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OPTION D: LESSON 5 Cosmology (Including the Big Bang) Newton’s model of Universe Newton Believed that the universe is infinite in both space and time. It is uniform and static. This means that there are an infinite number of stars heading out in all directions to infinity. If this were not the case, then the universe would collapse under its own gravitational force. Oblers’ Paradox If the universe extends infinitely, then eventually if we look out into the night sky, we should be able to see a star in any direction, even if the star is really far away. Since the universe was infinitely old, the light from stars at extremely far distances would have already reached us, even if they were 40 billion light years away. If there are infinite stars, then you should be able to see a star anywhere in the night sky, and so the sky should have the same brightness everywhere. But (at night) the sky is dark! (Ok, dark but speckled with bright points of light called stars!) How can this be explained? Something is not right with Newton’s model of the Universe. Oblers’ paradox Why is the night sky dark? or Why isn't the night sky as uniformly bright as the surface of the Sun? If the Universe has infinitely many stars, then it should be. Oblers’ Paradox in tree form With a big enough forest, you will see a trees no matter where you look… Solution to Oblers’ http://www.youtube.com/watch?v=gxJ4M7tyLRE Newton’s Model of the Universe is wrong. The Universe is expanding, so distant stars are red- shifted out of the visible spectrum. (Doppler effect) . The Universe is young (and not infinite in time). Light from really really distant light hasn't had time to reach us yet. We are looking back in time to see the Universe before the stars were created! THE BIG BANG MODEL Doppler effect • In astronomy, the Doppler effect was originally studied in the visible part of the electromagnetic spectrum. Today, the Doppler shift, as it is also known, applies to electromagnetic waves in all portions of the spectrum. • Also, because of the inverse relationship between frequency and wavelength, we can describe the Doppler shift in terms of wavelength. Radiation is redshifted when its wavelength increases, and is blueshifted when its wavelength decreases. Doppler effect • In astronomy, the Doppler effect was originally studied in the visible part of the electromagnetic spectrum. Today, the Doppler shift, as it is also known, applies to electromagnetic waves in all portions of the spectrum. • Astronomers use Doppler shifts to calculate precisely how fast stars and other astronomical objects move toward or away from Earth. • Notice how the absorption spectra of the sun (at the top) and the supercluster BAS11 (on the bottom) compare. • Both have the same pattern of absorption lines, indicating they are from the same elements, but the lines on the lower picture are shifted towards the right of the spectrum (shifted towards the red!). This indicates that BAS11 is moving away from us. Doppler Shift The change in wavelength due to the Doppler shift is related to the “speed” of the object moving by: λ − λ0 ∆λ 𝑣 = ≈ λ0 λ0 𝑐 Where: λ is the observed wavelength. λ0 is the wavelength emitted. Δ λ is the change in wavelength. v is the speed of the object. c is the speed of light. Note: This equation relies on the v<<c. In Astrophysics, we assign this ratio the letter z to indicate the redshift of a galaxy. ∆λ 𝑣 𝑧= ≈ λ0 𝑐 Hubble’s law Edwin Hubble (and a guy called Milton Humanson) noticed that all observed galaxies displayed a red shift. Hubble then used observed (type Ia) supernovae in distant galaxies as a “standard candle” to measure the distance to these galaxies. Hubble compared the distance to these galaxies with the speed they were receding. When a graph is plotted of speed of galaxies vs distance, we end up with a direct relationship. So the speed of recession of galaxies is related to their distance from Earth by: 𝑣 = 𝐻0 𝑑 Where: v is the speed of recession. d is the distance to the galaxy. H0 is the “Hubble Constant”. The current best estimate of the Hubble constant is 70 kms-1Mpc-1. Implication of Hubble Law and Hubble Constant. The fact that all there is a direct relationship between speed of galaxies and their distance from us implies that at an earlier point in time, everything in the Universe was much closer together. In fact, we can trace the universe backwards to a point in time (~13.7 billion years ago) when the Universe was compressed into a space smaller than the size of 1 atom. From this point in time, the Universe expanded in the “Big Bang” creating time and space. The Hubble constant gives us an estimate of the current rate of expansion of the universe. Background radiation • In 1960 two physicists, Dicke and Peebles, realising that there was more Helium in the universe than could be produced by stars. • They proposed that in the beginning of the Universe it was at a sufficiently high temperature to produce Helium through fusion. • In this process a great amount of highly energetic radiation would have been produced. However, as