edge rather than as absorption. Shapley’s globular-cluster distances gave a much larger system with the Sun far from the middle, and Shapley happened to be right partly because globular clusters are at high galactic latitude where there is far less dust in the way.

Reddening, which is the same thing and is measurable #

The reason extinction is correctable at all is that it is not grey. Blue light is removed more than red, so the light that gets through is reddened, and reddening can be detected without knowing anything about distance.

The observable is the colour excess. A star’s intrinsic colour is known from its spectral type — the spectrum classifies it, and the classification fixes what its unreddened $B-V$ should be. The difference between the observed and intrinsic colours is $E(B-V) = (B-V)_{\rm obs} - (B-V)_0$, and it is a property of the dust alone.

Converting that to the quantity actually needed, the extinction in the $V$ band, requires the ratio of total to selective extinction:

$$R_V = \frac{A_V}{E(B-V)} \approx 3.1.$$

The number 3.1 is an average, and treating it as a constant is the largest routine approximation in the subject. In dense molecular clouds, where grains grow by accreting mantles, $R_V$ reaches 5 or more; in some diffuse sight lines it falls to 2.5. Since $A_V = R_V E(B-V)$, an error of 0.5 in $R_V$ at a colour excess of 1 is half a magnitude of extinction, which is 26 per cent in distance.

The intrinsic colour has to come from somewhere #

Everything above rests on knowing what colour the star would have been, and that is a second inference rather than an observation.

That is the practical chain and it is worth stating as a chain, because each link is a separate assumption: a spectrum gives a spectral type; a type gives an intrinsic colour from a calibration built on nearby, unreddened stars; the observed colour minus the intrinsic colour gives $E(B-V)$; $E(B-V)$ times an assumed $R_V$ gives $A_V$; and $A_V$ enters the distance modulus. Five steps, each with its own uncertainty, to correct one number.

Where a spectrum is unavailable — a faint star in a survey of a hundred million — the modern substitute is a three-dimensional dust map. Gaia’s parallaxes give distances geometrically for stars within a few kiloparsecs, and combining those with infrared photometry from 2MASS and optical photometry from large surveys lets the reddening be solved for as a function of position and distance. The resulting maps have a resolution of a few arcminutes and are now the standard input, and their existence is the reason extinction has stopped being the dominant error in local astronomy.

The correction that decides the Hubble constant #

The single most consequential extinction correction anywhere is the one applied to Cepheids, and the technique used to make it is worth knowing because it is the only place in this essay where the problem is solved rather than estimated.

The solution is an index rather than a correction. Define a magnitude that combines a brightness and a colour in the proportion the reddening vector has:

$$W = V - R_V\,(B-V).$$

Redden a star and $V$ increases by $A_V$ while $(B-V)$ increases by $A_V/R_V$, so the two terms change by the same amount and $W$ does not change at all. This is the Wesenheit index, and it is reddening-free by construction: it is the projection of the colour–magnitude plane along the reddening vector, which is precisely the direction that carries no information.

That is why period–luminosity relations are quoted in Wesenheit magnitudes in every modern determination of the distance scale, usually in the near-infrared where the extinction is small to begin with. The price is that it is only free of reddening if $R_V$ is what was assumed — the construction cancels the extinction in the direction it was told to, and a sight line with a different $R_V$ leaks through in proportion to the error.

That residual leak is not academic. The disagreement between the two determinations of the Hubble constant is about eight per cent, and the extinction corrections applied to the Cepheids that anchor the local value are of order a magnitude in the visual band. Getting $R_V$ wrong by 10 per cent in the host galaxies would move the answer by a few per cent — not enough to explain the discrepancy, and not so far below it that it can be ignored either. Every serious analysis of that disagreement contains a section about dust.

Where the dust wins outright #

Toward the Galactic centre the visual extinction is about 30 magnitudes. That is a factor of $10^{12}$: of every trillion photons leaving a star at the centre in the visual band, one arrives.

Nothing survives that. The centre of the galaxy was not seen in visible light at all until it was seen in the infrared, where the extinction curve has fallen to a few tenths of its visual value — $A_K$ is about 3 magnitudes rather than 30, a factor of $10^{11}$ better. Every image of the stars orbiting Sagittarius A*, and the orbits from which the central mass is weighed, is infrared for exactly this reason. The choice of wavelength there is not a preference; it is the difference between a measurement and nothing.

Two screens, and only one of them is mapped #

Every correction described so far treats the dust as a screen: a layer of absorbing material between the observer and a point source, so that the light is attenuated by a single factor. For a star in this galaxy seen through a foreground cloud that is approximately right, and it is why the whole apparatus works.

For anything extragalactic there are two screens, and they are not alike.

The first is the Milky Way’s own dust, which really is a foreground. It is well mapped, the maps are calibrated against infrared emission, and for a high-latitude sight line the correction is small and reliable.

The second is the dust inside the host galaxy, and it is not a screen at all. The stars being observed are inside the dust rather than behind it: some sit in front of most of it, some behind, and the ones in the dustiest regions are the ones least likely to be seen. What is measured is therefore an average over a population weighted by which members got through, and the effective law relating attenuation to wavelength is not the extinction law of the grains.

