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## The origin of the elements

A couple of weeks ago this fascinating version of the periodic table of the elements was the NASA Astronomy Picture of the Day (APOD). Most people have seen the periodic table of the elements, it is shown on the wall of most high school chemistry classrooms. But, what is totally fascinating to me about this version is it shows the origin of each element.

It has been a long process of several decades to understand the origin of the elements. In fact, we have not totally finished understanding the processes yet. But, we do know the story for most elements. All the hydrogen in the Universe was formed in the big bang. This is true for nearly all the helium too. A small amount of the 25% or so of helium in the Universe has been created within stars through the conversion of hydrogen into helium. But, not much has been created this way because most of that helium is further converted to carbon.

The only other element to be formed in the big bang is lithium. About 20% of the lithium in the Universe was formed in the big bang, the rest has been formed since,

Together, hydrogen and helium comprise 99% of the elements in the Universe by number (not by mass).

Where Your Elements Came From – from the NASA Astronomy Picture Of the Day (APOD) 24 October 2017.

I have decided to use this fascinating table as the basis for a series of blogs over the next few weeks to explain each of the 6 processes in these six boxes

## The temperature of the Universe at recombination (decoupling)

Last week someone (“Cosm”) posted an interesting comment/question on my post “What is the redshift of the Cosmic Microwave Background (CMB)?” . The question asked how we can say that the temperature of the Universe at recombination is about 3000K when the energy of electrons with such a temperature would be

$E = \frac{ 3 }{ 2 } k T = 6.2 \times 10^{-20} \text{ J } = 0.39 \text{ eV }$

and the ionisation potential of hydrogen is 13.6 eV. This would imply, naively, that recombination would occur at a higher temperature, roughly $(13.6/0.39) \times 3000 \approx 105,000 \text{ Kelvin}$. But, it does not occur at a temperature of just over 100,000 K, but at about 3000 K. Why is this?

“Cosm” asked me this question on my blogpost about how do we know the redshift of the CMB

I decided that it was a sufficiently interesting point that I would go through the detail of why recombination (or decoupling as I prefer to call it) happened when the Universe was about 3,000K; even though electrons cease to be able to thermally ionise hydrogen at a much higher temperature of about 100,000K, so one might think that decoupling would happen earlier. The clue is that it has to do with something called equilibrium theory.

A cartoon of recombination (decoupling). As the temperature of the Universe fell, the free electrons combined with naked protons to produce neutral hydrogen, and the Universe became transparent. This is when the radiation (which was already there) was able to travel through the Universe, and it is this radiation which we see as the Cosmic Microwave Background (CMB).

## The temperature of decoupling based on equilibrium theory

One can get a reasonable estimate of the temperature (and redshift) when recombination (decoupling) took place by using equilibrium theory. This was developed in the 1920s and is based on the Saha ionisation equation, named after Indian astrophysicist Meghnad Saha.

We are going to assume that the process

$p + e^{-} \leftrightarrow H + \gamma$

is the dominant reaction for creating neutral hydrogen. That is, electrons and bare protons combining. When a free electron combines with a proton to create neutral hydrogen it will also create a photon, and that is what the $\gamma$ represents (it is not a gamma-ray photon, it is more likely to be a UV or visible-light photon). But, it is a two way process, as obviously electrons can also be ionised to go back to free electrons and bare protons.

We are going to denote the number density of free electrons (the number per unit volume) as $n_{e}$, the number density of free protons (ionised hydrogen) as $n_{p}$, and the number density of neutral hydrogen as $n_{H}$.