the Universe expanded and cooled, the energy of that radiation decreased as well (wavelength increased). • It was predicted that the actual photons would have an maximum λ corresponding to a black body spectrum of 3K. • Weins law tells us that the radiation from a black body of temperature 3 K would be in the microwave region of the spectrum. • So, we should be looking for microwave radiation. Background radiation • Shortly after this prediction, two other physicists Penzias and Wilson were working with a microwave aerial. They found that no matter in what direction they pointed the aerial it picked up a steady, continuous background radiation. Background radiation • In every direction, there is a very low energy and very uniform radiation that we see filling the Universe. This is called the 3 Degree Kelvin Background Radiation, or the Cosmic Background Radiation, or the Cosmic Microwave Background (CMB). • These names come about because this radiation is essentially a black body with temperature slightly less than 3 degrees Kelvin (about 2.76 K), which peaks in the microwave portion of the spectrum. Age of the Universe We can also use the Hubble constant to estimate the age of the universe. Since we can assume that all matter started out at the same location in space and travelled outwards. The speed of objects in the universe is related to their distance from us and the time since the start of the universe. 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑠𝑝𝑒𝑒𝑑 = 𝑡𝑖𝑚𝑒 𝑠𝑖𝑛𝑐𝑒 𝑡ℎ𝑒 𝑢𝑛𝑖𝑣𝑒𝑟𝑠𝑒 𝑏𝑒𝑔𝑎𝑛 So: 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑠𝑝𝑒𝑒𝑑 But Hubble's law tells us that the speed of an object in the universe is directly related to its distance: 𝑣 = 𝐻0 𝑑 𝑑 𝑡= 𝐻0 𝑑 So: 1 𝑡= 𝐻0 𝑡𝑖𝑚𝑒 𝑠𝑖𝑛𝑐𝑒 𝑡ℎ𝑒 𝑢𝑛𝑖𝑣𝑒𝑟𝑠𝑒 𝑏𝑒𝑔𝑎𝑛 = This gives us an upper estimate for the age of the universe. In fact the universe is likely younger since gravitational attraction will slow the rate of expansion of the universe over time. Background radiation Why is the background radiation an evidence for the Big Bang? • The cosmic background radiation (sometimes called the CBR), is the afterglow of the big bang, cooled to a faint whisper in the microwave spectrum by the expansion of the Universe for 15 billion years (which causes the radiation originally produced in the big bang to redshift to longer wavelengths). Big Bang The Big Bang Model is a broadly accepted theory for the origin and evolution of our universe. It postulates that 12 to 14 billion years ago, the portion of the universe we can see today was only a few millimetres across. It has since expanded from this hot dense state into the vast and much cooler cosmos we currently inhabit. We can see remnants of this hot dense matter as the now very cold cosmic microwave background radiation which still pervades the universe and is visible to microwave detectors as a uniform glow across the entire sky. Big Bang The singular point at which space, time, matter and energy were created. The Universe has been expanding ever since. Main evidence: Expansion of the Universe – the Universe is expanding (redshift) it was once smaller it must have started expanding sometime “explosion” Background radiation evidence of an hot Universe that cooled as it expanded He abundance He produced by stars is little there is no other explanation for the abundance of He in the Universe than the Big Bang model. The Big Bang If we mathematically trace the position of all the galaxies in the universe backwards in time, we get to a point approximately 13.8 billion years ago, when all matter is in the same location. To do this, we had to use general relativity. This implies a that there is a point when all matter was in a region that was infinitely dense. (Really it means that our ability to understand physics breaks down, or “the laws of physics cannot model the exact state of the universe at that point in time”). The Big Bang: Inflation and history of the universe. I don’t think you need to memorize this, but it is worth being familiar with the stages and the different processes. HL should be much more familiar than SL In the early stages of the universe (the first 10-45~10-36 seconds or so which was about 13.8 Billion years ago) , it was incredible hot and dense. This period is referred to as “Unification of Forces”, and is considered the start of the Universe. The next step, (between 10-36 to 10-32 seconds of the Universe’s age) there was a period of rapid expansion, where it grew exponentially. This is called Inflation. After inflation, the Universe was about 10-29 times its current size. The next period was between 10-32 and 10-5 seconds of Universe age. During this period the Universe continues to expand and cool, but at a slower rate. During this time Matter and Anti-Matter (in the form of quarks and leptons) interact. There appears to be more Anti-Matter than Matter. This period is called the Quark-Lepton Era. After the first 10-5 seconds it the Universe has cooled to a point protons and neutrons (Hadrons) could be formed. This is called the Hadron Era. The next stage 10-2s to 103 s Nucleosynthesis starts to occur. Protons and neutrons combine, forming deuterium and helium. The amount of matter left is a relatively small amount compared to what started, and it is what is left over after matter and anti-matter interacted during Quark-Lepton Era. By this stage the formation of light nuclei has generally finished, and the Universe exists as a plasma of electrons, protons, neutrons, and helium. At this stage photons are interact with matter. This stage is called the Plasma era. After approximately 3x105 years, it had cooled (3000K) enough to the point at which helium and hydrogen nuclei could join with electrons to form stable nuclei. At this point photons no longer interact with matter, and matter becomes “transparent to radiation”. What we observe as the CMB is radiation from this point onwards. 