Biting the dust

Sorry about the obvious pun in the title. Today's important announcement is of course the long-awaited Planck verdict on the level at which the BICEP2 "discovery" of primordial gravitational waves had been contaminated by foreground dust. That verdict does not look good for BICEP.

(Incidentally, back in July I reported a Planck source as saying this paper would be ready in "two or three weeks". Clearly that was far too optimistic. But interestingly many members of the Planck team themselves were confidently expecting today's paper to appear about 10 days ago, and the rumour is that the current version has been "toned down" a little, perhaps accounting for some of the additional delay. Despite that it's still pretty devastating.)

Let me attempt to summarize the new results. Some important points are made right in the abstract, where we read:

"... even in the faintest dust-emitting regions there are no "clean" windows in the sky where primordial CMB B-mode polarization measurements could be made without subtraction of foreground emission"

and that

"This level [of the dust power in the BICEP2 window, over the multipole range of the primordial recombination bump] is the same magnitude as reported by BICEP2 ..."

(my emphasis). Although

"the present uncertainties are large and will be reduced through an ongoing, joint analysis of the Planck and BICEP2 data sets,"

from where I am looking unfortunately it now does not look as if there is a realistic chance that what BICEP2 reported was anything more than a very precise measurement of dust.

The Planck paper is pretty thorough, and actually quite interesting in its own right. They make use of the fact that Planck observes the sky at many frequencies to study the properties of dust-induced polarization. Whereas BICEP2 was limited to a single frequency channel at 150 GHz, the Planck HFI instrument has 4 different frequencies, of which the most useful is at 353 GHz. Previous Planck results have already shown that dust emission behaves sort of like a (modified) blackbody spectrum at a temperature of 19.6 Kelvin. Since this is a significantly higher temperature than the CMB temperature of 2.73 K, dust emission dominates at higher frequencies, which means that the 353 GHz channel essentially sees only dust and nothing else. Which makes it perfect for the task at hand, since in this particular situation roles are reversed and it is the dust that is the signal and the primordial CMB is noise!

The analysis proceeds in a number of steps. First, they study the power spectra of the two polarization modes (EE and BB) in several different large regions in the sky:

The different large sky regions studied are shown as increments of red, orange, yellow, green and two different shades of blue. The darkest blue region is always excluded. Figure from arXiv:1409.5738.

In all these different regions, both power spectra $C_\ell^{EE}$ and $C_\ell^{BB}$ are proportional to $\ell^{\alpha}$, consistent with a value of $\alpha=-2.42\pm0.02$. Fixing $\alpha$ to this value, the amplitude of the power spectra in the different large regions then shows a characteristic dependence on the mean intensity of the dust emission — i.e. regions with more dust overall also show more polarization power — and this purely empirical relationship is characterized by
$$A^{EE,BB}\propto\langle I_{353}\rangle^{1.9},$$though with a bit of uncertainty in the fit. The amplitudes of the polarization power spectra then also show a dependence on frequency from 353 GHz down to 100 GHz which matches previous Planck results (the dependence is something close to a blackbody spectrum at 19.6 K, but with a specific modification).

It then turns out that if the sky is split into very many much smaller regions close to the poles rather than the 6 large ones above, the same results continue to hold on average, though obviously there is some scatter introduced by the fact that dust in different bits of the sky behaves differently. So this allows the Planck team to take the measured dust intensity in any one of these smaller regions and extrapolate down to see what the contribution to the BB power would be if measured at the BICEP2 frequency of 150 GHz. The result looks like this:

The level of dust contamination across the in measurements of the primordial B-mode signal. Blue is good, red is bad. The BICEP2 window is the black outline on the right.

This really sucks for BICEP2, who chose their particular patch of the sky precisely because, according to estimates of the 1990s and early 2000s, it was supposed to have very little dust. Planck is now saying that isn't true, and that there is a better region just a little further south. Even that better region isn't perfect, of course, but it may be clean enough to see a primordial GW signal of $r\sim 0.1$ to $0.2$ — if such a signal exists, and if we're lucky and/or figure out cleverer ways of subtracting the dust foreground.

The problem with the BICEP2 region is that Planck's estimate of the dust contribution there looks like this:

Planck's estimate of the dust contribution to the BB power spectrum at 150 GHz and in the BICEP2 sky window. The first bin is the one that's most relevant. The black line is the contribution primordial GW with $r=0.2$ would make, if they existed.

So it appears that in the BICEP2 window, in the $\ell$ region where primordial gravitational waves produce a measurable BB signal (and BICEP2 has measured something), dust is expected to produce the same amplitude of signal as does an $r=0.2$. In fact, even accounting for the uncertainties in the Planck analysis (the extent of the pink error bars on the plot) it is clear that (a) dust will be contributing significantly to the BICEP2 measurement, and (b) it's pretty likely that only dust is contributing.

Planck avoid explicitly saying that BICEP2 haven't seen anything but dust. This is because they haven't directly measured the dust contribution in that window and at 150 GHz. Rather what's shown in the plot above is based on a number of little steps in the chain of inference:

1. generally, the BB polarization amplitude is dependent on the average total dust intensity in a region;
2. the relationship between these two doesn't vary too much across the sky;
3. generally, the frequency dependence of the amplitude shows a certain behaviour;
4. and again this doesn't appear to vary too much across the sky
5. Planck have measured the average dust intensity in the BICEP2 window, and this gives the value shown in the plot above when extrapolated to 150 GHz;
6. and the BICEP2 window doesn't appear to be a special outlier region on the sky that would wildly deviate from these average relationships;
7. so, the dust amplitude calculated is probably correct.

Update: See the correction in the comments — the Planck paper actually does better than this. That is to say, they present one analysis that relies on all steps 1-7, but in addition they also measure the BB amplitude directly at 353 GHz and extrapolate that down to 150 GHz relying only on steps 3 and 4. The headline result is the one based on the second method, which actually gets a lower number for the dust amplitude. 

So they leave open the small possibility that despite having been unlucky in the original choice of the BICEP2 window, we've somehow ultimately got very lucky indeed and nevertheless measured a true primordial gravitational wave signal. 

Time will tell if this is true ... but the sensible betting has now got to be that it is not.

Incidentally, I have just learned that in two days' time I will be presenting a 30 minute lecture to a group of graduate students about this result. The lecture is not supposed to be very detailed, but I'm also not very much of an expert on this. So if you spot any errors or omissions above, please do let me know through the comments box!