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## How do we know that the CMB is from a hot, early Universe?

Towards the end of July I had an article published in The Conversation about the Cosmic Microwave Background, follow this link to read that article. After the article had been up a few days, I got this question from a Mark Robson, which I thought was an interesting one.

Mark Robson’s original question which be posed below the article I wrote for The Conversation.

I decided to blog an answer to this question, so the blogpost “What is the redshift of the Cosmic Microwave Background (CMB)?” appeared on my blog on the 30th of August, here is a link to that blogpost. However, it would seem that Mark Robson was not happy with my answer, and commented that I had not answered his actual question. So, here is his re-statement of his original question, except to my mind he has re-stated it differently (I guess to clarify what he actually meant in his first question).

I said I would answer this slightly different/clarified question soon, but unfortunately I have not got around to doing so until today due to various other, more pressing, issues (such as attending a conference last week; and also writing articles for an upcoming book 30-second Einstein, which Ivy Press will be publishing next year).

The questions and comments that Mark Robson has since posted below my article about how we know the redshift of the CMB

## What is unique about the CMB data?

The very quick answer to Mark Robson’s re-stated question is that “the unique data possessed by the CMB which allow us to calculate its age or the temperature at which it was emitted” is that it is a perfect blackbody. I think I have already stated in other blogs, but let me just re-state it here again, the spectrum as measured by the COBE instrument FIRAS in 1990 of the CMB’s spectrum showed it to be the most perfect blackbody spectrum ever seen in nature. Here is the FIRAS spectrum of the CMB to re-emphasise that.

The spectrum of the CMB as measured by the FIRAS instrument on COBE in 1990. It is the most perfect blackbody spectrum in nature ever observed. The error bars are four hundred times larger than normal, just so one can see them!

So, we know, without any shadow of doubt, that this spectrum is NOT due to e.g. distant galaxies. Let me explain why we know this.

## The spectra of galaxies

If we look at the spectrum of a nearby galaxy like Messier 31 (the Andromeda galaxy), we see something which is not a blackbody. Here is what the spectrum of M31 looks like.

The spectrum of our nearest large galaxy, Messier 31

The spectrum differs from a blackbody spectrum for two reasons. First of all, it is much broader than a blackbody spectrum, and this is easy to explain. When we look at the light from M31 we are seeing the integrated light from many hundreds of millions of stars, and those stars have different temperatures. So, we are seeing the superposition of many different blackbody spectra, so this broadens the observed spectrum.

Secondly, you notice that there are lots of dips in the spectrum. These are absorption lines, and are produced by the light from the surfaces of the stars in M31 passing through the thinner gases in the atmospheres of the stars. We see the same thing in the spectrum of the Sun (Josef von Fraunhofer was the first person to notice this in 1814/15). These absorption lines were actually noticed in the spectra of galaxies long before we knew they were galaxies, and were one of the indirect pieces of evidence used to argue that the “spiral nebulae” (as they were then called) were not disks of gas rotating around a newly formed star (as some argued), but were in fact galaxies outside of our own Galaxy. Spectra of gaseous regions (like the Orion nebula) were already known to be emission spectra, but the spectra of spiral nebulae were continuum spectra with absorption lines superimposed, a sure indicator that they were from stars, but stars too far away to be seen individually because they lay outside of our Galaxy.

The absorption lines, as well as giving us a hint many years ago that we were seeing the superposition of many many stars in the spectra of spiral neublae, are also very useful because they allow us to determine the redshift of galaxies. We are able to identify many of the absorption lines and hence work out by how much they are shifted – here is an example of an actual spectrum of a very distant galaxy at a redshift of $z=5.515$, and below the actual spectrum (the smear of dark light at the top) is the identification of the lines seen in that spectrum at their rest wavelengths.

The spectrum of a galaxy at a redshift of z=5.515 (top) (z=5.515 is a very distant galaxy), and the features in that spectrum at their rest wavelengths

Some galaxies show emission spectra, in particular from the light at the centre, we call these type of galaxies active galactic nucleui (AGNs), and quasars are now known to be a particular class of AGNs along with Seyfert galaxies and BL Lac galaxies. These AGNs also have spectral lines (but this time in emission) which allow us to determine the redshift of the host galaxy; this is how we are able to determine the redshifts of quasars.

Notice, there are no absorption lines or emission lines in the spectrum of the CMB. Not only is it a perfect blackbody spectrum, which shows beyond any doubt that it is produced by something at one particular temperature, but the absence of absorption or emission lines in the CMB also tells us that it does not come from galaxies.

## The extra-galactic background light

We have also, over the last few decades, determined the components of what is known as the extra-galactic background light, which just means the light coming from beyond our galaxy. When I say “light”, I don’t just mean visible light, but light from across the electromagnetic spectrum from gamma rays all the way down to radio waves. Here are the actual data of the extra-galactic background light (EGBL)

Actual measurements of the extra-galactic background light

Here is a cartoon (from Andrew Jaffe) which shows the various components of the EGBL.

The components of the extra-galactic background light

I won’t go through every component of this plot, but the UV, optical and CIB (Cosmic Infrared Background) are all from stars (hot, medium and cooler stars); but notice they are not blackbody in shape, they are broadened because they are the integrated light from many billions of stars at different temperatures. The CMB is a perfect blackbody, and notice that it is the largest component in the plot (the y-axis is what is called $\nu I_{\nu}$, which means that the vertical position of any point on the plot is an indicator of the energy in the photons at that wavelength (or frequency). The energy of the photons from the CMB is greater than the energy of photons coming from all stars in all the galaxies in the Universe; even though each photon in the CMB carries very little energy (because they have such a long wavelength or low frequency).

