Cosmology. Surrey U3A Network Friday November 20th, 2015 Stoke d Abernon Dr Roger Luther, Sussex University PHY306

Transcription

1 Cosmology Surrey U3A Network Friday November 20th, 2015 Stoke d Abernon Dr Roger Luther, Sussex University PHY306 1

2 Acknowledgements res.html g.ppt PHY306 2

3 The Big Bang Theory: Origin & Evolution of the Universe Hally Stone UB PASI 2010

4 Early ideas: astronomy Clearly understood concepts in Greek and Hellenistic astronomy shape and size of the Earth (Eratosthenes, BC ) size and distance of the Moon (Aristarchos, BC ) Sun is much larger than Earth (Aristarchos) exact value was wrong by a large factor: method sound in principle, impossible in practice! Ideas raised but not generally accepted Earth rotates on its axis (Heraclides, BC ) Sun-centred solar system (Aristarchos) PHY306 4

5 Early ideas: cosmology Aristotle/Ptolemy Earth-centred, finite, eternal, static Aristarchos/Copernicus Sun-centred, finite, eternal, static At this time, little observational evidence for Sun-centred system! PHY306 5

6 Renaissance Birth of modern science scientific method Galileo better observations Tycho, Galileo development of mathematical analysis Kepler, Galileo, Newton Newtonian cosmology PHY306 6

7 Newtonian Cosmology Newton s Philosophiae Naturalis Principia Mathematica, 1687 Newtonian gravity, F = GMm/r 2, and second law, F = ma Approximate size of solar system (Cassini, 1672) from parallax of Mars Finite speed of light (Ole Rømer, 1676) from timing of Jupiter s moons No distances to stars No galaxies PHY306 7

8 Newton s Static Universe Universe is static and composed of an infinite number of stars that are scattered randomly throughout an infinite space. Universe is infinitely old and will exist forever without any major changes. Time and Space are steady and independent of one another and any objects in existence within them.

9 Olber s Paradox (1823) If space goes on forever with stars scattered randomly throughout, then in any line of sight in any direction will eventually run into a star. Using this logic, the sky should be the average brightness of all of these stars; the sky should be as bright as the sun, even at night.

10 But isn t the sky dark at night? Yes, of course - that is what we observe now and have always observed. Something is wrong with Newton s idea of a static, infinite universe.

11 Light is absorbed by intervening dust suggested by Olbers doesn t work: dust will heat up over time until it reaches the same temperature as the stars that illuminate it Universe has finite size suggested by Kepler this works (integral is truncated at finite r) but now Newtonian universe will definitely collapse PHY306 Resolution(s) Universe has finite age equivalent to finite size if speed of light finite light from stars more than ct distant has not had time to reach us (currently accepted explanation) Universe is expanding effective temperature of distant starlight is redshifted down this effect not known until 19 th century (does work, but does not dominate (for stars) in current models) Olbers + Newton could have led to prediction of expanding/contracting universe 11

12 State of Play ~1900 We know PHY306 speed of light distance to nearby stars the Earth is at least several million years old Our toolkit includes Newtonian mechanics Newtonian gravity Maxwell s electromagnetism We don t know galaxies exist the universe is expanding the Earth is several billion years old We are worried about conflict between geology and physics regarding age of Earth about to be resolved lack of aether drift 12

13 What is a galaxy? A large group of stars outside of our own Milky Way Made of billions to trillions of stars Also may have gas and dust Spiral, or elliptical, or irregular shaped

14 Measuring Distances What is a Light Year? A light year is the distance light travels in a year. Light moves at a velocity of about 300,000 kilometers (km) each second; how far would it move in a year? About 10 trillion km (or about 6 trillion miles). Why do we use light years? Show me how far 5 centimeters is. Now show me 50 centimeters. Now tell me (without thinking about it, or calculating it in meters) how far 500 centimeters is? 2000? 20,000? We need numbers that make sense to us in relationship to objects; we scale up and use meters and kilometers for large numbers.

