Unit 1 Our Dynamic Universe

North Berwick High School Department of Physics Higher Physics Unit 1 Our Dynamic Universe Section 7 Big Bang Theory

Section 7 Big Bang Theory Note Making Make a dictionary with the meanings of any new words. How hot are the stars? 1. State that a star's colour depends on its surface temperature and give a couple of examples. 2. Briefly describe how astronomers are able to measure the surface temperature of a star. Cosmic microwave background 1. State what is meant by the called cosmic microwave background (CMB) radiation. 2. Describe how a blackbody spectrum of photons was produced and state this theory was verified using the COBE satellite. 3. Read the section on a 'fortunate accident' but do not take any notes. So what can the CMB tell us? 1. What can the CMB tell us?

Surface of last scattering 1. State what is meant by a GUT force. 2. What happened during the GUT era? 3. What happened during the electroweak era? 4. What happened during the particle era? 5. Make a timeline to show these eras. 6. State what is meant by the surface of last scattering. The Big Bang 1. Describe the Big Bang theory in simple terms. Clumping 1. Why is clumping a problem for the Big Bang theory and state the possible solution? Closed, open and flat 1. State what the above terms mean and explain how they are affected by critical density. Many theories 1. Read this section but do not take any notes.

How can knowing the elements in the universe tell us about the Big Bang? 1. Explain briefly how the Big Bang theory is supported by the nucleosynthesis era. 2. Why were elements heavier than helium not produced in the early universe? What can I look at to see the Big Bang? 1. Read the section up to Olber's paradox. Before you read any further, see if you can come up with an explanation. 2. Produce a short explanation of Olbers' paradox. (The BBC website gives a good, short explanation.)

Section 7 Big Bang Theory Contents Content Statements... 1 How hot are the stars?... 2 Cosmic microwave background Student activity... 5 A fortunate accident: how the CMB was discovered... 6 So what can the CMB tell us?... 7 Surface of last scattering... 8 Dark matter and the universe... 10 The Big Bang... 10 Clumping... 10 Closed, open and flat... 11 Many theories... 11 Links... 12 How can knowing the elements in the universe tell us about the Big Bang?... 13 Student activities... 14 What can I look at to see the Big Bang?... 14 Big Bang Theory Problems... 16 Solutions... 18

Content Statements Contents Notes Contexts a) The temperature of stellar objects. Stellar objects emit radiation over wide range of wavelengths. Although the distribution of energy is spread over a wide range of wavelengths, each object emitting radiation has a peak wavelength which depends on its temperature. The peak wavelength is shorter for hotter objects than for cooler objects. Also, hotter objects emit more radiation per unit surface area at all wavelengths than cooler objects. Thermal emission peaks allow the temperature of stellar objects to be measured. Remote sensing of temperature. Investigating the temperature of hot objects using infrared sensors. Change in colour of steel at high temperatures. Furnaces and kilns. b) Evidence for the Big Bang. The Universe cools down as it expands. The peak wavelength of cosmic microwave background allows the present temperature of the Universe to be determined. This temperature corresponds to that predicted after the Big Bang, taking into account the subsequent expansion and cooling of the Universe. History of Cosmic Microwave Background (CMB) discovery and measurement. COBE satellite. Other evidence for the Big Bang includes the observed abundance of the elements hydrogen and helium and the darkness of the sky (Olber s Paradox). 1