109 years to present…Finally gravitation can start to bring matter together, this leads to the formation of stars, galaxies etc… Cosmic Background Radiation The image on the right shows the CMB as seen from Earth. The variation in colours represents slight changes in temperature as measured by the CMB. Although there are slight differences (we’ll talk more about these later), on average, whatever direction we look, the CMB is pretty much the same. The image is this shape b/c it is a projection of the entire sky “wrapping around the Earth”. We say it is “Isotropic”, meaning equal in all directions. The fact the CMB is isotropic is very important. It implies that there is no “centre of the Universe”. This means that the Universe is not expanding in the same way as-say an exploding watermelon would expand into a room. If you were living on a chunk of exploding watermelon and you look in one direction (towards where the centre of the watermelon was) you would see remnants of the heat of the explosion (and you would see all the other chunks of watermelon moving away from you). If you look away from the centre of the watermelon in the direction you were moving, it would be colder (and you would see many fewer chunks of watermelon!) The CMB courtesy of NASA and ESA Slowmo guys! The Universe is not like that. Every direction you look, it is pretty much the same. There is no area of extra hot, nor is there an area of extra cold. The CMB is the pretty much the same temperature everywhere (Isotropic!) Indicating that there is no “centre” that we are expanding away Follow link to see exploding watermelon from. https://www.youtube.com/watch?v=hMjL76obRLI Big Bang and Expansion of the Universe. It is very important to realize that even though we say the Universe is expanding, it is not expanding “into anything”. Time and space are getting larger. The Universe is getting larger and larger, but there is nothing that exists “outside” the universe for it to grow into. And therefore whatever direction you look, you see the same amount of universe! In fact, time and space were created during the big bang! Cosmological Red-Shift The idea that the Universe isn’t expanding into anything, it is just getting bigger changes the way that we have to think about the motion of the galaxies. Other galaxies are not actually moving away from us, it is simply that space in-between us and them is getting bigger. Remember, we used the redshift of light from the Galaxies to determine the expansion of the Universe. Well, if the Galaxies are not moving away from us, then how is it that radiation from them is redshifted? Cosmological Red-Shift Since space is constantly growing, it is like the Universe is being “re-scaled”. This means that the space between distant galaxies and us is bigger, but it also means that over time, the space within a wavelength of a wave has also grown. This means that when we receive radiation from distant galaxies (that was sent a long time ago), the waves have effectively grown (since space within it has grown), meaning that we measure a longer wavelength when we receive the wave than we would have done when it was sent. Cosmological Redshift: Scale factor. The “cosmological redshift” is very similar to the “Doppler redshift”. Previously we saw the redshift was: ∆λ λ − λ0 𝑣 𝑍= = ≈ Only true if c>>v. λ0 λ0 𝑐 Where: λ is the wavelength of radiation measured. λ0 is the wavelength of radiation emitted. v is the velocity of the motion of the object emitting radiation. c is the speed of light. We can rearrange this. ∆λ λ − λ0 λ = = −1 λ0 λ0 λ0 Well, now instead of it being a “receding” star that is emitting light. It is actually a “rescaling” of the universe. 