We can calculate the relative abundance of the free electrons to protons and neutral hydrogen via the Saha equation

$\frac{ n_{p} n_{e} }{ n_{H} } = \left( \frac{ m_{e} k_{B} T }{ 2 \pi \hbar^{2} } \right)^{3/2} \; exp \left( - \frac{ E_{1} }{ k_{B} T } \right) \text{ (1) }$

Where $m_{e}$ is the mass of an electron, $k_{B}$ is Boltzmann’s constant, $T$ is the temperature, $\hbar$ is the reduced Planck constant (which is defined as $\hbar=h/2\pi$ where $h$ is Planck’s constant), and $E_{1}$ is the ionisation potential of hydrogen (13.6 eV). We know from charge neutrality that $n_{e} = n_{p}$. We are going to define $x_{e}$ as the fraction of free electrons, so by definition

$x_{e} = \frac{ n_{e} }{ (n_{p} + n_{H} ) } \text{ (2) }$

Because $n_{e} = n_{p}$ we can re-write Equation (1) as

$\frac{ n_{e}^{2} }{ n_{H} } = \left( \frac{ m_{e} k_{B} T }{ 2 \pi \hbar^{2} } \right)^{3/2} \; exp \left( - \frac{ E_{1} }{ k_{B} T } \right) \text{ (3) }$

and from (2) we can write

$x_{e}^{2} = \frac{ n_{e}^{2} }{ ( n_{p} + n_{H} )^{2} } \text{ (4) }$

We can also write
$1 - x_{e} = 1 - \frac{ n_{e} }{ (n_{p} + n_{H} ) } = \frac{ n_{p} + n_{H} - n_{e} }{ (n_{p} + n_{H} ) } = \frac{ n_{H} }{ (n_{p} + n_{H} ) } \text{ (5) }$

Dividing Eq. (4) by Eq. (5) we have

$\frac{x_{e}^{2} }{ ( 1 - x_{e} ) } = \frac{ n_{e}^{2} }{ ( n_{p} + n_{H} )^{2} } \; \cdot \; \frac{ (n_{p} + n_{H} ) }{ n_{H} } = \frac{ n_{e}^{2} }{ (n_{p} + n_{H} ) } \; \cdot \; \frac{ 1 }{ n_{H} } \text{ (6) }$

But

$\frac{ n_{e}^{2} }{ n_{H} } = \left( \frac{ m_{e} k_{B} T }{ 2 \pi \hbar^{2} } \right)^{3/2} \; exp \left( - \frac{ E_{1} }{ k_{B} T } \right)$

so we can re-write Eq. (6) as

$\frac{x_{e}^{2} }{ ( 1 - x_{e} ) } = \frac{ 1 }{ (n_{p} + n_{H} ) } \left( \frac{ m_{e} k_{B} T }{ 2 \pi \hbar^{2} } \right)^{3/2} exp \left( - \frac{ E_{1} }{ k_{B} T } \right) \text{ (7) }$

Most of the quantities on the right hand side are physical constants, and the rest are known functions of redshift $z$. For example, the temperature history of the CMB at any redshift $z$ is just given by

$T(z) = 2.728 (1 + z) \text{ (8) }$

where $T=2.728$ is the CMB’s current temperature. The total number density of hydrogen (neutral and ionised), $(n_{p} + n_{H})$ is also a function of redshift, and is given by

$(n_{p} + n_{H}) (z) = 1.6(1+z)^{3} \text{ per m}^{3} \text{ (9) }$

where $1.6 \text{ per m}^{3}$ is the currently observed density. So, we will re-write Eq. (7) as

$\frac{x_{e}^{2} }{ ( 1 - x_{e} ) } = \frac{ 1 }{ 1.6(1+z)^{3} } \left( \frac{ m_{e} k_{B} }{ 2 \pi \hbar^{2} } \right)^{3/2} T^{3/2} \; exp \left( - \frac{ E_{1} }{ k_{B} T } \right) \text{ (10) }$

Equation (10) cannot be solved analytically, only numerically.

We will assume that we need a fraction of free electrons of $x_{e} = 50\%$ for decoupling to have occurred (in other words, $50\%$ of the electrons have bound to protons to form neutral hydrogen). We will try different temperatures to see what fraction $x_{e}$ they give. Note: when we assume a particular temperature, this will fix the redshift, because of Eq. (8).

Let us first try a temperature of $T=3000 \text{ Kelvin}$. From Eq. (8) this gives $z \approx 1100$. Plugging these values of $T$ and $z$ into Eq. (10) gives

$\frac{x_{e}^{2} }{ ( 1 - x_{e} ) } = 2.8 \times 10^{-6} \rightarrow x_{e}^{2} + 2.8 \times 10^{-6} x_{e} - 2.8 \times 10^{-6} = 0$

Solving this quadratic equation gives $\boxed{ x_{e} = 1.67 \times 10^{-3} \text{ if } T=3000 \text{ K } }$

This is obviously much less than $50\%$, by the time the Universe has cooled to 3000K there are very few free electrons, decoupling is essentially complete.

