| From: Magic Chicken (Avatar) | 25/10/2002 16:08:22 |
| Subject: BB 1 - The Evidence | post id: 217658 |
Hi and welcome to the first in a series of tutorials on Big Bang Theory. These tutorials will each be labelled BB#, and will aim to cover a broad range of what we understand about the evolution of the universe. This first tutorial in the series, BB1, explains what Big Bang Theory is, and the evidence which supports it. Then we'll start getting into the detail! As per usual, the tutorial could be read from start to end by just reading the white text. Extra detail is added in colour: harder sections which may add value for more technical readers are coloured red, while more elementary sections which explain concepts in the text in more detail are green. Mathematical support or working for the main text is in yellow. As always, please post any questions or clarifications to the follow-up question thread rather than in this thread. 1.0 What is Big Bang Theory? The "Big Bang" Theory first got its name in 1950. The name was coined by astrophysicist Fred Hoyle, who was actually a strong opponent of the theory - he intended the name "Big Bang" to be derisive! The idea of a universe which started at a particular point in the past has been around for millennia, however it is only this century that it has gained (modern) scientific support and credence. So what is the theory? Simply put, it is this: That the universe started at a fixed point some finite time interval into the past, and it has evolved to be what it is today from a hotter, denser state. That's it! Of course a lot of extra detail is added by general relativity, inflation theory, stellar and galactic astrophysics, particle and high energy physics, etc, and we will cover that detail in succeeding tutorials. But it is important to realise that the Big Bang theory doesn't live and die by these details. That the universe started at some time in the past, and that it has evolved is as strongly supported as biological evolution - and as widely accepted. (Interestingly, people who disbelieve evolution and disbelieve the Big Bang theory seem to be very similar!) Lets take some time to examine the evidence which supports the general theory, and consider some of the more popular alternative explanations along the way. | |
| From: Magic Chicken (Avatar) | 25/10/2002 16:09:11 |
| Subject: re: BB 1 - The Evidence | post id: 217659 |
1.0.1 Evidence for the Big Bang Theory Evidence for the general big bang theory has been accruing since the early 20th Century. We'll examine in detail the most significant evidence. 1.1 The Hubble Redshift In 1926 Edwin Hubble published his first catalogue of galaxies. Hubble noted that there was a shift in the spectra of the observed galaxies towards the red. You're probably aware that white light is made up of different coloured light mixed together. Each of those independent colours has an associated wavelength, from red light (long wavelength) to blue light (short wavelength). Galaxies output energy across a whole range of wavelengths in visible light, microwave, radiowave and even X-rays. When you plot the amount of energy received at different wavelengths your graph makes a characteristic shape, like this:  A Galaxy's spectrum In redshifting, the whole shape of the graph is moved to the right in the picture - towards longer wavelengths. The physical interpretation of this is of a Doppler Shift. In the Doppler shift, wavelengths get stretched by the relative motion of the receiver and source - in the same way that the sound of a siren on a speeding ambulance changes as it approaches you (blue shift = shorter wavelength = motion towards) and then passes and speeds away (red shift = longer wavelength = motion away). The redshifting of all the galaxies' spectra is that they're all moving away from us. Hubble claimed that the redshifting obeyed a linear relationship, and that the interpretation of the shift was as of a Doppler shift of relative motion. In 1929 published this claim as Hubble's Law: v = HoR Here v is the apparent recession velocity of a distant galaxy, R is the distance to the distant galaxy and Ho is Hubble's constant. If you plot a graph with the recessional speed on the y-axis and the distance R on the x-axis, then the slope of the line of best fit gives you the value for Hubble's constant. Hubble's original data was sloppy at best, and his line of best fit was somewhat dubious. From it he calculated a value for Ho of 464km.s-1.Mpc-1. (The usual units for the Hubble constant is kilometres per second per Megaparsec, since galactic recessional velocities (v) are usually given in km/s and long distances (R) in Mpc). Since then increasingly accurate surveys of the sky have produced more data and more detail, and it increasingly supports Hubble's linear relationship:  Type Ia Supernova data from Riess, Press and Kirshner (1996) The slope of the above graph suggests a value for Ho of 64km.s-1.Mpc-1. The actual value lies somewhere between 55 and 75 - the difficulty in precise determination lies in precisely determining R. The Hubble law given above is a linear law, v is directly related to R. A consequence of this is that the Copernican view of the universe holds true - we occupy no special place in the cosmos. Because the law is linear, the redshift observed by us is the same as the redshift