Yesterday’s post on the sound of the big bang generated quite a bit of discussion about the cosmic microwave background (CMB), how it’s measured, and what it tells us. One of the challenges in interpreting the CMB data is that it’s very heavily processed. Some skeptics argue it’s too processed, so today I thought I’d talk about how we go from raw data to a detailed study of the early moments of the universe.

Early observations of the background (open circles) vs a theoretical blackbody. Credit: Brooks/Cole

When Penzias and Wilson discovered the CMB in 1965, they didn’t create an image map. What they did was to show that in all directions of the sky there is a uniform microwave background of a particular intensity. This intensity was in agreement with the prediction of a uniform thermal background due to the big bang. Over the next couple of decades, both ground based observations and observations made from high altitude balloons found that the cosmic background did indeed seem to follow the intensity curve of a thermal blackbody with a temperature of about 3 K. Since our atmosphere absorbs quite a bit of the shorter wavelengths of the blackbody curve, it was hard to pin down the temperature too precisely. To do that we needed to go beyond the atmosphere.

The COBE results at different sensitivities.

A big breakthrough came in 1989 with the Cosmic Background Explorer (COBE). This was a space-based observer that made a high-resolution survey of the sky. As expected, COBE observed a very uniform thermal background with a temperature of 2.728 K. The observations matched a blackbody curve more precisely than any experiment done thus far. If you plot the results as a temperature projection, what you get is a uniform temperature across the entire sky give or take a few thousandths of a Kelvin. We finally had definitive proof of the big bang. But COBE was designed not only to measure the overall temperature of the sky, but also to measure small variations in temperature at different points in the sky. From this we could determine not only the existence of the big bang but some of its details.

If you subtract out the average temperature from the CMB data, what you’re left with are variations on the order of milliKelvin. One of the first things we notice is that about half the sky is a bit warmer than the average, and about half is a bit cooler. You can see this in the projection maps of the relative temperatures across the sky. The yin-yang shape seen in the map is a dipole distribution, and it’s due to the motion of the Earth relative to the cosmic background. If the Earth is moving toward an object, the light we observe is shifted slightly toward the blue end of the spectrum (shorter wavelengths). For the CMB this means it looks a bit warmer than it actually is, since warmer objects emit shorter wavelengths. Likewise, if the Earth is moving away from an object, its light is shifted toward the red (longer wavelengths) and as a result the CMB looks a bit cooler in that direction. This shift of wavelengths due to relative motion is known as the Doppler effect, and is a basic tool of modern astronomy. From this dipole moment we find that galaxy is moving about 360 km/s relative to the cosmic background, which is actually faster than we expected.

CMB at different resolutions.

If you subtract the dipole moment from the data, then you can see fluctuations on the order of microKelvin. This is where the real meat of the CMB data is. Unfortunately at this level the interference from the Milky Way is a major source of the fluctuations. You can see it as a warm band across the center of the map. This is because we are within the Milky Way, and our view of the deep sky is somewhat obscured. To overcome this problem we have to distinguish between light coming from things like galaxies (called the foreground) and light actually coming from the cosmic background. To do this we observe the sky at several wavelength ranges. Foreground objects have a different spectral distribution than the cosmic background, so by observing the sky at several ranges we can make accurate maps of the foreground in order to subtract it from the data. The COBE satellite mapped the sky at three different ranges. WMAP made five maps in 2003, and Planck made nine sky maps in 2013. With more and more detailed foreground maps, we can more accurately subtract the “noise” from the real data.

Credit: Wayne Hu

With an accurate map of the fluctuations in the CMB we can then study the scales at which fluctuations occur. In mathematical terms we expand the ripples into a sum of multipole moments, of which the dipole is only the first. Basically just take the total average temperature of the whole sky, then split the sky into two regions and take an average of each section, then split and average again, and so on. Keep doing that, and you get an “average” temperature at each scale. From this we can create a power spectrum showing the strength of fluctuations at each scale. Within this power spectrum there are several peaks. The first three peaks of the spectrum tell us about the structure and history of the cosmos. The first peak tells us how flat the universe is (perfectly flat to the limit of observation). The second tells us the amount of regular matter in the universe (about 4.9% of the total mass-energy) and the third tells us the amount of dark matter (about 26.8% of the mass-energy). From the CMB we have moved beyond simply proving the big bang, and are now studying the details of cosmology. We have other sources of data beyond the CMB, and they generally agree with the results of the cosmic background.

At higher and higher multipoles (or smaller fluctuations) the foreground becomes increasingly difficult to remove. Gas and dust throughout the universe becomes a significant problem. This is part of the reason why it’s been so difficult to find evidence of cosmic inflation and why the results of BICEP2 were so controversial. It remains to be seen whether we can pull ever more signal out of the noise, and whether that will be enough to answer some of the basic questions of the origin of the universe. But even if we fail, we’ve come an astonishingly long way toward understanding our universe.

