Tuesday, August 26, 2014

The Cold Spot is not particularly cold

(and it probably isn't explained by a supervoid; although it is still anomalous)

In the cosmic microwave background (CMB) there is a thing that cosmologists call "The Cold Spot". However, I'm going to try to argue that its name is perhaps a little, well, wrong. This is because it isn't actually very cold. Although, it is definitely notably spotty.

That's the cold spot. It even has its own Wikipedia page (which really does need updated).

Why care about a cold spot?

This spot has become a thing to cosmologists because it appears to be somewhat anomalous. What this means is that a spot just like this has a very low probability of occurring in a universe where the standard cosmological model is correct. Just how anomalous it is and how interesting we should find it is a subject for debate and not something I'll go into much today. There are a number of anomalies in the CMB, but there is also a lot of statistical information in the CMB, so freak events are expected to occur if you look at the data in enough different ways. This means that the anomalies could be honest-to-God signs of wonderful new physical effects, or they could just be statistical flukes. Determining which is true is very difficult because of how hard it is to quantify how many ways in which the entire cosmology community have examined their data.

However, if the anomalies are signs of new physics, then we should expect two things to happen. Firstly, some candidate for the new physics should come up, which can create the observed effect and produce all of the much greater number of other measurements that fit the standard cosmological model well. If this happens, then we would look for additional ways in which the universe described by this new model differs from the standard one, and look for those effects. Secondly, as we take more data, we would expect the unlikeliness of the anomaly to increase. that is, it should become more and more anomalous.

In this entry, I'm not going to be making any judgement on whether the cold spot is a statistical fluke or evidence of new physics. What I want to do is explain why, although it still is anomalous, and is definitely a spot, the cold spot isn't very cold. Then, briefly, I'll explain why, if it is evidence of new physics, that new physics isn't a supervoid.

So, what is the cold spot, and why is it anomalous?

If one wants to find isolated spots/patches in any image it helps reduce the effects of noise in the image by filtering it. The idea behind this is that the filter will have a certain characteristic width, and then any features in the image that are notable over a size equivalent to that width will remain notable after the filtering and any other features in the image arising due to noise will be reduced.

The cold spot was found in maps of the CMB when they were filtered with a "spherical Mexican hat wavelet" (SMHW) filter. The motivation for using this filter is that it has a central region with a positive value, and an outer region with a negative value. Therefore, it works especially well as a filter. A strictly positive filter, will filter out fluctuations in an image that occur on smaller scales than the filter; however any larger scale features will remain and could hide features that occur on the size of the filter. However, by having this compensating negative region, the SMHW filter also filters out the larger scales. This happens because any larger scale features will have the same magnitude in the central region and outer region, and thus the total filtered signal of a large scale feature will be close to zero. However, crucially, an isolated patch will only contribute in the centre and thus an image filtered with a compensated filter like the SMHW will more clearly isolate patches of a certain size than a non-compensated filter.

The cold spot is the coldest spot that exists in the map of the CMB, once that map has been filtered with the SMHW filter. It is interesting and anomalous because, if one makes simulated CMB maps of "typical" universes, the coldest filtered spot rarely has as cold a filtered signal as ours does. In fact, it seems like less than one in one three hundred filtered spots would be that cool.

This seems to indicate that something which isn't captured by our standard model has caused this spot.

What do these typical maps look like then?

While it is true that it is rare for a simulated map of the CMB to have a filtered cold spot that is as cold as our own, it is worth asking what the typical coldest filtered spots actually look like (i.e. before they're filtered). This will help to determine whether the shape of our spot is typical and it is just colder than usual, or, whether its shape is also somehow anomalous.

The limits of expected temperature profiles around cold spots. Red dashed is our cold spot's profile. It doesn't really look anomalously cold, does it? But it does have an anomalous profile!
I've shown exactly this in the figure above. It depicts the 1 and 2 "sigma" bands of the angular profile of the coldest filtered cold spot in simulated CMB maps. That is, at each angle, \(\sim 68\%\) of the coldest filtered spots in each simulated map had an unfiltered temperature within the inner band and \(\sim 95\%\) of the coldest spots had an unfiltered temperature within the outer band. The red, dashed curve is the unfiltered profile for the actual coldest filtered spot in the real CMB map (i.e. "The Cold Spot").

This figure was produced for a recent paper I wrote with Seshadri Nadathur, Mikko Lavinto and Syksy Rasanen (all based in Helsinki). When I first saw this plot, I thought we must have made a mistake. As you can see, our "anomalous" cold spot lies entirely within the bands. It seems to be entirely typical of a coldest filtered cold spot.

Huh? So why claim that it is anomalous?

Well, the point is that this type of profile is not how the anomalousness of the cold spot was first determined. The initial measure of its anomalousness used the filtered signal. Now, I'd like to point you to an interesting feature of the red curve. Although it is always within the bands, it starts in the lower half of the bands and ends in the upper half.

This is crucial and is the source of the anomalousness of the cold spot. In fact, very few of the simulated coldest filtered spots will have this behaviour.

So, where is the anomaly?

The "cumulative filtered signal" (see text for description). Note that the red dashed line just keeps on decreasing, whereas the bottom bit of the bands comes back up. Cold spots don't want to have hot rings. Our's does.

Now, remember the curious feature of the SMHW filter, which is that it has a positive inner region and a negative outer region. It just so happens that our cold spot fits that filter shape quite well, or at least, much better than a typical coldest filtered spot. It gains signal in both regions of the filter, which is what makes its total filtered signal so anomalously cold. Importantly, the simulated spots that are colder in the centre are also wider, and thus still quite cold in the compensating region of the filter; whereas those that are narrower, or have hot rings, aren't very cold in the centre.