What if we use $T=4000 \text{ K}$? Doing the same thing we find $z \approx 1500$ which then gives

$\frac{x_{e}^{2} }{ ( 1 - x_{e} ) } = 0.85 \rightarrow x_{e}^{2} + 0.85 x_{e} - 0.85 = 0$

Solving this quadratic gives $\boxed{ x_{e} = 0.6 \text{ if } T=4000 \text{ K } }$. This means that $60\%$ of the electrons are free when the temperature is 4000K, meaning $40\%$ of the hydrogen atoms have become neutral.

Thirdly, let us try 3800K. This gives $z \approx 1400$. Plugging this into Eq. (9) gives

$\frac{x_{e}^{2} }{ ( 1 - x_{e} ) } = 0.1225 \rightarrow x_{e}^{2} + 0.1225 x_{e} - 0.1225 = 0$

Solving this gives $\boxed{x_{e} = 0.29 \text{ if } T=3800 \text{ K}}$

At a temperature of T=3800K just under $30\%$ of the electrons are free, so some $70\%$ of the hydrogen atoms are neutral.

So, we can surmise from this that the Universe had decoupled enough to be about $50\%$ transparent to radiation by the time the temperature was a little below $\boxed{ T=4000 \text{ Kelvin} }$. This is why the temperature of decoupling (recombination) is usually given as lying between a temperature of $T= 4000 \text{K and } 3000\text{K}$.

## Why is this just an approximation?

As I mentioned above, this is just an approximation, but not a bad one. It’s an approximation because it is a simplification of what is actually going on. In 1968, Jim Peebles (who had done the work in the 1965 Dicke etal. paper) and, independently, Yakov Zel’dovich (he of the Sunyaev-Zel’dovich effect) in the USSR, worked out a more complete theory where the hydrogen has three energy levels, rather than what we have done here where we assume the free electrons go straight into the ground-state (i.e. only two energy levels). Their third level was the n=2 state, the energy level just above the ground state. This is an important energy level for hydrogen, as it is transitions down to the n=2 level which give rise to visible-light photons. Using this more complicated 3-level model gives a Universe which is 90% neutral at $z \approx 1100$, which would correspond to a temperature of T=3000K, which is why this temperature is most often quoted. You can read more about their 3-level model here.

## Summary

Using equilibrium theory, which is an oversimplification, gives the following fractions of neutral hydrogen for three different temperatures

• At T=3000K the Universe would have been more than 99% neutral
• At T=4000K the Universe would have been about 40% neutral
• At T=3800K the Universe would have been about 70% neutral

Using a more correct 3-level model developed by Peebles and, independently, by Zel’dovich, gives that the Universe would have been about 90% neutral by the time the temperature had dropped to T=3000K. It is this temperature which is usually quoted when we talk about the temperature of the Universe when recombination (decoupling) occurred.

## 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!

## To catch a comet – Rosetta public lecture

Last night (Monday the 24th of August) I went to a public lecture about the Rosetta mission
at the National Museum of Wales in Cardiff. The lecture was given by Mark McCaughrean, who is senior science advisor at the European Space Agency (ESA) and, if I’m correct, also either heads up or is very senior in their public outreach efforts. It was one of the best public lectures I’ve ever attended, and in writing that statement I am trying to figure out how many public lectures I have actually attended. In addition to having given probably over 100 public lectures myself, I have probably attended some 150-200 public lectures given by others in the last 40-odd years.

The opening slide of Mark McCaughrean public lecture about the Rosetta mission at the National Museum of Wales

In addition to learning a lot about the Rosetta mission (I will blog about some of what I learnt next week), the lecture got me thinking about what makes a good public lecture. I have also been thinking about this the last few days because my book on the Cosmic Microwave Background has been reviewed by Physics World (the magazine of the Institute of Physics), and that review will apparently appear in their October magazine. But, the reviewer shared with me some of her observations about the book, and one point she raised is that she felt I was inconsistent in my level of explanations in the book. What she meant was that there are some things I explain so that complete novices can follow my arguments, but other things where more of a physics/astronomy background would be necessary to follow that I am saying.