15 The Milky Way

16 Our Galaxy: the Milky Way has about 200 billion stars, and lots of gas and dust is a barred-spiral (we think) about 100,000 light-years wide our Sun is halfway to the edge, revolving at half a million miles per hour around the center of the Galaxy takes our Solar System about 200 million years to revolve once around our galaxy

17 Where the Galaxies Are And When Galaxies Collide First, let us recall the scale of the universe and its structures 17

18 The Local Group Our Local Group is composed of : Two large spirals (MW & Andromeda) A moderate sized spiral (M33) 30 odd dwarf elipticals (Leo I & II, Fornax ) A few irregular galaxies 500 kpc = 1,650,000 light years Small Groups like our Local Group are very common in the universe. These small groups add up to form larger coherent structures, including super clusters. However, some galaxies are not members of small groups, but of the large clusters themselves. 18

19 Ring Galaxies High speed, single-pass, collisions sometimes occur and this can create a new burst of star formation. In this case, the compression wave moved out like a outward ripple in a pond and created a ring of new stars! These particular two galaxies will never strike each other again. 19

20 Virgo cluster

21 Relativity Principle of relativity not a new idea! Basic concepts of special relativity an idea whose time had come Basic concepts of general relativity a genuinely new idea Implications for cosmology PHY306 21

22 The bending of light 22

23 Light bent by gravity First test of general relativity, 1919 Sir Arthur Eddington photographs stars near Sun during total eclipse, Sobral, Brazil results appear to support Einstein (but large error bars!) PHY306 photos from National Maritime Museum, Greenwich 23

24 Light bent by gravity lensed galaxy member of lensing cluster PHY306 24

25 Curved spacetime and implications for cosmology General Relativity implies spacetime is curved in the presence of matter since universe contains matter, might expect overall curvature (as well as local gravity wells ) how does this affect measurements of large-scale distances? what are the implications for cosmology? PHY306 25

26 Open, closed, or flat?: Expansion will stop at t = infinity Curvature: Three possibilities: Open Negative curvature Infinite in extent Will expand forever Closed Positive curvature Finite Will collapse (big crunch/oscillate?) Flat In essence, no curvature Infinite

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28 Implications of Einstein s Ideas Based on the general relativity equations, the structure of universe is either always expanding, always contracting, or always static. To agree with the ideas of the time (Newton s), Einstein added a cosmological constant which yielded a static universe.

29 Cosmological Constant Represents the pressure that allows the universe s expansion to directly balance gravitational collapse due to the objects existing within the universe, thus yielding a static universe. Without this idea of a cosmological constant, Einstein could ve been the first to predict that the universe is not static.

30 The critical density: But clusters are older than this! How the universe is curved depends on the density The density which would make the universe flat is called the critical density ρ c ρ c ~ 9 x g/cm 3 ρ < ρ c => open ρ > ρ c => closed All observable matter ~ 5% of ρ c Hubble time revisited: If flat 2 flat [ years ] 3 H 14 billion years 0 9 billion years [ years] H 0

31 Cosmological models Cosmological distances Single component universes radiation only matter only curvature only Λ only Multi component universes PHY306 31

32 State of Play: theory Friedmann model plus cosmological constant can describe wide variety of behaviour expanding, recollapsing or static also bouncing and loitering models this technology all available in 1920s However, models have free parameters H 0, Ω m0, Ω r0, Ω Λ0 need to determine these to see what model predicts for our universe PHY306 32

33 Hubble s Discovery Edwin Hubble s observations of remote galaxies, and the redshift of their spectral lines (1924). Hubble noticed that the further away the galaxy, the greater the redshift of its spectral lines. This linear relationship is called Hubble s Law.

34 Redshift The wavelengths of the light emitted by distant objects is elongated as it travels to earth. Longer the light travels, the more it gets redshifted.

35 Hubble s Law v = H 0 d v = recessional velocity of the galaxy H 0 = Hubble constant d = distance of galaxy to earth Galaxies are getting farther apart as time progresses, therefore the universe is expanding.