Section 7 The Big Bang Theory Whatʼs stellar temperature got to do with Big Bang theory? The Big Bang theory states that the universe started with a sudden appearance of energy at a singular point, which consequently (and very quickly) became matter, and then expanded and cooled rapidly. The theory therefore predicts that the universe should now, 13.7 billion years later, have a very cool temperature. If we can measure this temperature we can see if it accords with Big Bang theory. If we can understand stellar temperatures, it can help us know how to find the average temperature of the universe. How hot are the stars? We typically think of stars as bright white pinpoints of light in our night sky. However, if you look carefully at the stars, even without binoculars or a telescope, you will see a range of colours from red through yellow to blue. For example, Betelgeuse (Orion s armpit) looks red, Pollux (in Gemini) is similar to the Sun and is yellow, and Rigel has a blue tint. A star s colour depends on its surface temperature. Dark red stars have surface temperatures of about 2500 K. The surface temperature of brighter red stars is approximately 3500 K, yellow stars, like our Sun, are roughly 5500 K, whilst blue stars range from about 10,000 to 50,000 K in surface temperature. Thermal emission peak Stars emit radiation over a wide range of wavelengths. The graph to the right is called a thermal emission peak which shows how the intensity of radiation produced (y-axis) from stars of different temperatures (the different lines on the graph) is related to the wavelength of light emitted from the star. Essentially thermal emission peaks allow the temperature of stellar objects to be determined. 2

Three details emerge from studying these peaks: 1. Stellar objects emit radiation over the complete electromagnetic spectrum. 2. Each stellar object has a peak wavelength that depends on its temperature. 3. As the temperature of the star increases: a. There is more energy (intensity of radiation) at each wavelength b. The peak wavelength shifts to shorter wavelengths. Stars appear to the naked eye to be only one colour but they actually emit a broad spectrum of colours. You can see that starlight consists of many colours when using a prism to separate and spread the colours of the light of the Sun, a yellow star. These colours range from red, produced by the photons (particles of light) with the least energy, to violet, produced by the most energetic photons. Astronomers are able to make accurate measurements of surface temperature by comparing the star s apparent brightness through different filters. The thermal radiation spectra have very distinct shapes; the difference in apparent brightness allows astronomers to match the light emitted to surface temperature. Visible light is one of the bands of the electromagnetic radiation spectrum. These range from the least energetic, radio waves, to the most energetic, gamma rays. All six bands can be emitted by stars, but most individual stars do not emit all of them. Astronomers study a star s spectrum by separating it, spreading it out and displaying it. The display itself is also known as a spectrum. The scientists study thin gaps in the spectrum. When the spectrum is spread out from left to right, the gaps appear as vertical lines. The spectra of stars have dark absorption lines where radiation of specific energies is weak. In a few special cases in the visible spectrum stars have bright emission lines where the radiation of specific energies is especially strong. An absorption line appears when a chemical element or compound absorbs radiation that has the amount of energy corresponding to the line. For 3

example, the spectrum of the visible light coming from the Sun has a group of absorption lines in the green part of the spectrum. Calcium in an outer layer of the Sun absorbs light rays that would have produced the corresponding green colours. Although all stars have absorption lines in the visible band of the electromagnetic spectrum, emission lines are more common in other parts of the spectrum. For instance, nitrogen in the Sun s atmosphere emits powerful radiation that produces emission lines in the ultraviolet part of the spectrum. The following webpage has an activity on this subject: http://www.astrosociety.org/education/publications/tnl/32/starscience3.html. 4

Cosmic microwave background Student activity There is a student activity available called CMB_Kerrigan.pdf. According to Big Bang theory, the early universe was a very small, hot and dense place, and as it expanded, the gas within it cooled. Thus the universe should be filled with radiation that is literally the remnant heat left over from the Big Bang, called cosmic microwave background (CMB) radiation. When the universe was half its current size, matter was eight times denser and the CMB was twice as hot. So when the universe was one hundredth of its present size, the CMB was a hundred times hotter (273 degrees above absolute zero, 0 C). In addition to this CMB radiation, the early universe was filled with hot hydrogen gas with a density of about 1000 atoms per cubic centimetre. When the visible universe was only one hundred millionth its present size, its temperature was 273 million degrees above absolute zero and matter had a density comparable to the density of air at the Earth s surface. At these high temperatures, the hydrogen was completely ionised into free protons and electrons. Since the universe was so very hot, atoms did not form in the early universe, only free electrons and nuclei. The CMB photons easily scattered off electrons. So photons were sent in every direction by the early universe, just as light scatters through a dense fog. This process of multiple scattering produces what is called a thermal or blackbody spectrum of photons. According to the Big Bang theory, the frequency spectrum of the CMB should have this blackbody form. This was indeed measured with tremendous accuracy by the FIRAS experiment on NASA s COBE satellite. 5