observed from anywhere else in the universe. If the Hubble relation was not linear then we would actually be at the centre of the universe. As a result, we find ourselves in a universe which is not static in space, but is constantly expanding. This implies that the universe was smaller in the past, and by extension that at one point in the past it definitely started. In fact the Hubble law gives us an estimate of the age of the universe. Given that v has units of distance/time and R has units of distance we discover that Ho has units of 1/time. Inverting the Hubble constant gives us an approximate age of the universe: Ho = 65 km.s-1.Mpc-1 1 Mpc = 3.26 million light years = 30841981340613408000km Ho = 65 km.s-1.Mpc-1 / 30841981340613408000km/Mpc 1/Ho = 30841981340613408000/65 seconds This gives an age for the universe of about 15 billion years. More accurate determinations of the constant would give more accurate universal ages - and vice versa. | |
| From: Magic Chicken (Avatar) | 25/10/2002 16:10:16 |
| Subject: re: BB 1 - The Evidence | post id: 217661 |
1.2 The Dilation of Distant Supernova The mathematical model for the universe's evolution comes from Einstein's general theory of relativity. In this theory space and time don't have independent, absolute existences like in Newton's mechanics, instead they are linked into one 4 dimensional geometry called space-time. More detail on that in a coming tutorial. For now, we note that if we see a universe expanding in space (as evidenced by the Hubble redshift above) then we should also observe expansion in time. What does this mean? In cosmology we define a redshift factor z: z = ( l - lo ) / lo or z + 1 = l / lo z gives us the fractional increase in wavelength, and is often used by astronomers to indicate a cosmic distance to an observation, eg: on 23 Apr 2001 - SDSS found a quasar at redshift z = 6.28. This means that the wavelengths of light received were 7 times longer than the original wavelengths emitted by the quasar. From this we can infer that distance intervals - as marked by the wavelength of the light from the quasar - have increased by a factor of 7; what measured as 1 metre near the quasar now has expanded to 7 metres. Similarly we expect time intervals to increase. A day measured at redshift z=1 should measure as two days when observed from earth. So what we need to do is look for something which marks a standard time interval (like a clock), so we can see if its ticks are getting further apart. Unfortunately there are no giant clocks in space, but there are other phenomena which are just as good. One such example is a type of supernova (SN) called a Type Ia SN. This SN has a very regular decay cycle - it peaks in brightness and then fades over a strict timeline. This makes a Type Ia SN a good "clock". If this type of SN typically takes 90 days to decay near us, it should take longer to decay further away - and this is precisely what we observe. SN at a redshift of z = 1 take 180 days to decay (twice as long - see redshift formula above). The observational evidence for these has been published by: Leibundgut etal, 1996, ApJL, 466, L21-L24 Goldhaber etal, in Thermonuclear Supernovae (NATO ASI), eds. R. Canal, P. Ruiz-LaPuente, and J. Isern. Riess etal, 1997, AJ, 114, 722. Perlmutter etal, 1998, Nature, 391, 51. Goldhaber etal, ApJ in press. So the universe is expanding in time and space. | |
| From: Magic Chicken (Avatar) | 25/10/2002 16:11:11 |
| Subject: re: BB 1 - The Evidence | post id: 217662 |
1.3 The Cosmic Microwave Background Radiation In 1948 the irrepressible George Gamow, with colleague Ralph Alpher, made a model of the creation of matter in the early universe. The model is called nucleosynthesis, and we'll discuss it in detail in a later tutorial. Gamow estimated the temperature in the early universe to be about a billion degrees Kelvin at about 200 seconds after the Big Bang. Later Alpher and Herman (1948) claimed that given the universal expansion, there should be a relic of this earlier hot time in a sea of left over radiation. Alpher estimated the current temperature of the radiation to have dropped with the expansion to about 5K. Expansion temperatures: Consider a finite box filled with radiation. At temperature T, the number n of photons at some normal mode of oscillation of frequency n in the box is given by the Bose-Einstein distribution function for bosons: n(n) = ( ehn/kT - 1 )-1 Now suppose we increase the linear dimension of the box by some factor x. The wavelength of the mode also increases by x, and hence the frequency falls to n' = n/x. Provided the expansion proceeds slowly, the number of photons n doesn't change, so we can say n(n') = ( ehn/kT - 1 )-1 substitute in the new frequency n' = n/x n(n') = ( exhn'/kT - 1 )-1 which is obviously still a thermal distribution, but with a new T' = T/x. This confirms that expansion by a given factor x results in a change in the thermal radiation temperature by 1/x. In fact it turns out that T' = T(1 + z) In 1965 Gamow and Alpher's model became the "hottest" thing in cosmology when Penzias and Wilson actually detected this left over radiation, as confirmed by Dicke et al (1965). What they had discovered was a spectrum of radiation which peaked in the microwave - corresponding to a blackbody temperature of about 3K. Since then the radiation sea