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Physics 270 – The Universe: Astrophysics, Gravity and Cosmology •Andris Skuja, May 9, 2006 -- Physics 270 The History of Cosmology • Mythology vs the scientific method • Cosmos = Earth solar system Milky Way Hubble sphere • Copernicus, Brahe, Kepler, Galileo •Andris Skuja, May 9, 2006 -- Physics 270 Newton: Cosmology as a Science • Galileo: The Scientific method & the universality of scientific laws • Newton’s laws • Newton’s gravity: The heavens and the Earth follow the same scientific principles • Galileo: Relativity before Einstein •Andris Skuja, May 9, 2006 -- Physics 270 Einstein’s Theories of Special and General Relativity • Principle of Relativity • Giving up absolute space and time • Space and time: where common sense makes no sense • what is here and there or now and then ? •Andris Skuja, May 9, 2006 -- Physics 270 Special Relativity • All inertial frames of reference are equivalent • The speed of light is absolute (invariant) • Maxwell’s equations are invariant under Lorentz transformation • Newton’s laws, which are based on absolute space and time, need to be modified •Andris Skuja, May 9, 2006 -- Physics 270 Some open problems • How to treat accelerations ? • How to deal with gravity ? • Newton’s gravity acts instantaneously, i.e. it is inconsistent with special relativity’s conclusion that information cannot be communicated faster than the speed of light. • Distance is relative, so which distance to use in computing the gravitational force ? •Andris Skuja, May 9, 2006 -- Physics 270 Non-inertial reference frame • Non-inertial frames fictitious forces – centrifugal force – Coriolis force •Andris Skuja, May 9, 2006 -- Physics 270 Why is the Space Shuttle orbiting? The space Shuttle is continuously falling towards the Earth •Andris Skuja, May 9, 2006 -- Physics 270 Is there no gravity in space ? No, there is gravity (actually Earth’s gravity at the orbit of the Shuttle is still ~80-90% of its strength on the ground So why do astronauts appear to be weightless ? •Andris Skuja, May 9, 2006 -- Physics 270 What effect does mass have? • Gravity: tendency of massive bodies to attract each other • Inertia: resistance of a body against changes of its current state of motion •Andris Skuja, May 9, 2006 -- Physics 270 Is gravity and inertia the same thing ? • No. They are completely different physical concepts. • There is no a priori reason, why they should be identical. In fact, for the electromagnetic force (Coulomb force), the source (the charge Q) and inertia (m) are indeed different. • But for gravity they appear to be identical Equivalence Principle •Andris Skuja, May 9, 2006 -- Physics 270 Eötvös experiment Gravity Coriolis •Andris Skuja, May 9, 2006 -- Physics 270 Result of the Eötvös experiment • Gravitational and inertial mass are identical to one part in a billion • modern experiments: identical to one part in a hundred billion •Andris Skuja, May 9, 2006 -- Physics 270 What effect does mass have? • Source of gravity F G M mgravity r 2 • Inertia F minertia a •Andris Skuja, May 9, 2006 -- Physics 270 Principle of Equivalence F minertial a G M mgravity r 2 mgravity M G 2 a m r inertial =1 •Andris Skuja, May 9, 2006 -- Physics 270 Weak equivalence principle The laws of mechanics are precisely the same in all inertial and freely falling frames. In particular, gravity is completely indistinguishable from any other acceleration. Strong equivalence principle The laws of physics are precisely the same in all inertial and freely falling frames, there is no experiment that can distinguish them. •Andris Skuja, May 9, 2006 -- Physics 270 Consequences of the equivalence principle: mass bends light Observer in freely falling reference frame •Andris Skuja, May 9, 2006 -- Physics 270 Consequences of the equivalence principle: mass bends light Outside Observer •Andris Skuja, May 9, 2006 -- Physics 270 Examples for light bending •Andris Skuja, May 9, 2006 -- Physics 270 Some effects predicted by the theory of general relativity • • • • gravity bends light gravitational redshift gravitational time dilation gravitational length contraction •Andris Skuja, May 9, 2006 -- Physics 270 Least action principle • light travels on a path that minimizes the distance between two points for flat space: straight line • a path that minimizes the distance between two points is called a geodesic • Examples for geodesics – plane: straight line – sphere: great circle •Andris Skuja, May 9, 2006 -- Physics 270 What is the shortest way to Europe? •Andris Skuja, May 9, 2006 -- Physics 270 Spacetime • Fourth