36 Hubble s distances Hubble used Cepheid variables as calibrated by Shapley (1930) brightest stars in galaxies as calibrated by Cepheids total luminosities of galaxies calibrated by Cepheids and brightest stars Wrong by factor of 2! Wrong by factor of ~4! Wrong because calibration wrong PHY306 36

37 Hubble s Law (published 1929): v = H 0 d H 0 =100h Expansion allows a rough estimate of the age of the Universe: t = d/v = 1/H 0

38 H 0 = 72 (+/-5) km/s per Mpc

39 History of H Compilation by John Huchra H0 (km/s/mpc) Baade identifies Pop. I and II Cepheids Brightest stars identified as H II regions 200 Jan Oort Date PHY306 39

40 Hubble Wars general cosmology dependent Key project Sandage camp de Vaucouleurs camp H0 (km/s/mpc) PHY Date reasonable convergence only in last decade see later 40

41 Conclusions Precision of Hubble constant measurements driven by systematic errors in calibration best long-range geometric measurements are lower than best conventional values, but not convincingly so Best estimate (HST Key Project 2001, WMAP fit 2008) is ~70 km/s/mpc error ~10% from HST, ~2% from CMB much better than factor 2 error in 1980s! PHY306 41

42 Hubble s Constant Expansion rate measured using Type 1A Supernovae. The age of the universe can be derived from Hubble s constant: T 0 = d T 0 = 1 H 0 d H 0 For example, if H 0 = 73 km/s*mpc, then T 0 = 13.4 Billion years old

43 Age of Universe Currently, after taking into account differences in expansion rate over time and our movement through space: T 0 ~ 13.7 ± 0.2 byo Age of stars: ~13.4 byo ± 6% Therefore, oldest stars are younger than the age of universe.

44 The Big Bang Big Bang: the event from which the Universe began expanding. Into what did the Universe expand? Where was the Big Bang? Where is the center of the Universe?

45 Expanding Universe Space itself is expanding, not matter flying apart within space. Examples: dots rubber band raisin bread ants on a balloon It does not mean we are at the center of the Universe every part of the Universe sees everything moving away from it

46 How the Universe Expands The space between galaxies expands, not the galaxies themselves; objects held together by their own gravity are always contained within a patch of nonexpanding space. Example: raisins in a loaf of bread. As the dough rises, the overall loaf of bread expands; the space between raisins increases but the raisins themselves do not expand.

47 Origins of the Big Bang Theory Georges Lemaître (1927) expanded on idea of expanding universe, realizing that the universe was smaller yesterday than today, and so on until a day that would not have had a yesterday : the moment of creation. The moment of creation would be the sudden explosion that started the expansion of the universe as we know it today. This idea wasn t widely accepted at first: Fred Hoyle dismissed this hot Big Bang, noting that there wasn t any record or remnants. He argued for a steady state universe.

48 Origins of the Big Bang Theory George Gamow (1948) suggested that if the universe was created with a hot Big Bang, then: Various elements, such as H and He, would be produced for a few minutes immediately after the Big Bang due to the extremely high temperatures and density of the universe at this time. The high density would cause rapid expansion. As the universe expanded, H and He would cool and condense into stars and galaxies. Today, due to continued cooling, radiation left over from the epoch of recombination, when neutral atoms formed (~380,000 years after Big Bang) should be about 3K.

49 Big Bang Nucleosynthesis First detailed calculations by Wagoner, Fowler and Hoyle Basic principles at very high energies neutrons and protons interconvert: p + e n + ν neutron:proton ratio given by exp( Δmc 2 /kt) where Δm is the neutron-proton mass difference and T is the temperature at which the neutrinos freeze out (~10 10 K) this is ~1:5 Wagoner, Fowler, Hoyle, ApJ 147 (1967) 3 PHY306 49

50 Big Bang Nucleosynthesis As universe cools, start fusion reactions PHY306 p + n d + γ deuterium starts to build up below T~10 9 K background photons are no longer energetic enough for back reaction d + p 3 He + γ d + n 3 H + γ d + d 3 H + p or 3 He + n various reactions then lead to 4 He (and a bit of 7 Li) eventually every neutron winds up in 4 He 4 He fraction ~1:8 by number, 1:2 by mass actually rather less because some neutrons decay Wagoner, Fowler, Hoyle, ApJ 147 (1967) 3 50