This is a valid point, and it shows the quandary I was in when trying to decide at what level to pitch the book. My primary audience was that I hoped the book will be used by undergraduates in the Disunited Kingdom and graduate students in the United States as a background text to any course they may be doing on the early Universe. But, in the back of my mind, I also had the interested lay-reader in mind, which is why I explained some things at a level for them. What I probably ended up doing was falling between two stools, and that is not always good in communicating science to the public.

Last night’s lecture by Mark did a wonderful job, as it seemed to me that he was able to keep it at a level that (hopefully) everyone could understand, but at the same time there was some specialist information in there for professional astronomers to give them (and me) the impression that we too had learnt something. This is a difficult tightrope to walk, but Mark did it very well.

Audience participation time – the audience had to jump 4cm in the air to simulate the acceleration felt by Philae when landing on comet 67/P

This is what I try to do in my own public lectures, but I doubt I do it as well as Mark did last night. Whether I’m talking to school groups, astronomical societies, on the radio or TV or lecturing on a cruise, I always try to make sure that I don’t lose any of my audience in the first three quarters or so of the lecture by keeping things as simple as possible. At the same time, I always try to make sure that there is some information in the lecture (maybe some 25% of it) which will be news to even a professional in the field, as even in a public lecture you may have professionals in the audience. This was the case, for example, in lectures I gave on the cruise I did in South America in March – one of my regular attendees had worked at NASA JPL and he and I would have long chats after each lecture where he would quiz me further, or impart some information that I did not know about.

Last night, Mark had a perfect mixture of videos, cartoons, animations, humour and exciting information, and it was all delivered in a relaxed and humorous way. As I say, one of the best public lectures I have ever attended.

## What is the redshift of the Cosmic Microwave Background (CMB)?

Last week, as I mentioned in this blog here, I had an article on the Cosmic Microwave Background’s accidental discovery in 1965 published in The Conversation. Here is a link to the article. As of writing this, there have been two questions/comments. One was from what I, quite frankly, refer to as a religious nutter, although that may be a bit harsh! But, the second comment/question by a Mark Robson was very interesting, so I thought I would blog the answer here.

This article on the Cosmic Microwave Background was published in The Conversation last Thursday (23rd July 2015)

Mark asked how we know the redshift of the CMB if it has no emission or absorption lines, which is the usual way to determine redshifts of e.g. stars and galaxies. I decided that the answer deserves its own blogpost – so here it is.

## How does the CMB come about

As I explain in more detail in my book on the CMB, the origin of the CMB is from the time that the Universe had cooled enough so that hydrogen atoms could form from the sea of protons and electrons that existed in the early Universe. Prior to when the CMB was “created”, the temperature was too high for hydrogen atoms to exist; electrons were prevented from combining with protons to form atoms because the energy of the photons in the Universe’s radiation (given by $E=h \nu$ where $\nu$ is the frequency) and of the thermal energy of the electrons was high enough to ionise any hydrogen atoms that did form. But, as the Universe expanded it cooled.

In fact, the relationship between the Universe’s size and its temperature is very simple; if $a(t)$ represents the size of the Universe at time $t$, then the temperature $T$ at time $t$ is just given by

$T(t) \propto \frac{ 1 }{ a(t) }$

This means that, as the Universe expands, the temperature just decreases in inverse proportion to its size. Double the size of the Universe, and the temperature will halve.

When the Universe had cooled to about 3,000K it was cool enough for the electrons to finally combine with the protons and form neutral hydrogen. At this temperature the photons were not energetic enough to ionise any hydrogen atoms, and the electrons had lost enough thermal energy that they too could not ionise electrons bound to protons. Finally, for the first time in the Universe’s history, neutral hydrogen atoms could form.