The unique thing about our cold spot is therefore that it has a common cold central region, with an uncommon hot ring around it.

This is shown in the second figure above. This is the cumulative filtered signal as a function of the angle. This might be a slightly confusing figure, but I think it is incredibly illustrative once you understand what it is showing so it's worth trying to follow. To filter a point on an image you take the surroundings of the point and weight these surrounding regions by the amplitude of the filter in each region. The SMHW filter changes as a function of the angle a surrounding region is away from the point being filtered. The final filtered value at the point is the sum of all those weighted surrounding regions. The figure above shows the cumulative contribution to that final filtered signal, as a function of the angle. Essentially, you add up all the contributions to the full filtered signal which come from the region between the centre and the angle \(\theta\), and that provides the value in the figure.

Why is this plot useful? Because it shows how the different angles contribute to the final filtered signal. For the red curve (again, that's our, real world cold spot), there are two regions of substantial downward trend. It is in these two regions that the final filtered signal picks up its value. The bands are the same as the bands in the previous figure. That is, the inner band shows what \(68\%\) of simulated maps would do and the outer band shows what \(96 \%\) would do. We can see that the red curve also takes two downward jumps compared to these bands. The first occurs near the centre, but it isn't until the second jump that the real world curve becomes anomalous and ends up outside the bands.

If you look at this figure for a very long time you can also see that the bands widen at intermediate angles and then shrink precisely at the point where our universe becomes anomalous. This is somewhat interesting. It shows that the simulated maps that have cold values in the centre of their coldest spots actually lose signal in the outer region (i.e. the bottom of the band increases); whereas, those simulated maps that were comparatively warmer in the centre continue gaining signal at the larger angles (i.e. the top of the band decreases). However, crucially, our universe's line decreases in both regions.

So, again, what is special about the "cold" spot, is not its coldness. That coldness is clearly not anomalous at all. What is special, is the spottiness of the cold spot and the fact that it is surrounded by a hot ring.

Should we care about the cold spot?

Yes, no, maybe.

This result might make the anomalousness of the cold spot seem horribly arbitrary. Why the SMHW filter that just happens to fit our cold spot? Why should we care care if our not-anomalously-cold cold spot has an anomalously hot ring around it? Well, maybe you shouldn't. But, remember that this particular filter was well motivated a priori. It has spotted our cold spot and called it anomalous because of the hot ring, rather than its coldness; however the filter was chosen because it is ideal for removing noise on both small and large scales. While other filters without the compensating edge wouldn't call our cold spot anomalous, they would also have much larger noise on large scales, which could mimic our cold spot. In other words, they're not as good at picking out true spots as the SMHW filter is.

But, yes, it isn't quite as cut and dried as one might think without this knowledge. Our spot isn't particularly cold compared to simulated coldest spots, so it is the hot ring that makes our spot special. This has an important corollary: If you think that the cold spot is evidence of something new and you want to explain its origin, you can't just explain its coldness, you also need to explain that hot ring. In fact, if you just produced a cold spot that would have an equally large filtered signal, but without a hot ring, you've actually failed to explain the cold spot. Your spot wouldn't have a profile that looks like our cold spot at all.

I'd actually go a bit further. To explain the cold spot you probably shouldn't even try to reproduce the full coldness at the centre. Some, or even most of that will be describable by already known physics, as the two figures in this entry show. Moreover, you don't need to just explain why a hot ring can exist. What you need to explain is why there is a hot ring and why it is precisely around that cold spot.

What about a supervoid?

The paper I took the two figures from above was titled "Can a supervoid explain the cold spot?" As is typical for an article with a question in the title, our answer was a resounding no. Although that question was the main theme of the paper, it wasn't what I found most interesting in it, which is why I've focussed on the stuff to do with the exact nature of our coldspot and what makes it anomalous. This is interesting/important, because if the cold spot is due to a new physical effect, this tells us something very specific about that new physics.

However, we did also conclude that the cold spot can't be explained by a supervoid. Sesh has already written a blog article about this conclusion, so you should go and read that, if you're interested. I'll summarise the argument super briefly here. The argument for why a supervoid can explain the cold spot, presented in this paper, is that it is the result of a gravitational effect very similar to the ISW effect (which I discussed in these posts). Here is why that doesn't work:
  • Most importantly, we just don't reproduce the result of the other group. They claim a particular temperature imprint on the CMB coming from a particular type of supervoid. When we calculate the expected signal for that supervoid, in two different ways, we get a much smaller result (consistent between our two methods). Incidentally, our result also matches what another, simultaneous, result from another group (well, person) saw.
  • Using the results of our calculation we would expect that the probability of a supervoid existing that can explain the coldspot is utterly negligible in the standard cosmological model. Given that the coldspot itself is only a 1 in ~ 300 anomaly, this makes a supervoid a highly unlikely "explanation" of that anomaly.
  • There are other supervoids that have been detected that are just as big and deep as the one proposed to explain the cold spot. If there is some physical mechanism that allows supervoids to affect the CMB so strongly, there should be more than one anomalous coldspot.
The end

So, if you find the cold spot anomalous, looking for its explanation in a supervoid is a dangerous path. If it is due to a supervoid, then the standard cosmological model is substantially wrong, and either the effects of voids on light is different to General Relativity, or very extreme voids are much, much more likely than previously expected. 

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