51 Big Bang Nucleosynthesis Final yields of 2 H, 3 He, 4 He and 7 Li depend on the neutron lifetime (measured in lab) 885.7±0.8 s (PDG, 2004) the number of neutrino species (measured in e + e ) because in radiation dominated era H 2 ρ rel = ρ γ + N ν ρ ν 2.984±0.008 (combined LEP experiments) H (measured by HST, WMAP) 72±8 km/s/mpc (HST), 70.1±1.3 km/s/mpc (WMAP) baryon density (i.e. number density of protons+neutrons) PHY306 51

52 21.4 The Formation of the Elements Some of these elements are formed during normal stellar fusion. Here, 3 helium nuclei fuse to form carbon:

53 21.4 The Formation of the Elements Carbon can then fuse, either with itself or with alpha particles, to form more nuclei:

54 21.4 The Formation of the Elements The elements that can be formed through successive alpha-particle fusion are more abundant than those created by other fusion reactions:

55 21.4 The Formation of the Elements The last nucleus in the alpha-particle chain is nickel-56, which is unstable and quickly decays to cobalt-56 and then to iron-56. Iron-56 is the most stable nucleus, so it neither fuses nor decays. However, within the cores of the most massive stars, neutron capture can create heavier elements, all the way up to bismuth-209. The heaviest elements are made during the first few seconds of a supernova explosion.

56 21.2 The End of a High-Mass Star A high-mass star can continue to fuse elements in its core right up to iron (after which the fusion reaction is energetically unfavored). As heavier elements are fused, the reactions go faster and the stage is over more quickly. A 20-solar-mass star will burn carbon for about 10,000 years, but its iron core lasts less than a day.

57 21.3 Supernovae A supernova is incredibly luminous, as can be seen from these curves more than a million times as bright as a nova.

58 21.5 The Cycle of Stellar Evolution Star formation is cyclical: stars form, evolve, and die. In dying, they send heavy elements into the interstellar medium. These elements then become parts of new stars. And so it goes.

59 The Cosmic Microwave Background: Theory Prediction of CMB trivial in Hot Big Bang model hot, ionised initial state should produce thermal radiation photons decouple when universe stops being ionised (last scattering) expansion by factor a cools a blackbody spectrum from T to T/a therefore we should now see a cool blackbody background Alpher and Herman, 1949, a temperature now of the order of 5 K Dicke et al., 1965, <40 K note that the Alpher and Herman prediction had been completely forgotten at this time! PHY306 59

60 Creating the CMB Big Bang dense hot expansion cooling rarified cool Now ionized foggy atomic transparent hot glowing fog we see a glowing wall of bright fog us orange light redshift z = 1000 microwaves

61 The Cosmic Microwave Background: Observations First seen in 1941 (yes, 1941) lines seen in stellar spectra identified as interstellar CH and CN (Andrew McKellar, theory; Walter Adams, spectroscopy) comparison of lines from different rotational states gave rotational temperature of 2-3 K unfortunately Gamow et al. do not seem to have known about this CN CH PHY306 spectrum of ζ Oph, Mt Wilson coudé spec., Adams

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63 The Cosmic Microwave Background: Observations Discovered in 1965 Penzias and Wilson observe excess antenna temperature of 3.5±1.0 K from the Holmdel microwave horn interpreted by Dicke et al. at Princeton they had independently rediscovered the prediction and were just about to start looking for the radiation! note: this is one point (not a blackbody spectrum!) PHY306 63

64 COBE Launched November 1989 After two years of data: spectrum is a precise blackbody (no measurable deviations) T = 2.725±0.002 K At this point all cosmological models other than Hot Big Bang are effectively dead no other model expects this good a blackbody background PHY306 Mather et al., ApJ 354 (1990) L37 9 minutes of data!! 64

