II. The Universe Around Us ASTR378 Cosmology : II. The Universe Around Us 23
Some Units Used in Astronomy 1 parsec distance at which parallax angle is 1 ; 1 pc = 3.086 10 16 m ( 3.26 light years; 1 kpc = 3.086 10 19 m, 1 Mpc = 3.086 10 22 m) 1 M = 1.989 10 30 kg, 1L = 3.839 10 26 W 1 Å = 10-10 m (0.1 nm) 1 ev = 1.602 10-19 J ASTR378 Cosmology : II. The Universe Around Us 24
Stars (Sun: 1 M, 1 L ) The Visible Universe Galaxies (MW: 10 11 10 12 M ) Local Group (MW + M31 +...): scale ~1 Mpc Clusters/superclusters of galaxies, voids: scale ~100 Mpc ~Smooth on larger scales... ASTR378 Cosmology : II. The Universe Around Us 25
Other Wavelengths of Light Microwaves: the Cosmic Microwave Background (CMB), black body spectrum corresponding to 2.7 K Radio, Infrared: can penetrate (IR can be emitted by) dust, see obscured star formation / objects at high redshift (+...) X-ray: hot gas, important for measuring the mass of galaxy clusters (+...) ASTR378 Cosmology : II. The Universe Around Us 26
The Cosmological Principle Considering the largest scales in the Universe, we make the following fundamental assumptions: 1) Homogeneity: On the largest scales, the Universe has the same physical properties Every region has the same physical properties (mass density, expansion rate, visible vs. dark matter, etc.) 2) Isotropy: On the largest scales, the Universe looks the same in any direction We should see the same largescale structure in any direction 3) Universality: The laws of physics are the same everywhere in the Universe ASTR378 Cosmology : II. The Universe Around Us 27
Homogeneity and Isotropy Cosmological principle: on large scales the Universe is homogeneous and isotropic homogeneous (Universe looks the same at each point) isotropic (Universe looks the same in all directions) but isotropic at every point = homogeneous large scales: > 100 Mpc Perfect cosmological principle: the Universe is homogeneous and isotropic in space and time Steady State Universe (not true!) CMB ASTR378 Cosmology : II. The Universe Around Us 28
Olbers Paradox Heinrich Olbers (1826): Why is the night sky dark? n = mean number density of stars, L = mean stellar luminosity flux at Earth: f (r) = L 4πr 2 power (unit area) -1 (steradian) -1 : total intensity of starlight: Yet the night sky is dark...? dj(r) = J = nl 4π L 4πr 2 n r2 dr r= 0 dr = ASTR378 Cosmology : II. The Universe Around Us 29
The Expanding Universe Blueshift Redshift z : z λ obs λ em λ em z v c (SR: 1 + z ) ( ) = 1 + v /c 1 v /c Redshift 1920 s: Hubble (and Humason) discovered a proportionality between a galaxy s redshift and its distance (Hubble Law) z = H 0 c r v = H 0 r ASTR378 Cosmology : II. The Universe Around Us 30
The Hubble Constant Hubble found a value for the Hubble Constant H 0 500 km s -1 Mpc -1 (bad calibration!) For decades H 0 disputed (50 100); current consensus H 0 70 km s -1 Mpc -1 Outside the Local Group, virtually every galaxy is moving away from us -- why doesn t this violate the Cosmological Principle? If no acceleration/deceleration, galaxies were together at time: Original Hubble Diagram More Recent Version t 0 = r v = r H 0 r = H 1 0 H 0 70 H 1 0 14 Gyr, (Hubble Time) c 4300Mpc (Hubble Distance, H 0 or horizon distance) ASTR378 Cosmology : II. The Universe Around Us 31
How can the Hubble Law be Isotropic? Three galaxies (1,2,3) in a triangular configuration, with sides r12, r23, r31 Homogeneous, uniform expansion means shape preserved expansion law of form r12(t) = a(t)r12(t0) a(t): scale factor; a = 1 @ t= t0 At time t, an observer in galaxy 1 will see the other galaxies receding with velocity: dr a 1 r12 ( t ) dt a dr a v 31 (t) = 31 = a r31 ( t 0 ) = r31 ( t ) dt a v12 (t) = 12 2 = a r12 ( t 0 ) = 3 the velocity distance relation takes the linear form v = Hr, with H=å/a ASTR378 Cosmology : II. The Universe Around Us 32