has been explored by numerous experiments to pin down its properties and get a more accurate reading on the temperature. The radiation is called the Cosmic Microwave Background Radiation (CMBR). Let's look at its significant properties: * The radiation spectrum is a Blackbody spectrum. The remarkable fit of the CMBR spectrum to the ideal blackbody curve rules out any other photon source. Interstellar dust clouds, molecular hydrogen, etc (all suggested as alternative sources of the radiation) do not radiate evenly over the spectrum, but rather peak at certain characteristic points in the spectrum. Most of our detailed data about the CMBR comes from the http://space.gsfc.nasa.gov/astro/cobe/cobe_home.html COsmic Background Explorer (COBE) satellite. The blackbody spectral data comes from the http://space.gsfc.nasa.gov/astro/cobe/cobe_home.html#firas Far InfraRed Absolute Spectrophotometer (FIRAS) experiment on board.  The CMBR spectrum, data from the FIRAS experiment Compare the CMBR spectrum to (say) the galactic spectrum above. What is Blackbody radiation, and what is a Blackbody? An ideal "blackbody" absorbs and then re-radiates all the radiation which is incident upon it. Max Planck drew a smooth radiation curve, like the curve in the picture above, which describes the intensity over different frequencies for radiation from an ideal blackbody. In practice most things in nature do not emit as ideal blackbodies - they absorb radiation preferentially and/or emit only at certain frequencies. The CMBR radiation curve is particularly close to an ideal blackbody (see picture above), and so is unlikely to have been emitted recently. You can discover more about the physics of blackbody radiation. | |
| From: Magic Chicken (Avatar) | 25/10/2002 16:11:55 |
| Subject: re: BB 1 - The Evidence | post id: 217664 |
* Homogeneity and Isotropy The CMBR sky is remarkably homogenous and isotropic. The figures below demonstrate what these two concepts mean:  The left picture is homogenous but not isotropic, the right picture is isotropic but not homogenous The lack of directionality in the sky supports our current models of an expanding universe - recall from above that the linear Hubble relationship implies that the universe has no "centre". The uniformity of the sky rules out local or directional sources for the radiation. The isotropy is remarkably uniform. The DMR (Differential Microwave Radiometer) experiment is actually looking for anisotropies in the sky. These small deviations - on the order of 1 part in 100 000 - are interpreted as the seedings for eventual massive object (galaxy) formation. More on that in a later tutorial. The CMBR is strong physical evidence of a hot big bang. 1.4 CMBR temperature vs time In December 2000 Raghunathan Srianand, Patrick Petitjean, and Cedric Ledoux published an article in Nature claiming to have indirectly measured the temperature of the CMBR in the past. The present temperature of the CMBR is generally accepted to be 2.726±0.010K. Srianand et al looked at the interaction of the CMBR photons with atoms at long redshift to determine the temperature. At a redshift of z = 2.33771 they measured the CMBR temperature to be 10±4K, where Big Bang Theory predicts a temperature of 9.1K. Now remember that when you look a long way out into space, you're also looking back in time because of the finite speed of light (and hence the time taken for distant images to reach us). This effectively means that the CMBR was discovered to be hotter in the past than it is now - which confirms that the universe has evolved from a hotter state. 1.5 Radio Source vs Flux Counts Suppose the galaxies are distributed fairly evenly across the sky, as suggested by the homogeneity/isotropy evident in the CMBR. This means the number of galaxies within a distance R increases uniformly with R3. Suppose each galaxy has an intrinsic luminosity L. Then the apparent luminosity, S, as measured at earth is: S = L / 4pR2 (assuming flat space) From the above we can see that our volume R3 is proportional to S-3/2. It follows then in a uniform distribution the number of galaxies with apparent brightness greater than S is proportional to S-3/2: N(>S) µ S-3/2 Note that the proportionality doesn't depend on L, which makes it ideal for a sky survey. If our initial supposition of homogeneity is correct then surveys for given ranges of S should conform to the proportionality above. Which they do. From Hubble's surveys of 1926 to 1936 all the way to the more recent surveys (eg Peebles 1993) the optical brightness of nearby galaxies matches the proportionality given, and reinforces the homogenous/isotropic picture. But… interestingly radio sources such as radio galaxies and quasars do not agree with the proportionality. There is an excess of radio sources at low brightness, which can be explained by either a change in luminosity with time or density with time. Either way this points to a universe which is not steady in time, but rather has evolved in time. This contradicts the Perfect Cosmological Principle which is a requirement for the Steady State Theory supported by Bondi and Gold, and also by Hoyle. The Perfect Cosmological Principle requires the universe to be homogenous not only in space, but also in time. Clearly the radio source flux over time shows this is not the case, and so it falsifies the Steady State Theory. Schmidt (1970, 1972) confirms that the density of quasars in particular must have been greater in the past, which supports the theory that quasars are early galaxies from when the universe was young. | |