For reasons that I have never properly understood, astronomers and cosmologists tend to call this event recombination, although really it was combination, without the ‘re’ as it was happening for the first time. A term I prefer more is decoupling, it is when matter and radiation in the Universe decoupled, and the radiation was free to travel through the Universe. Before decoupling, the photons could not travel very far before they scattered off free electrons; after decoupling they were free to travel and this is the radiation we see as the CMB.

## The current temperature of the CMB

It was shown by Richard Tolman in 1934 in a book entitled Relativity, Thermodynamics, and Cosmology that a blackbody will retain its blackbody spectrum as the Universe expands; so the blackbody produced at the time of decoupling will have retained its blackbody spectrum through to the current epoch. But, because the Universe has expanded, the peak of the spectrum will have been stretched by the expansion of space (so it is not correct to think of the CMB spectrum as having cooled down, rather than space has expanded and stretched its peak emission to a lower temperature). The peak of a blackbody spectrum is related to its temperature in a very precise way, it is given by Wien’s displacement law, which I blogged about here.

In 1990 the FIRAS instrument on the NASA satellite COBE (COsmic Background Explorer) measured the spectrum of the CMB to high precision, and found it to be currently at a temperature of $2.725 \text{ Kelvin}$ (as an aside, the spectrum measured by FIRAS was the most perfect blackbody spectrum ever observed in nature).

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!

It is thus easy to calculate the current redshift of the CMB, it is given by

$z \text{ (redshift)} = \frac{3000}{2.725} = 1100$

and “voilà”, that is the redshift of the CMB.  Simples 😉

## The CMB: how an accidental discovery became the key to understanding the universe

Over the last couple of weeks I have been writing about the Cosmic Microwave Background, as this month of July marks the 50th anniversary since the paper announcing its discovery was published. In this blog here I showed the original 1948 paper in which Ralph Alpher and Robert Hermann predicted its existence, and in this blog here, I re-posted something that I had written back in April 2013, before I had started research for the book I have published on the CMB.

Today I had been planning to write about its accidental discovery by Bell Labs astronomers Arno Penzias and Robert Wilson, but on Thursday of last week I had the following article published in The Conversation, if you follow this link you can read the original article. This article obviates the need for me to blog about the history of the discovery, you may as well just read it in The Conversation.

This article on the Cosmic Microwave Background was published in The Conversation last Thursday (23rd July 2015)

However, what is contained in this article is a summary of an even-more fascinating story, which you can read about in all its wonderful detail in my book, which can be bought directly from Springer, or from other booksellers such as Amazon.

My book “The Cosmic Microwave Background – how it changed our understanding of the Universe” is published by Springer and can be found by following this link.

To finish up this series on the CMB and its discovery, next week I will write about the Penzias and Wilson paper, and the accompanying paper by Robert Dicke and his Princeton team which attempted to explain the observation that Penzias and Wilson had made.

## The Prediction of the Cosmic Microwave Background – the original paper

Last week I reposted my blog about the prediction of the cosmic microwave background (CMB), which I had originally written in April 2013. This month, July, marks the 50th anniversary of the first detection of the CMB, and I will blog about that historic discovery next week. But, in this blog, I wanted to show the original 1948 paper by Alpher and Hermann that predicted the CMB’s existence.

I learnt far more about the history of the CMB’s prediction whilst researching for my book on the CMB, which was published at the end of 2014 (follow this link to order a copy). In doing my research, I found out that many of the things I had been been told or had read about the prediction were wrong, so here I wanted to say a little bit more about what led up to the prediction.

My book “The Cosmic Microwave Background – how it changed our understanding of the Universe” is published by Springer and can be found by following this link.

## Gamow did not predict the CMB

Many people either do not know of the 1940s prediction of the CMB, or they attribute its prediction to George Gamow. In fact, it was his research assistants Ralph Alpher and Robert Hermann who made the prediction, but as head of the group it is often Gamow who gets the credit.

Ralph Alpher had just finished his PhD on the origin of the elements, and after the publication of the famous Alpher, Bethe, Gamow paper (see my blog here about that), Gamow started writing a series of papers on the nature of the early Universe. One of these papers was entitled “The Evolution of the Universe”, and it appeared in Nature magazine on the 30th of October 1948 (Nature 1948, volume 162, pages 680-682) – here is a link to the paper.

