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Midterm exam: astrophysics • date: March 17, 2006, 8:15 a.m. • location: Conrad Naber Hall • bring pocket calculator • NO text books, notes laptops etc. • do NOT bring your own paper • write on exam sheets directly Spacephysics: see web site Sir Isaac Newton: (1643-1727) Cosmology as a Science • Mathematical description of the Universe • The same physical laws apply to earth and Universe Newton: Fundamental contributions •Mathematics: - series expansions - differential calculus - approximation methods -… • Optics: - spectral analysis of white light • Physics: - ‘Principia mathematica…’ • Astronomy: - derive Kepler’s laws from gravitational forces • ….. A toy universe constant density (homogeneous) boundary According to Newton, what is going to happen ? The model Universe is going to collapse under its own gravity Newton’s Conclusion: In order to avoid collapse homogeneous isotropic infinite size no center infinite in time has always been will always be perfect cosmological principle The perfect cosmological principle homogeneous: the universe looks the same everywhere on large scales there is no special place (center) isotropic: the universe looks the same in all directions on the sky there is no special direction unchanging: The universe looks the same at all times there is no special epoch Olber’s Paradox • If the universe is i) eternal ii) (more or less) uniformly filled with stars iii) infinite • then there is a star along each line of sight so: Why is the night sky dark ? Problems with an infinite universe Olber’s Paradox: Why is the night sky dark? Shell of radius r312:= 4r 2r1 : r12 1)2 Surface: S321=4 (4r (2r 2x r12x Volume: V321=4 (4r ) (2r 1 2x r12x # of stars: N321= 4 (4r ) (2r 1 luminosity per star: l*/16 /4 luminosity of shell: 2x r12x L321 = 4 (4r ) (2r /4 1 l* l*/16 = 4 r12x l* = L1 Olber’s Paradox: Each shell contributes L1 = 4 r12x l* infinite number of shells infinite luminosity (at least) one of the assumptions must be wrong ! How to solve Olber’s paradox ? Universe is finite Universe has finite age The distribution of stars throughout space is not uniform The wavelength of radiation increases with time Note: for the big bang model, all these conditions are satisfied Einstein: • speed of light = const relativity of simultaneity, special relativity • general relativity: space-time is curved • prediction of black holes • prediction of gravitational waves Einstein • Universe has to be static! • only possible if extra-term is included in equations to counter-balance attraction cosmological constant • Einstein’s “biggest blunder” Edwin Hubble (1889-1953) Four major accomplishments in extragalactic astronomy The establishment of the Hubble classification scheme of galaxies The convincing proof that galaxies are island “universes” The distribution of galaxies in space The discovery that the universe is expanding Doppler effect (for light) The light of an approaching source is shifted to the blue, the light of a receding source is shifted to the red Doppler effect The light of an approaching source is shifted to the blue, the light of a receding source is shifted to the red. blue shift red shift Doppler effect redshift: obsem z em z=0: not moving z=2: v=0.8c z=: v=c The redshift-distance relation Key results Most galaxies are moving away from us The recession speed v is larger for more distant galaxies. The relation between recess velocity v and distance d fulfills a linear relation: v = H0 d Hubble’s measurement of the constant H0: H0 = 500 km/s/Mpc today’s best fit value of the constant: H0 = 71 km/s/Mpc (WMAP) Question: If all galaxies are moving away from us, does this imply that we are at the center? Answer: Not necessarily, it also can indicate that the universe is expanding and that we are at no special place. Einstein’s General Relativity + observation of expanding Universe: Universe started from a point: “Big Bang Model” Big Bang Model Big Bang in a nutshell: Cosmological redshift While a photon travels from a distant source to an observer on Earth, the Universe expands in size from Rthen to Rnow. Not only the Universe itself expands, but also the wavelength of the photon . received Rnow emitted Rthen Cosmological redshift General definition of redshift: received emitted z emitted for cosmological redshift: 1 z received emitted Rnow Rthen A large redshift z implies ... The spectrum is strongly shifted toward red or even infrared colors The object is very far away We see the object at an epoch when the universe was much younger than the present day universe most distant astrophysical object discovered so far: z= 6.3 (in 2005) z>5.8: “dark ages” Are there any indications that this picture is correct? Yes ! Primordial Nucleosynthesis Cosmic Microwave background Primordial Nucleosynthesis Georgy Gamov (1904-1968) If the universe is expanding, then there has been a big bang Therefore, the early universe must have been very dense and hot Optimum environment to breed the elements by nuclear fusion (Alpher, Bethe & Gamow, 1948) success: predicted that helium abundance is 25% failure: could not reproduce elements more massive than lithium and beryllium ( formed in stars) The Cosmic Microwave Background (CMB) Last scattering surface transparent opaque Penzias and Wilson 1965 Working at Bell labs Used a satellite dish to measure radio emission of the Milky Way They found some extra noise in the receiver, but couldn’t explain it discovery of the background radiation Most significant cosmological observation since Hubble Nobel prize for physics 1978 The cosmic microwave background radiation (CMB) Temperature of 2.728±0.004 K isotropic to 1 part in 100 000 perfect black body 1990ies: CMB is one of the major tools to study cosmology Note: ~1% of the noise in your TV is from the big bang More results from the CMB The Earth is moving with respect to the CMB Doppler shift The emission of the Galaxy Fluctuations in the CMB •Fluctuations in CMB responsible for structure formation in the universe Cosmic Structure formation New developments: Science discovery of the year 1998 fainter q0 = 0 q0 = 0.5 Data indicates: q0 < 0 Expansion is accelerating more distant From Supernova observations: The expansion of the universe is accelerating !!! But gravity is always attractive, so it only can decelerate Revival of the cosmological constant The fate of the Universe for >0 k=+1 >0 =0 Wilkinson Microwave Anisotropy Probe (WMAP) (2003) COBE (1992) WMAP (2003) Summary of most important results of WMAP • Age of the Universe: 13.7 billion years • First stars: 200 million years after Big Bang • CMB: decoupled 379 000 years after Big Bang • Hubble constant: H0= 71 (km/s)/Mpc • Content of the Universe: - 4% Atoms - 23 % cold, dark matter - 73 % ‘Dark Energy’