What s the Universe Made Of? 2 E total E γ = hf = m 2 c 4 + p 2 c 2 E total = mc 2 1 + p2 m 2 c 2 1/ 2 Energy of a particle mc 2 + 1 2 p 2 m ( hν ) Energy of a photon in the nonrelativistic limit Baryons Particle Symbol Rest Energy (MeV) Charge proton p 938.3 +1 neutron n 939.6 0 electron e - 0.511-1 neutrino e,,?,?,? 0 photon 0 0 dark matter??? 0 ASTR378 Cosmology : II. The Universe Around Us 33
Sneak Peek: What is the Universe Made of? 0.6% in Stars ASTR378 Cosmology : II. The Universe Around Us 34
Blackbody Radiation In thermodynamic equilibrium, photons have a energy density in the frequency interval df around frequency f given by the blackbody (BB) function: ε( f )df = 8πh c 3 ε γ = αt 4, α = π 2 k B 4 f 3 df exp(hf /k B T) 1 The number density of photons is: n γ = βt 3, β = 2.404 π 2 15h 3 c 3 7.565 10-16 J m -3 K -4 k B 3 h 3 c 3 2.03 10 7 m -3 K -3 ASTR378 Cosmology : II. The Universe Around Us 35
Blackbody Radiation II Peak frequency of BB distribution: f peak 2.8k B T/h Peak energy of BB distribution: E peak = hf peak 2.8k B T Mean photon energy: E mean = hf mean 2.7k B T ASTR378 Cosmology : II. The Universe Around Us 36
The Cosmic Microwave Background Discovered in 1965 by Penzias and Wilson, BB spectrum with T=2.725±0.001 K Big Bang vs. Steady State Once dipole (motion towards Hydra, 630 km s -1 ) and Galactic emission subtracted, extremely isotropic / homogeneous (10-5 ) Note: ~1% of the static on TV is due to the CMB! ASTR378 Cosmology : II. The Universe Around Us 37
How is the CMB a Relic of the Big Bang? Hot Big Bang: Early Universe very dense and very hot (T>>10 4 K) baryonic matter completely ionised, free electrons made Universe opaque to photons As Universe expanded, T ; when T~3000 K, neutral atoms formed, no longer many free electrons photons free to go So why is the CMB a 2.7 K BB, not a 3000 K BB? V a( t) 3, ε γ = αt 4, P γ = ε γ 3 dq = de + PdV, dq = 0, de dt = P ( t ) dv dt E = ε γ V = αt 4 V, P = P γ = αt 4 3 dt α 4T 3 dt V + T dv 4 = 1 dt 3 αt dv 4 dt 1 T dt dt = 1 3V ASTR378 Cosmology : II. The Universe Around Us 38 dv dt ; V a ( t ) 3 d ( dt lnt ) = d ( dt lna ) T(t) a(t) 1 The CMB was a 3000 K BB when the Universe was ~1100 smaller!
Looking at the Last Scattering Surface Today, at z = 0 the universe is fairly transparent At higher redshift, z (looking backward in time) the universe was denser (ρ = ρ0 (1+z)3) and hotter (T=T0 (1+z)) At z 1100, the universe was so dense that T > 3000 K At z > 1100 there is a transition: the universe becomes completely ionised and opaque to visible light the last scattering surface The universe was ~350,000 years old at z 1100 ASTR378 Cosmology : II. The Universe Around Us 39
Should the CMB be Smooth? There are people, planets, stars, galaxies, galaxy clusters and galaxy superclusters today, so we expect some non-uniformities (wiggles, etc.) in the CMB ASTR378 Cosmology : II. The Universe Around Us 40
The Cosmic Background Explorer (COBE) Objectives: Accurately measure the CMB temperature Find expected CMB fluctuations ASTR378 Cosmology : II. The Universe Around Us 41
Basic results from COBE ASTR378 Cosmology : II. The Universe Around Us 42
More Results from COBE The Earth is moving with respect to the CMB detectable Doppler shift! Earth s motion around the Sun Sun s motion around the Galaxy the Galaxy s motion w/rt other galaxies (large scale flows) Microwave emission from the Galaxy Fluctuations in the CMB ASTR378 Cosmology : II. The Universe Around Us 43
The CMB Today COBE (1990 s) WMAP (2000 s) ASTR378 Cosmology : II. The Universe Around Us 44
The Latest: Planck (2009 ) ASTR378 Cosmology : II. The Universe Around Us 45
Olbers Paradox Revisited What are our assumptions? Unobstructed line of sight to every star in the Universe? not true some could be blocked by foreground stars, intervening dust but still night sky should look like the surface of a star! Number density n and mean luminosity L constant w/rt r? Universe is infinitely large? (And filled with stars?) Universe is infinitely old? Flux from distant sources follows inverse square law? ASTR378 Cosmology : II. The Universe Around Us 46