Gamow’s October 1948 paper in Nature was entitled “The Evolution of the Elements”.

Although a man of huge intellect and inventiveness, Gamow was often sloppy on mathematical detail. Alpher and Hermann spotted an error in some of Gamow’s calculations on the matter-density, and so wrote a short letter to Nature magazine to correct these mistakes. The letter is entitled “Evolution of the Universe”, nearly the same title as Gamow’s paper, but with no “The” at the start. The letter is dated 25 October 1948. It appeared in Nature magazine on the 13th of November 1948 (Nature 1948, volume 162, pages 774-775) – here is a link to the paper.

Here is the paper in its entirety (it is short!), and I have highlighted the part which refers to a relic radiation from the early Universe, what would become known as the cosmic microwave background.

The original paper (letter) by Alpher and Hermann which makes the first prediction of the cosmic microwave background (CMB). It was published in Nature magazine on the 13th of November 1948.

As you can see, the prediction is not the main part of the paper, it just forms two sentences!

Next week, I will blog about the accidental discovery of the CMB by Penzias and Wilson, which was published 50 years ago to this month (July).

## My CMB book is finally published!

Rather than do my usual Friday post about music, today I am giving an update on my Cosmic Microwave Background (CMB) book, which I am pleased to say has finally been published. I even got my own hardcopy yesterday, although I’ve had access to the electronic copy for several weeks.

My book “The Cosmic Microwave Background – how it changed our understanding of the Universe” is published by Springer

In the book I attempt to give the background to the accidental discovery of the CMB, and what studying it has taught us about the properties of the Universe. In chapters 1 and 2 I give the background to how we know that our Earth is not the centre of the Universe, and how we know that our Milky Way galaxy is just one of billions. In Chapter 3 I tell the story of the prediction and accidental discovery of the CMB, and in Chapter 4 I discuss the COBE satellite, which in 1992 discovered in the CMB the first seeds of what would grow into galaxies. In Chapter 5 I discuss ground-based observations to study the CMB in more detail, in Chapter 6 I discus the WMAP satellite’s findings. In the final chapter I discuss the latest results, including from the Planck satellite and also the BICEP2 results claiming to have found evidence for ‘cosmic inflation’.

I got my first hard copy of the book yesterday, Thursday the 12th of February.

I have tried to write the book at a level which I hope will make it accessible to anyone. Any physics knowledge required is explained when I introduce the particular idea, and I’ve included diagrams wherever possible to help illustrate and explain key concepts.

The book is available from the Springer website in both electronic and hardcopy versions,and also through Amazon and other booksellers.

This is the link to the Springer page for the book. On the Springer website you can look at the preface to the book.

And this is the link to the Amazon page. On the Amazon website you can read the first dozen or so pages of the book, including the table of contents and the opening pages of the first chapter.

I am now working on two other books, you can find more details on a Facebook page which I have recently created

## BICEP2 and Planck to share data

I thought it was about time I gave another update on currently the most important story in astrophysics – the BICEP2 team’s possible detection of B-mode polarisation in the cosmic microwave background. I have previously blogged about this story, for example here, here and here. But, just to quickly recap, in March the BICEP2 team announced that they had detected the B-mode polarisation in the cosmic microwave background (CMB), and argued that it was evidence of gravitational waves and cosmological inflation in the very early Universe.

Since then, controversy has been the order of the day as other astrophysicists and cosmologists have argued that the BICEP2 detection was not due to the CMB at all, but rather to emission from dust in our own Milky Way galaxy. BICEP2 on their own do not have sufficient data to rule out this possibility, something they concede in their published paper. However, it would seem that the European satellite Planck do, as it has not only observed the whole sky (including the part of the sky observed by BICEP2), but has done so at five different frequencies, compared to BICEP2’s single frequency measurement.

In the last few days, it has been announced that the BICEP2 team will formally collaborate and share data with the Planck team, which I think is good news in sorting out the controversy over the BICEP2 detection sooner rather than later.

The BICEP2 team and Planck team have announced that they will collaborate and share data to help clear up the controversy over the source of the B-mode polarisation detected by BICEP2.