The graph below, NASA, shows the prediction of the energy spectrum of CMB radiation compared to the observed energy spectrum. The FIRAS experiment measured the spectrum at 34 equally spaced points along the blackbody curve. The error bars on the data points are so small that they cannot be seen under the predicted curve in the figure! There is no alternative theory yet proposed that predicts this energy spectrum. The accurate measurement of its shape was another important test of the Big Bang theory. A fortunate accident: how the CMB was discovered See http://www.teachersdomain.org/resource/ess05.sci.ess.eiu.microwave/. The existence of CMB radiation was first predicted in the1940 s, but in 1965 Arno Penzias and Robert Wilson at the Bell Telephone Laboratories in Murray Hill, New Jersey, discovered the noise by accident. The radiation was acting as a source of excess noise in a radio receiver they were building. Coincidentally, researchers at nearby Princeton University, led by Robert Dicke and including Dave Wilkinson of the WMAP science team, were devising an experiment to find the CMB. When they heard about the Bell result they immediately realised that the CMB had been found. Penzias and Wilson 6

shared the 1978 Nobel Prize in physics for their discovery they may not have set out to find CMB radiation, but they were the first to do so. Today, CMB radiation is very cold, only 2.725 K above absolute zero and this cooling of the photon means its frequency has reduced until the radiation shines primarily in the microwave portion of the electromagnetic spectrum and is invisible to the naked eye. However, it can be detected everywhere we look in the universe. In fact, if we could see microwaves, the entire sky would glow with a brightness that was astonishingly uniform in every direction. The temperature is uniform to better than one part in a thousand! This uniformity is one compelling reason to interpret this radiation as remnant heat from the Big Bang; it would be very difficult to imagine a local source of radiation that was this uniform. In fact, many scientists have tried to devise alternative explanations for the source of this radiation but none have succeeded. So what can the CMB tell us? We have already seen that in looking at stars and galaxies we are looking at the past. Most stars visible to the naked eye in the night sky are about 10 to 100 light years away, so we see them as they were 10 to 100 years ago. We see Andromeda, the nearest big galaxy, as it was about 2.5 million years ago. Observing distant galaxies with the Hubble Space Telescope, astronomers see them as they were a few billion years after the Big Bang (between 12 and 14 billion years ago). CMB radiation was emitted only a few hundred thousand years after the Big Bang, and therefore long before stars or galaxies ever existed. Thus, by studying the physical properties of the radiation, we can learn about conditions in the universe during very early times and on very large scales, since the radiation we see today has travelled over such a large distance. 7

Surface of last scattering We ve seen that in the early universe temperatures were so high that matter as we typically describe it didn t exist. The first 10 43 s after the initial big bang is known as the Planck era. This was a time of quantum fluctuations on a vast energy scale. At the moment there are not any thorough explanations of this period. Between 10 43 s and 10 38 s there was a period known as the GUT era. A GUT force is a unification of the strong, weak and electromagnetic forces, and generated a very brief but hugely significant period of expansion lasting approximately 10 36 s. During this time parts of the universe grew from the size of an atom to the size of a solar system. After this rapid expansion came the electroweak era. The universe continued to expand, but at the same time it was cooling. The GUT force separated into strong and electroweak forces, and gravity was also a significant force. This is the first period after the Big Bang for which we can find evidence to support the theoretical predictions; when CERN was able to detect for the first time W and Z bosons, it was only able to achieve them at energies equivalent to a temperature greater than 10 15 K. This is what had been predicted by Big Bang theory for when the universe had an age of 10 10 s. After the electroweak era was the particle era; photons that had been the dominant form of energy were able to form into quarks, the component parts of protons and neutrons. By the end of this era, when the universe was around 1 millisecond old, all the quarks had formed protons and neutrons, and other particles such as electrons, neutrinos and possibly WIMPs had formed. Eventually, the universe cooled to around 3000 K cool enough for protons and electrons to combine to form neutral hydrogen. This occurred roughly 400,000 years after the Big Bang, when the universe was about one eleven hundredth its present size. CMB photons are known to interact very weakly with neutral hydrogen. 8