The difference has a direction. Because the least obscured sources dominate the light, the observed attenuation is flatter — greyer — than the underlying extinction curve, and the flattening depends on the geometry rather than on the grains. Two galaxies with identical dust can show different attenuation laws if their stars and dust are arranged differently.

That is why the literature distinguishes an extinction curve, measured toward a single star and a property of the material, from an attenuation law, measured for a whole galaxy and a property of the material and its arrangement together. Applying one where the other is required is a routine error, and it biases in the direction of underestimating how much light was lost.

A correction derived for a point source behind a screen does not transfer to a source embedded in what is absorbing it, and the second case is the one every measurement of a distant galaxy is in.

Where the grains come from, and the budget that will not balance #

Dust is manufactured, destroyed and re-formed, and the accounting is worth stating because it does not close.

The recognised factories are the cool extended envelopes of evolved stars, where the gas is dense enough and cool enough for solids to condense out, and the ejecta of supernovae, where the same happens in the expanding debris. Both have been observed directly — the envelopes as infrared sources far brighter than the stars inside them, the supernova dust in the remnants of nearby explosions.

The recognised destruction mechanism is shocks. A supernova blast wave sweeping through the interstellar medium sputters grains away in the hot gas behind it, and since a given parcel of interstellar material is swept by such a shock every hundred million years or so, the destruction timescale is short.

The trouble is that the destruction timescale comes out shorter than the production timescale, by a factor of several. If the only sources were stellar, the galaxy should contain far less dust than it does.

The standard resolution is that most of the mass in grains was not made in a star at all but accreted onto existing grains in cold dense clouds, where atoms stick to whatever surface they meet. The stellar sources then supply the seeds and the interstellar medium supplies the bulk, which also explains why grains are larger in dense regions — the observation that shows up in this essay as a larger ratio of total to selective extinction.

A discrepancy in a budget is evidence about a process nobody observed, and here it is the main argument that grains grow where they cannot be watched growing.

The one place the dust is the signal #

Everything so far treats the dust as an obstruction, which is how an optical astronomer meets it. Turn the wavelength up and the same grains become the brightest thing in the sky.

Energy is conserved: what the grains absorb, they re-radiate. A grain in the general interstellar radiation field sits at 15 to 20 kelvin, and a blackbody at that temperature peaks near 200 microns. So the far-infrared and submillimetre sky is a map of exactly the material that ruins optical photometry, seen in emission rather than in absorption — and because emission is proportional to column density in the same way absorption is, the two measurements can be checked against each other.

That cross-check is the basis of the reddening maps in general use, which are built from infrared emission and calibrated into optical extinction. It is a satisfying arrangement: the quantity that cannot be measured directly where it matters is measured at a wavelength where it is the only thing there.

What the picture cannot show #

Grey extinction. The whole correction machinery works because extinction is selective. A population of grains large compared with optical wavelengths would remove light without reddening it, and there is no photometric test that would reveal it. It cannot be excluded and it is not thought to be large, and the reason it is worth naming is that the supernova cosmology that found the expansion accelerating rests on distant objects being 0.25 magnitudes fainter than expected — which grey dust at high redshift would also produce. The argument against it is indirect: grey dust in the right quantity would also distort the microwave background’s spectrum, and it does not.

The two-dimensional map. The classic maps of galactic reddening give the total extinction through the whole galaxy in a given direction, which is the right quantity for an extragalactic object and the wrong one for a star inside the disc. Using a total-column map for a nearby star over-corrects it, sometimes by a large factor, and the error is worst exactly where the dust is thickest. This is a mistake that still appears in the literature, and the three-dimensional maps exist to make it avoidable rather than because anybody wanted more parameters.

Patchiness. Extinction is drawn here as a smooth function of distance and it is nothing of the kind. It is clumpy on every scale down to arcseconds, so two stars a few arcminutes apart can differ by a magnitude, and a map’s resolution sets a floor on how well any individual star can be corrected.

And the curve is a fit. Every figure here uses a published parameterisation of observed extinction, indexed by one number. It is not derived from grain physics — the sizes, shapes and compositions that produce it are inferred from it, and the 2,175 Å bump has been attributed to graphite, to polycyclic aromatic hydrocarbons and to several other carriers over fifty years without resolution. The correction is empirical, and it is applied to nearly every photometric measurement ever made.

And it cannot show what a magnitude of extinction means for a survey. A limiting magnitude defines a volume, and dimming everything by one magnitude shrinks the volume surveyed by a factor of four. So extinction does not merely displace the objects that are seen; it removes objects from the sample entirely, and removes them preferentially from the directions where the dust is. Every star count in the plane of the galaxy is a count through a filter whose transmission varies from place to place, and correcting a distance is a much easier problem than correcting a census.

The two halves of the correction — how much light is lost and how the loss depends on colour — are each worth reading at a second value.

Where the ladder goes next #

The rung above is polarisation: the same grains, if they are elongated and aligned by the galactic magnetic field, extinguish one direction of vibration more than the other, so the reddening comes with a small linear polarisation — which turns a nuisance into a map of the magnetic field. The rung beside it is emission: the energy the grains absorb has to go somewhere, and it comes back out in the far infrared, so the same dust that hides the galaxy is what the galaxy looks brightest in at 100 microns.