## Why are there no absorption lines in the CMB?

If the CMB comes from the early Universe, then its light has to travel through intervening material like galaxies, gas between galaxies and clusters of galaxies. You might be wondering why we don’t see any absorption lines in the CMB’s spectrum in the same way that we do in the light coming from the surfaces of stars.

The answer is simple, the photons in the CMB do not have enough energy to excite any electrons in any hydrogen or helium atoms (which is what 99% of the Universe is), and so no absorption lines are produced. However, the photons are able to excite very low energy rotational states in the Cyanogen molecule, and in fact this was first noticed in the 1940s long before it was realised what was causing it.

Also, the CMB is affected as it passes through intervening clusters of galaxies towards us. The gas between galaxies in clusters is hot, at millions of Kelvin, and hence is ionised. The free electrons actually give energy to the photons from the CMB via a process known as inverse Compton scattering, and we are able to measure this small energy boost in the photons of the CMB as they pass through clusters. The effect is known as the Sunyaev Zel’dovich effect, named after the two Russian physicists who first predicted it in the 1960s. We not only see the SZ effect where we know there are clusters, but we have also recently discovered previously unknown clusters because of the SZ effect!

I am not sure if I have answered Mark Robson’s question(s) to his satisfaction. Somehow I suspect that if I haven’t he will let me know!

## Red stars, white stars, blue stars

Anyone who has looked at the night-time sky for any length of time will have noticed that stars have different colours. Some stars are red, some are white, and some are blue. A nice example of this can be seen in the Orion constellation. Betelgeuse, the star in the top left hand corner, has a distinct red colour, Rigel, the star in the bottom right hand corner, has a distinct blue colour, and Saiph, the star in the bottom left hand corner is white.

The Orion constellation. Betelgeuse in the top left is a distinct red colour, Rigel in the bottom right is a distinct blue colour, and Saiph in the bottom left is white.

## Stars have different temperatures

These differences in colour are due to stars having different surface temperatures. As the figure below shows, the blackbody curve peaks at different wavelengths depending on a star’s temperature, so a red star is cooler than a white star, which in turn is cooler than a blue star. This is because of Wien’s displacement law, which I discussed in this blog.

Stars with different surface temperatures will appear to have different colours. This is due to their blackbody spectra peaking at different wavelengths.

## Fraunhofer’s spectrum of the Sun

In 1817 the German scientist Joseph von Fraunhofer published a spectrum of the Sun showing the continuum spectrum which had long been familiar, but superimposed on this were a series of dark lines. These dark lines were shown by Kirchhoff and Bunsen in 1859 to be due to absorption lines being produced by different elements. I discussed absorption spectra in this blog. We now know that the gases which produce the absorption lines are in the atmosphere of the Sun. The visible surface of the Sun is called the photosphere, and it is the photosphere of the Sun which produces its blackbody spectrum. The overlying, thinner gases in the Sun’s atmosphere produce the numerous absorption lines which Fraunhofer saw.

The spectrum of the Sun sketched by Fraunhofer in 1814/15, showing the dark lines he observed, superimposed on the Sun’s continuum spectrum.

## The Harvard stellar classification scheme

In the 1880s the Harvard College Observatory, under the Directorship of Edward C. Pickering, set about gathering the spectra of thousands of stars. The initial catalogue was published as the Draper Catalogue of Stellar Spectra in 1890. Williamina Fleming classified the spectrum using the letters of the alphabet, with with stars with the strongest Hydrogen absorption lines having the designation A, then the next strongest B, then C etc.

The Harvard stellar classification scheme was originally in alphabetical order based on the strength of the hydrogen absorption lines of a star You can see in this figure how the strength of the Hydrogen absorption lines (e.g. the $H\alpha, H\beta \text{ and } H\gamma$ lines) are strongest for the A, B and F-type stars.

In 1901 Annie Jump Cannon revised the system. First of all she dropped most of the letters, leaving A,B,F,G,K,M and O. Secondly she subdivided each of these into 10 divisions, so for example A0, A1, A2…. A9. Thirdly, she re-ordered the letters based on the stars’ surface temperatures, not the strength of the Hydrogen line, with the hottest stars first. This is what has led to the O,B,A,F,G,K,M (Oh Be A Fine Girl/Guy Kiss Me) system we have today. The O-class stars are the hottest, the B-class stars the next hottest, all the way down to the M-class stars which are the coolest.

Annie Jump Cannon

## The strength of the lines of different elements and their ions

The figure below shows the variation of the strength of the absorption lines of different elements and their ions as a function of temperature. Stars which have the strongest Hydrogen lines (A-class stars) have a surface temperature of around 10,000 K. The bright star Vega is an A0-class star, and is white in appearance. The Sun is a G2-type star, and its strongest lines are the Calcium II lines (singly ionised Calcium).

The strengths of the absorption lines of different elements (and their ions) as a function of temperature. The nomenclature e.g. Ca II means “singly ionised Calcium”, He I means “neutral Helium”, He II means “singly ionised Helium”, etc.

The reason the strength of the Hydrogen absorption lines peak at around 10,000 K whereas the singly ionised Calcium lines (Ca II) peak at around 6,000 K is something I will explain in a future blog.