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SEO, or Search Engine Optimization, is a method of trying to game search engines in order to raise the impact of your website or post. One of the common ways has traditionally been through the use of keywords. In astronomy a similar method is used to raise the impact of new research. One of the most effective methods is to use the keywords Exoplanet, Earth, and Habitable. If you can add a nice concept sketch of a watery landscape with double suns, that’s good too.

It’s no wonder then that news of the discovery of three super Earths in the habitable zone of Gliese 667C was so popular. It’s a type of finding that can get a strong signal over the internet noise. Of course, search optimization is exactly the type of method the researchers needed to do to find the planetary signals in the noise.

These particular planets were confirmed using a variety of data from multiple sources. They used data from the Very Large Telescope (VLT) in Chile, which is a high resolution visible spectrum telescope, to determine the properties the star Gliese 677C. Since these planets were confirmed using the Doppler motion, they needed to know the star’s precise mass. They then used Doppler data of the star from the Carnegie Planet Finder Spectrograph,, the Keck HIRES spectrograph, and the the High Accuracy Radial velocity Planet Searcher (HARPS). They then had to analyze all this data to find the planetary signals.

The basic idea is pretty simple. Since a star and planet gravitationally attract each other, as a planet orbits its star, the star wobbles slightly with the same period as the planet. As the star wobbles, the wavelength (color) of light changes slightly, being blueshifted or redshifted as the star wobbles toward or away from us, which is known as the Doppler shift. By observing the light from a star you can detect its wobble, thus detecting the planet.

Credit: Guillem Anglada-Escude’, et al.

In practice, it isn’t quite that simple. For one, the Doppler shift is a measure of the motion of the star’s surface, and while a wobble of the star itself is one way for that to occur, other effects such as solar flares can give Doppler effects as well. Then there is the fact that there are likely multiple planets, which means there are multiple wobble effects in your signal. The Doppler measurement only gives us the motion of the star toward and away from us, so if the planetary orbits are at an angle relative to us, the star’s wobble is also at an angle, but we can’t directly see that. Plus the wobbles due to planets are generally quite small, so all the random noise can give the appearance of a planetary signal when there isn’t one. To rule out the false signals you have to test whether the planets you think you’ve found have stable orbits. That means you have to simulate the star system to see if the planets stay in their same general orbit.

So to find the planetary signals, you have to do some pretty complex statistical analysis. For example, the figure above is a plot of the Baysean periodograms for the seven planets in the system. Where each of the periodograms has the largest spike is a likely planet, and the larger the spike the more strongly the data confirms the planet. As you can see, the locations of the first six planets are pretty clear. The seventh one is a bit iffy, but the researchers counted it because it is a signal in a stable location for the system. In other words, assuming the other six planets exist, then the orbit of this seventh planet would be stable. If it were in an unstable orbit they wouldn’t have counted it.

Once the likely planets are determined, you can then go back and determine things like the shape and inclination of the planetary orbits, as well as their likely masses. These planets are all quite close to their star. Six of them are closer to the star than Mercury is to our Sun. But since Gliese 667C is a red dwarf, the habitable zone is also quite close to the star.

The habitable zone of a star is typically taken as the distance range where the temperature of a planet is sufficient for liquid water. This would depend on other factors such as atmospheric density and composition, but for our solar system it spans the range from Venus to Mars, or about 0.7 to 1.4 AU, where 1 AU is the distance of Earth from the Sun. For 667C, the range is from about 0.10 to 0.25 AU, and it turns out that three of the planets fall within that range.

These three planets are referred to as “super Earths” because they are more massive than Earth, but not as massive as Uranus and Neptune. The innermost of the three has a mass of about 3.8 Earths, while the outer two have masses of about 2.7 Earths. The Doppler data doesn’t tell us anything about their size or atmospheres. If we assume they are about the same density as Earth, then they would be about 1.5 times larger, or about as much larger than Earth as Earth is to Mars.

That doesn’t mean that these planets would be similar to Earth in general. For one thing, the habitable zones of red dwarfs are so close to the star that any planets in the zone would likely be tidally locked. This means they would have one side that always faces the star. If they have a thick atmosphere that might provide a mechanism for heat to be transferred between the near and far sides for a more even temperature, but a thick atmosphere could also trap too much heat (such as Venus) or reflect too much light away. These planets could also experience tidal heating that could cause them to lose much of their water before completely forming. So its very possible that these planets are more like Venus than Earth.

But then calling them super Venuses wouldn’t have the same impact factor.

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