𝑍= So if the redshift “Z” is 2, then this means that the measured wavelength is 3 times the size it was when it was emitted. This can be interpreted to means that the universe is 3 times larger than it was when the radiation was emitted. So now: Where: ∆λ λ 𝑅 𝑍= = −1= −1 λ0 λ0 𝑅0 True irrespective of the “speed” of growth of the universe. R is the size of the observable universe. R0 is the radius of the observable universe when the light was emitted. Cosmological Redshift: Scale factor. So now: λ 𝑅 𝑍 = −1= −1 λ0 𝑅0 We call “R” the “cosmic scale factor”. HL Only The fate of the Universe. So what will happen to the universe? Three different possibilities: It will keep expanding forever. “Open Universe” Expansion will gradually slow down until at a point infinitely far into the future, it will stop expanding and start to contract (at infinity, ie never). “Flat Universe” It will start contracting due to its own gravitational pull . “Closed Universe” HL Only Fate of the Universe The three different theories are shown in a graph of “radius (or size) of the universe” vs. “Time” Notice each different model has the start (Big Bang) at a slightly different point in time in the past. With the “open universe” starting the furthest back. Fate of the Universe HL Only Universe Closed Enough matter density is high enough to stop expansion gravity will stop the Universe expansion and cause it to contract (Big Crunch) Flat Critical density Universe will only start to contract after an infinite amount of time Open Not Enough matter density is such that gravity is too weak to stop the Universe expanding forever HL Only Fate of the Universe It is the “mass density” of the Universe that will control which of the three fates will occur. Mass density is the amount of matter per unit volume. “Critical Density” (ρc) is the value for mass density that is the dividing line between an open universe and a closed universe. If the density of the universe is less than critical density, If ρ<ρc the universe will be “Open” expanding forever. If the density of the universe is greater than critical, If ρ>ρc the universe will be “Closed”, ultimately stopping its expansion and then contracting. If the density of the universe is the same as the critical density If ρ=ρc the universe will be “Flat”, it will expand forever at a rate that approaches zero. Critical density is approximately ρc≈10-26 kgm-3 HL Only Density of the Universe. It is difficult to estimate the density of the Universe by determining the mass of all the objects we can see within a large volume of space and dividing by that volume, because when this was tried, the density of Galaxies wasn’t even enough to keep a galaxies moving around a “cluster centre” (the way we see that they actually are!) We now know that we can see only about 10% of the Universe. The rest of the matter in the Universe is “Dark Matter” (dark b/c we cannot see it!) Dark Matter. There are two proposed forms of dark matter to explain the discrepancy between the density calculated by observation, and the density necessary to bind the universe together as we observe it. MACHO’s WIMP’s Massive compact halo objects – brown and black dwarfs or similar cold objects and even black holes. Non-barionic weakly interacting massive particles (neutrinos among other particles predicted by physics of elementary particles) MACHOs Massive Compact Halo Objects. Really big astronomical things that we can’t see. Include Brown Dwarfs, Black Holes, even Neutron Stars and Planets that drift through space unassociated from any objects. Wimps Weakly Interacting Massive Particles. Tiny elementary particle that do not interact with other elements. Examples of these are Neutrinos and other elementary particles. So? Turns out that distance objects are moving away from us much faster than predicted by the big bang. Based on Gravitation, we would expect them to be slowing down, but they are not. In fact observational data suggests that the rate that they are moving away from us is INCREASING. This suggests that the Universe is more OPEN than expected. This must explained by the existence of some energy that we can’t measure (or observe). We call this energy “Dark Energy” “Dark Energy” is the name of the energy that creates a repulsive force that explains the acceleration of the universe. So although there is evidence that the Universe is at “Critical Density”, it is not expanding as suggested by any of the graphs. HL Only http://upload.wikimedia.org/wikipedia/commons/thumb/6/6f/CMB_Timeline300_no_W MAP.jpg/440px-CMB_Timeline300_no_WMAP.jpg Astrophysics is International… For example the Atacama Large Millimeter Array is a large radio telescope in Chile. It is an international partnership between Europe, the United States, Canada, East Asia and the Republic of Chile. Costing more than a billion US dollars, it is the most expensive ground-based telescope in operation. ALMA began scientific observations in the second half of 2011 and the first images were released to the press on 3 October 2011. By the summer of 2011 sufficient telescopes were operational during the extensive program of testing prior to the Early Science phase for the first images to be captured. These early images give a first glimpse of the potential of the new array that will produce much better quality images in the future as the scale of the array continues to increase. Atacama Large Millimeter array. An early observation of the array was a pair of colliding galaxies with dramatically distorted shapes, known as the Antennae Galaxies. Although ALMA did not observe the entire galaxy merger, the result is the best submillimeter-wavelength image ever made of the Antennae Galaxies, showing the clouds of dense cold gas from which new stars form, which cannot be seen using visible light