Although the Planck measurements of the polarisation of dust in our Milky Way will presumably become public at some point (as is normal with publicly funded science projects), this would not be for many more months. By formally collaborating with Planck, the BICEP2 team will get not only earlier access to the Planck data, but just as importantly will get the experts in the Planck collaboration working with them to properly interpret the Planck measurements. It is hoped by all in the astrophysics and cosmology communities that this collaboration between BICEP2 and Planck will lead to the issue of the origin of the detected B-mode polarisation being sorted out in a timely fashion, possibly even by the end of this year.

We shall have to wait and see!

## The prediction of the Cosmic Microwave Background

In this blog I described the first results from the Planck satellite, which is studying the Cosmic Microwave Background in greater detail than we have ever done before. But, what exactly is the Cosmic Microwave Background? Where does it come from? How was it produced?

## The origin of the elements

In 1929 Edwin Hubble published evidence that the speed with which galaxies were moving away from the Milky Way was directly related to their distance from us. Although Hubble himself never explicity stated it, this is clear evidence that the Universe is expanding. If the Universe is expanding, then of course one would expect it to have been smaller in the past.

In the 1940s the Russian-American physicist George Gamow started thinking about what the early Universe would have been like. He worked on two related theories, the first that the elements would have been created in the early Universe. The second related to the fact that a smaller, denser Universe would also have been hotter in the past.

In 1948, with his PhD student Ralph Alpher, the two published a paper titled “The Origin of Chemical Elements“. As a joke, Gamow decided to add the well-known physicist Hans Bethe’s name to the paper, so that it could be called “Alpher, Bethe, Gamow” (alpha,beta, gamma – geddit? 🙂 ).

George Gamow, who worked with his PhD student Ralph Alpher on the primordial nucleosynthesis theory.

Ralph Alpher, who was George Gamow’s PhD student at the time of writing the paper.

Hans Bethe, who played no part in writing the paper.

The famous “Alpha, Bethe, Gamow” paper from Physical Review 1948

Although the Alpher, Bethe, Gamow paper was groundbreaking, it was wrong in some of its details. It suggested that all the elements were created in the hot, early Universe. We now think (know?) this is not the case. Only hydrogen and helium were created in the early Universe, the other elements have all been created inside stars, something Sir Fred Hoyle worked out with co-workers in the 1950s.

## Alpher and Herman’s paper on the Cosmic Microwave Background

In a related paper, Alpher and Robert Herman, who was working as a post-doctoral research assistant for Gamow, calculated that the early Universe would have been a hot opaque plasma (ionised gas), and would thus have radiated like a black body. However, this radiation would not have been able to travel through the plasma as the photons would scatter of the free electrons.

The abstract of the paper by Alpher and Herman, which predicts a cosmic microwave background at a temperature of 5K (5 degrees above absolute zero).

Gamow’s article in Nature, which summarises the work on the origin of the elements and of the existence of a cosmic microwave background

But, as the Universe expanded and cooled the plasma would become a neutral gas, in that the electrons would combine with the nuclei to produce neutral atoms, allowing the photons to travel unimpeded. They calculated that these photons, which would be able to thence travel unimpeded, would now be at a characteristic black-body temperature of 5K due to the expansion of the Universe. This in the microwave part of the spectrum, hence the name Cosmic Microwave Background.

Our current understanding is pretty much what was derived in this 1948 paper, with a few refinements. Perversely, the moment the plasma became a neutral gas, which we believe to be when the Universe was about 350,000 years old, is referred to as “re-combination”, but as I tell my students, the electrons were combing with the nuclei for the first time. This is when the fog of the early Universe lifted and is the earliest radiation we can see.

In a separate blog on the history of the Cosmic Microwave Background (CMB) I will discuss how

1. the CMB was accidentally discovered in 1964
2. Gamow’s work was ignored, only to be worked out again in the early 1960s

## Update

You can read far more about the prediction of the CMB, and its accidental discovery, in my new book, “The Cosmic Microwave Background – How it changed our understanding of the Universe”.

My book “The Cosmic Microwave Background – how it changed our understanding of the Universe” is published by Springer and can be found by following this link.

The book can be found on the Springer website here, and on the Amazon website here.