| From: Magic Chicken (Avatar) | 25/10/2002 16:12:58 |
| Subject: re: BB 1 - The Evidence | post id: 217667 |
1.6 The Abundance of Light Elements In 1948 Alpher and Gamow proposed a model for the synthesis of all atomic nuclei from the big bang. Meanwhile Burbidge, Fowler and Hoyle were working out how nuclei were synthesised in stars. In the end both are right: our current model suggests that all the universe's hydrogen and the greater proportion of helium was created in a period after the Big Bang called the Nucleosynthesis era. Lithium and Beryllium are generally created by the interaction of cosmic rays with Carbon. Nuclei of Carbon to Iron are manufactured in the fusion cores of stars, and elements heavier than iron are produced in supernova explosions. More on the detail of Nucleosynthesis in a later tutorial, we'll look at the predictions here. By analysing the temperature and energy density vs time in early universe models we can set limits on the production of certain nuclei. Unlike stars where the fusion conditions remain stable for some time, the conditions in the early universe changed quickly as expansion dropped the energy density and temperature. Accordingly we can build up a picture from theory of the ratios of production of various elements in the Nucleosynthesis era.  The relative abundances of light nuclei vs time (top) and temperature (bottom) On the graph above H and He(4) have trapped most of the early matter to survive to today. There is about 25% as much He(4) as H. Also note that H(3) - tritium - decays into He(3) with a half life of 12 years, Be(7) decays into Li(7) with a half life of 53 days, and the free neutrons decay with a half life of 615 seconds (note the neutron line on the graph already looks like a decay curve), so none of these three survives from nucleosynthesis to today. The predicted abundances made by the model are matched to observed abundances today. The following graph shows predicted abundances for four nuclei against observed abundances:  The Abundance relative to hydrogen on the vertical, various baryon densities on the horizontal In this graph various abundances for Helium (3 and 4), Deuterium and Lithium are shown against initial baryon density WB. The curved lines show the abundancy predicted by theory at various densities, the flat lines show the observed abundancies. Note that at one particular value for WB (the vertical line) all four nuclei observed abundancies agree with theory's predictions. This is an astonishing agreement between theory and prediction, and strong support for the nucleosynthesis model in hot big bang theory. 1.7 The Tolman Surface Brightness Test The surface brightness of a galaxy is simply its luminosity per unit surface area. As early as the 1930s Richard Tolman of CIT proposed a direct test for the expansion of the universe, by measuring how the surface brightness of distant galaxies falls off with redshift. The elegance of the Tolman test is that it discriminates widely between expanding universe models and static ones where the perceived redshift is due to tired light or other such explanations. The surface brightness in an expanding universe falls off as (1 + z)4, whereas in a static universe where the redshift results from Zwicky's tired light model it falls off as (1 + z). In 2001 Sandage and Lubin were finally able to perform Tolman's test and determine whether the expansion is "real". Their results confirm the expansion of the universe to spectacular degree, and consign tired light models to the scrapheap. You can read their paper, which contains a very readable introduction to the history of the various tests on the expansion (covered above) as well as interesting personality-bites. For example Hubble himself was initially reluctant to accept that the expansion of the universe was real! | |
| From: Magic Chicken (Avatar) | 25/10/2002 16:13:39 |
| Subject: re: BB 1 - The Evidence | post id: 217669 |
1.8 Conclusions Big Bang theory is as robust as biological evolution. Outlined above, the redshift observations and Supernova time dilation observations support the expansion of space and time. The Tolman test supports an expanding metric. The CMBR provides a relic from the early universe. The relative abundance of light nuclei supports the nucleosynthesis model (which depends on a hot, dense, early universe). And the change of CMBR temperature with time and the radio source flux demonstrate the universe has evolved with time. Steady State alternatives are ruled out by showing the universe has evolved. Tired light models are specifically ruled out by the Tolman test. So…where to from here? The next tutorial will take us step by step through the modelling of an expanding universe. After that we will look in detail at the universe's life story - the early periods through to the ultimate fate. Resources: http://www.astro.ucla.edu/~wright/cosmolog.htm Ned Wright's Cosmology site Various abstracts linked in the document. Gravitation and Space-time by Ruffini and Ohanian Gravitation by Misner, Thorne and Wheeler NASA's COBE web pages (linked within the document). The Chicken. :o) | |