The behaviour of CMB photons moving through the early universe is analogous to the propagation of optical light through the Earth s atmosphere. Water droplets in a cloud are very effective at scattering light, while light moves freely through clear air. Thus, on a cloudy day, we can look through the air out towards the clouds, but cannot see through the opaque clouds. Cosmologists studying CMB radiation can look through much of the universe back to when it was opaque: a view back to 400,000 years after the Big Bang. This wall of light is called the surface of last scattering since it was the last time most of the CMB photons directly scattered off matter. When we make maps of the temperature of the CMB, we are mapping this surface of last scattering. As shown above, one of the most striking features about the CMB is its uniformity. Only with very sensitive instruments, such as COBE and WMAP, can cosmologists detect fluctuations in the CMB temperature. By studying these fluctuations, cosmologists can learn about the origin of galaxies and their large-scale structure, and measure the basic parameters of the Big Bang theory. An alternative view is presented here: http://www.deceptiveuniverse.com/chapter5.htm. 9

Dark matter and the universe The search for dark matter is about more than explaining discrepancies in galactic mass calculations. The missing matter problem has people questioning the validity of current theories about how the universe formed and how it will ultimately end. The Big Bang In the mid-1950s a new theory of how the universe formed emerged. The Big Bang theory says that the universe began with a great explosion. The theory evolved from Doppler shift observations of galaxies. It seems that, no matter which direction astronomers point their telescopes, the light from the centre of the galaxies is red-shifted. (Doppler shift caused by rotational velocity can only be detected at the sides of a galaxy.) Observing red-shifted galaxies in every direction implies expansion in all directions: an expanding universe. The Big Bang theory is a current model for the origin of our universe and proposes that all the matter that exists was, at one time, compressed into a single point. The Big Bang distributed all the matter evenly in all directions. Then the matter started to clump together, attracted by gravity, to form the stars and galaxies that we see today. The expansion generated by the Big Bang was great enough to overcome gravity. We still see the effects of that force when we see red-shifted galaxies. Clumping One of the problems with the Big Bang theory is its failure to explain how stars and galaxies could form in a young universe that was evenly distributed in all directions. What started the clumping? In a smooth universe, every particle would have the same gravitational effect on every other particle and the universe would remain the same. But something supplied the initial gravity to allow galaxies to form. Physicists suggest dark matter WIMPs as the solution. Since WIMPs only affect baryon matter gravitationally, physicists say this dark matter could be the seed of galactic formation. We don t have a completely successful model of galaxy formation, explains Walter Stockwell, but the most successful models to date seem to need plenty of non-baryonic dark matter. 10

Closed, open and flat There are three current scenarios that predict the future of the universe. If the universe is closed, gravity will catch up with the expansion and the universe will eventually be pulled back into a single point. This model suggests an endless series of big bangs and big crunches. An open universe has more bang than gravity it will keep expanding forever. The flat universe has exactly enough mass to gravitationally stop the universe from expanding, but not enough to pull itself back in. A flat universe is said to have a critical density of 1. What does the expansion of the universe have to do with the missing mass? The more mass, the more gravity. Whether the universe is closed, open or flat depends on how much mass there is. This is where dark matter com es into the picture. Without dark matter, critical density lies somewhere between 0.1 and 0.01, and we live in an open universe. If there is a whole lot of dark matter, we could live in a closed universe. Just the right amount of dark matter and we live in a flat universe. The amount of dark matter that exists determines the fate of the universe. Many theories Scientists are tossing theories back and forth. Some are skeptical of WIMPs; particle physicists say MACHOs will never account for 90% of the univer se. Some, like H.C. Arp, G. Burbage, F. Hoyle and J.V. Narlikan claim that discrepancies like the dark matter problem discredits the Big Bang theory. In the scientific journal Nature they proclaim, We do not believe that it is possible to advance science profitably when the gap between theoretical speculation becomes too wide, as we feel it has over the past two decades. The time has surely come to open doors, not to seek to close them by attaching words like standard and mature to theories that, judged from their continuing non-performance, are inadequate. Others say there is no missing mass. In his book What Matters: No Expanding Universe No Big Bang, J.L. Riley claims that galactic red shift is just the effect of light turning into matter as it ages, and not the universe expanding. But most scientists, like Walter Stockwell, have faith in the Big Bang. The theorists will come up with all sorts of reasons why this or that can or cannot be and change their minds every other year, he says. We experim entalists will trudge ahead with our experiments. The Big Bang theory will outlive any 11