65 CMB Image Exceedingly uniform, with two contaminants : 1) dipole : MW 540 km/s towards Virgo 2) MW plane contamination Remove these to reveal : Highly uniform no stars or galaxies : diffuse hot gas Very slight patchiness: ~10-5 variations = sound waves; grow into galaxies

66 Observations & the Hot Big Bang Predictions of Hot Big Bang model ~mid 1960s background radiation ( smoking gun ) discovered by accident in 1965, but about to be found on purpose! age of universe 1/H 0 reasonably OK by this time discovery of quasars helped establish evolution primordial deuterium and helium abundance calculated by Jim Peebles, 1966 Really a set of models, so need to measure parameters PHY306 66

67 Case for the Hot Big Bang The Cosmic Microwave Background has an isotropic blackbody spectrum it is extremely difficult to generate a blackbody background in other models The observed abundances of the light isotopes are reasonably consistent with predictions again, a hot initial state is the natural way to generate these Many astrophysical populations (e.g. quasars) show strong evolution with redshift this certainly argues against any Steady State models PHY306 67

68 Big Bang Theory: Timeline of Universe Hubble s Law shows that the universe has been expanding for billions of years - the universe is denser the further back in time you look. At some point, you reach an infinitely dense point at which T age of universe = 0 Big Bang

69 T = 0 seconds to seconds BIG BANG occurs. Something causes infinitely dense point to expand (into Nothing). Density of universe is so high that time and space are curled up and the laws of physics that we know today do not apply. All four forces in nature were unified the theory of everything. This is time is called the Planck Time.

70 Separation of Forces After the Planck time, the temperature had decreased to10 32 K and gravity was the first force to separate. The remaining three forces were still united - these are the conditions that particle physicists today try to replicate.

71 T = to seconds Inflation caused the size to the universe to increase exponentially by a factor of This time is called the inflationary epoch.

72 After Inflation Stops Matter is created: Photons collide and produce pairs of elementary particles such as electrons and positrons, and quarks and antiquarks. Pair production continues until too cold to be produced - pair annihilation happens - result: symmetry breaking. Reason for slight excess of matter over antimatter is because of an unknown reaction known as baryogenesis, in which conservation of baryon number is violated. Pair Production occurred until T = 6 x10 9 K, but pair annihilation happens independent of temperature.

73 Particle Production in Early Universe As the size of the universe increases and the temperature decreases, the particles produced are of decreasing energy. The fundamental forces and parameters of elementary particles at the time that symmetry was broken are the same as they are today. The time between the birth of the universe and t=10-11 sec is rather unknown, but we can speculate what is happening based on other observations; beyond this time is less speculative as these are conditions that particle physicist try to replicate.

74 T = 10-6 seconds Temperature has cooled enough for baryons (Protons, Neutrons) to form. Like the leptons, baryons form in pair production. Once the temperature has decreased past the point at which baryons can no longer be produced, pair annihilation occurs again, leaving a slight excess of baryons over antibaryons. Also, at this temperature, all particles are no longer moving relativistically, so the universe becomes dominated by the higher energy photons (radiation-dominated universe).

75 T = few minutes Temperature ~ 1 GK, density ~ that of air. Neutrons combine with protons making deuterium and helium nuclei, and some protons remain independent (hydrogen nuclei). Called Big Bang nucleosynthesis. Temperature is still too high to form atoms as they would be ionized immediately. The universe would appear opaque during all this time because photons and matter would be interacting due to high temperatures.

76 T = 379,000 years Universe is now cool enough that matter energy is greater than radiative energy, thus allowing atoms to form. Radiation is decoupled from matter and photons are free-streamed throughout space - origin of CMB radiation. This time is known as the epoch of recombination. Universe is now matter-dominated.

77 T ~ 400 million years Since epoch of recombination, slightly denser regions attracted matter nearby and the first stars begin to form. Regions continue to acquire matter and other objects like galaxies and gas clouds form. Universe begins to look like how we know it today (still expanding and still cooling).

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80 "turns into people." Hydrogen is a light, odourless gas, which, given enough time, turns into people. Edward Robert Harrison