This blog post was written by Aurélien Benoit-Lévy.

There’s a lot of activity on this blog about the cosmic microwave background (CMB) and Planck, and on  how much Planck has improved our view of the baby universe compared to its predecessors WMAP and COBE. One of the things that have drastically improved  between those satellites is the angular resolution. This simply means that Planck is able to see finer details in the CMB and is therefore able to extract more cosmological information.

However, getting the physical sense of a finite resolution instrument is not always easy, especially since we don’t know what the CMB fluctuations should look like. That’s why we can use a familiar object and play around with the resolution parameter. So let’s consider our planet Earth, which indeed we know quite well!

So, what would the Earth look like if it was seen by a satellite with an angular resolution similar to that of COBE (about 7 degrees), WMAP (about 14 arc-minutes), or Planck (5 arc-minutes)? Let’s first clarify what we mean by observation of the Earth by a satellite. We can very easily find online topographic data of the Earth that indicates the altitude of continents and the depth of seabeds. Let’s now make the following analogy: instead of having a satellite that measures the energy (or temperature) of the photons of the CMB, we have a satellite that measures the altitude of the Earth, this altitude being negative when we’re looking at oceans. And then, we can create a map of the altitude of the Earth:

Full resolution map, given by the resolution of the initial data of about 1 arc-minute.

The following animation shows the Earth as seen first by a very basic satellite that would only be sensitive to structure at the scale of 180 degrees. At this scale, the only thing we can see is the average altitude of the Earth, and that is why the animation starts with a monotonic blue map. The resolution can therefore be thought of as the scale at which details are smoothed and cannot be easily discerned. Then the resolution increases  (i.e., the smallest visible altitude decreases, I know that’s confusing), and we see the highest regions of the Earth coming into view one by one: first the Himalayas, and then the Antarctic, and all the other mountains.

At the COBE resolution (7 degrees) we can distinguish the large continents, but we cannot resolve finer details like the South-East Asian Islands or Japan. Another interesting fact is that it seems that there’s not much difference between the Planck and WMAP resolutions. That is mostly because the image is too small to be sensitive to such fine resolution, and thus we need to zoom in, in order to see the improvement of Planck compared to WMAP.

We can now concentrate on an even more familiar region. The following figures show how the British Isles would appear as seen by COBE, WMAP, Planck, and the original data.

And this comes quite as a surprise: at the COBE resolution, England is totally overpowered by France, and does not seem to exist at all! This might actually be a good thing if harmful aliens were to observe the Earth at COBE resolution before launching an attack: they would not spot England and would strike at France!

More seriously, we have seen previously that, at the 7 degree resolution, islands are not yet resolved and are hidden by the high mountains that spread their intensity (in this case their altitude) over large angular distances. However, at WMAP resolution the British Isles are perfectly resolved but everything appears blurred. The situation improves with Planck resolution and then we can see the improvement between WMAP and Planck. Note that even at the Planck resolution, we miss fine details and there is much more information in the original data. That is, however, not the case for the CMB, as physical processes at recombination actually damp the signal at small scales, and Planck indeed extracts all the information in the primary CMB.

To conclude this post, the following animation shows the “Rise of the British Isles”.

The topographic data is from the ETOPO1 global relief website, and could in principle be found here.