of this stuff. It works very well as the overall framework to explain how the universe is today. Now the missing mass problem is threatening humankind s place in the universe again. If non-baryonic dark matter does exist, then our world and the people in it will be removed even farther from the centre. Dr Sadoulet tells the New York Times, It will be the ultimate Copernican revolution. Not only are we not at the center of the universe as we know it, but we aren t even made up of the same stuff as most of the universe. We are just this small excess, an insignificant phenomenon, and the universe is something completely different. If scientists prove that non-baryonic matter does exist, it would mean that our world and the people in it are made of something which comprises an insignificant portion of the physical universe. A discovery of this nature, however, probably will not affect our day-to-day process of living. It s hard for me to imagine people getting bothered by the fact that most of the universe is something other than baryonic. How many people even know what baryonic means? comments Walter Stockwell. Most of the universe is something other than human. If their philosophy already accepts that humans are not the center of the universe, then saying protons and neutrons aren t the center of the universe doesn t seem like much of a stretch to me. Perhaps the only thing a dark matter discovery will give us is some perspective. Links Design of the universe: http://www.ted.com/talks/george_smoot_on_the_design_of_the_universe.html 12

How can knowing the elements in the universe tell us about the Big Bang? The most abundant element in the universe is the simplest atom, hydrogen, and there are many theories to support why there is so much of it. However, just over a quarter of the ordinary matter in the universe is made up of helium. Some of this comes from hydrogen fusion in the stars, but this source can only account for about 10% of the observed helium in the universe. The rest must have already been in existence in the clouds of matter that formed the galaxies. The helium has been created by fusion, but not in the stars. The heat for this fusion must have come from the universe itself. Knowing the current temperature of the CMB lets us know how hot the universe has been in the past, and how much helium could have been made. The Big Bang theory is again supported by this evidence. Twenty-five per cent of the universe would have become helium during the nucleosynthesis era. In the early parts of this 5-minute era, the universe s temperature was 10 11 K and protons were able to be made into slightly heavier neutrons. As temperatures cooled, neutrons stopped being formed, but there was still sufficient energy for protons and neutrons to fuse into deuterium (the isotope of hydrogen containing a proton and neutron). These deuterium nuclei fused to become helium. At about 1 minute old, the universe stopped destroying the newly formed nuclei with gamma rays, and almost all the neutrons had gone into creating helium. The calculated 7:1 hydrogen: helium ratio at that time would give the elemental universe 75% hydrogen and 25% helium at the end of the nucleosynthesis era. So with all this energy about, why were only hydrogen and helium produced by the Big Bang? The reason is related to how rapidly the universe was expanding at the time. When the universe reached an age of 1 minute, the density and temperature had fallen so low that producing heavier elements such as oxygen or carbon was impossible. Some helium, deuterium and protons did combine to form small amounts of lithium, but only really trace quantities. All the heavier elements created were fused and formed in stars nearly a billion years later. 13

Student activities Some student activities can be seen at: http://imagine.gsfc.nasa.gov/docs/teachers/elements/imagine/activities.html. What can I look at to see the Big Bang? Throughout this section there have been links questioning the existence of the Big Bang. Being the pre-eminent model of how the universe was created, and matching with the standard model of particle physics, it is the main target to be shot at, and unless we continue to question it then, as a theory, it cannot grow stronger. As much of this section of the course has been based on the knowledge gained from using the world s leading telescopes and detectors, there has been little in the way of observation or practical work. However, here is a practical we can all do to observe the universe s origins. Go out on a clear night, away from street lights, and ask yourself this question. Why is it dark? Well the obvious answer is because your side of the Earth has spun away from the Sun; it is night time. But the universe is infinite and unchanging, with an infinite number of stars evenly arranged, radiating in all directions. Kepler realised that if this was the case then the entire night sky would be as bright as daytime. We know, of course, that this is not true and the scenario is named after a German astronomer of the 1800s as Olber s paradox. To explain how this comes about imagine you are sitting in the middle of the school dining hall at lunchtime. If you look in any direction you re likely to see another student. On a quiet day, you may be able to see through the gaps and glimpse the walls of the room, but the busier it gets, the fewer gaps there are. In an infinite dining hall there would be no gaps at all; in every possible direction a student would be blocking your view. In an infinite, uniform, unchanging universe the stars are like the students in our infinite dining hall. This means we would see a star in every direction, and everywhere in the night sky would be as bright as the surface of the Sun. Any matter blocking our view would be heated to such a point as to glow with the same radiance or be evaporated away. 14

Our options to rationalise what we see in reality are either that there are a finite number of stars or that the universe isn t unchanging. Remember that until the middle of the 20th century the historical scientific view hadn t found any evidence to change the literal biblical translation that creation had been completed and that the cosmos was, therefore, unchanging. So the only logical conclusion, as supported by Kepler, was that there were only a limited number of stars, with nothing beyond them. In the early 20th century this view changed. It was thought that the Milky Way contained all the stars, but that the universe was infinite. Stars were a little like all the tables and chairs being arranged near the middle of o ur infinite dining hall. However, later on Hubble and others observed galaxies distributed through space with a pretty uniform pattern and at distances beyond the Milky Way. Big Bang theory takes an alternative view of the universe. The theory suggests that we can only see a limited number of stars because there was a starting point to the universe. There may be an infinite number of stars, but we can only see those inside our cosmological horizon. Not all the tables and chairs are finally arranged yet. There are other explanations for this paradox, but none other than the Big Bang theory explains all our observations so neatly. See the following websites: http://www.bbc.co.uk/dna/h2g2/a765029 http://www.williams.edu/astronomy/course-pages/419t/olbers.pdf 15

Big Bang Theory Problems 1. The graphs below are obtained by measuring the energy emitted at different wavelengths from an object at different temperatures. P Q (a) (b) (c) (d) Which part of the x-axis, P or Q, corresponds to ultraviolet radiation? What do the graphs show happens to the amount of energy emitted at a certain wavelength as the temperature of the object increases? What do the graphs show happens to the total energy radiated by the object as its temperature increases? Each graph shows that there is a wavelength max at which the maximum amount of energy is emitted. (i) Explain why the value of max decreases as the temperature of the object increases. 16

(ii) The table shows the values of max at different temperatures of the object. Temperature /K max / m 6000 4 8 10 7 5000 5 8 10 7 4000 7 3 10 7 3000 9 7 10 7 Use this data to determine the relationship between temperature T and max. Choose a suitable unit for your relationship. (e) Use your answer to (d) (ii) to calculate: (i) (ii) (iii) (iv) the temperature of the star Sirius where max is 2 7 10 7 m the value of max for the star Alpha Crucis which has a temperature of 23,000 K the temperature of the present universe when max for the cosmic microwave radiation is measured as 1 1 10 3 m. the approximate wavelength and type of the radiation emitted by your skin, assumed to be at a temperature of 33 o C. 17

Solutions 1. (a) P (b) (c) Energy emitted increases Increases (d) (ii) T x max = 2 9 10 3 m K (e) (i) T =11, 000 K (ii) max = 1 3 10 7 m T = 2 6 K max = 9 5 10 6 m, infrared 18