coordinate: ct • time coordinate has different sign than spatial coordinates • spacetime distance: s c t ct x x 2 2 2 • , , : metric coefficients •Andris Skuja, May 9, 2006 -- Physics 270 2 Weak equivalence principle The laws of mechanics are precisely the same in all inertial and freely falling frames. In particular, gravity is completely indistinguishable from any other acceleration. Strong equivalence principle The laws of physics are precisely the same in all inertial and freely falling frames, there is no experiment that can distinguish them. •Andris Skuja, May 9, 2006 -- Physics 270 General relativity • Mass tells space how to curve • Space tells mass how to move •Andris Skuja, May 9, 2006 -- Physics 270 Why does space curvature result in attraction ? •Andris Skuja, May 9, 2006 -- Physics 270 Euclidean (flat) geometry: • Given a line and a point not on the line, only one line can be drawn through that point that will be parallel to the first line • The circumference of a circle of radius r is 2 r • The three angles of a triangle sum up to 180 •Andris Skuja, May 9, 2006 -- Physics 270 Spherical geometry: • Given a line and a point not on the line, no line can be drawn through that point that will be parallel to the first line • The circumference of a circle of radius r is smaller than 2 r • The three angles of a triangle sum up to more than 180 •Andris Skuja, May 9, 2006 -- Physics 270 Hyperbolic geometry: • Given a line and a point not on the line, an infinite number of lines can be drawn through that point that will be parallel to the first line • The circumference of a circle of radius r is larger than 2 r • The three angles of a triangle sum up to less than 180 •Andris Skuja, May 9, 2006 -- Physics 270 Tidal forces (I) •Andris Skuja, May 9, 2006 -- Physics 270 Tidal forces (II) •Andris Skuja, May 9, 2006 -- Physics 270 Tidal forces (III) •Andris Skuja, May 9, 2006 -- Physics 270 Tidal forces (IV) •Andris Skuja, May 9, 2006 -- Physics 270 So does the existence of tidal forces violate the equivalence principle ? • there is no freely falling frame of reference in which gravity vanishes globally • there is a freely falling frame of reference in which gravity vanishes locally • equivalence principle holds for small labs, “small” in comparison to distances over which the gravitational field changes significantly. • spacetime is locally flat •Andris Skuja, May 9, 2006 -- Physics 270 Towards a new theory for gravity ... Requirements: • it should locally fulfill the equivalence principle • it should relate geometry of space to the distribution of mass and energy • it should be locally flat • it should reduce to Newtonian gravity for small velocities (compared to c) and for weak gravitational fields •Andris Skuja, May 9, 2006 -- Physics 270 The entire Universe in one line G 8 G 4 T c Geometry of spacetime (Einstein tensor) Distribution of mass and energy in the universe (stress-energy tensor) •Andris Skuja, May 9, 2006 -- Physics 270 Why is general relativity (GR) difficult ? • conceptually difficult (relativity of space and time, curvature of spacetime) • set of 10 coupled partial differential equations • non linear (solutions do not superpose) • space and time are part of the solution exact solution known only for a very few simple cases •Andris Skuja, May 9, 2006 -- Physics 270 Checklist • How to deal with accelerations ? • How to deal with gravity ? • Newton’s gravity acts instantaneously, i.e. it is inconsistent with special relativity’s conclusion that information cannot be communicated faster than the speed of light. • Distance is relative, so which distance to use in computing the gravitational force ? •Andris Skuja, May 9, 2006 -- Physics 270 So what is left to do ? • Show that general relativity provides a consistent and accurate description of nature test it by experiment/observation •Andris Skuja, May 9, 2006 -- Physics 270 Some open problems • How to deal with accelerations ? • How to deal with gravity ? • Newton’s gravity acts instantaneously, i.e. it is inconsistent with special relativity’s conclusion that information cannot be communicated faster than the speed of light. • Distance is relative, so which distance to use in computing the gravitational force ? •Andris Skuja, May 9, 2006 -- Physics 270 Boost factor • special relativity: 1 1 v2 c2 • general relativity: 1 1 2 2 GM v esc 1 Rc2 1 c2 •Andris Skuja, May 9, 2006 -- Physics 270 First test: bending of light • Star light should be bend as it passes through the gravitational field of the Sun, i.e., it should be possible to see a star behind the Sun •Andris Skuja, May 9, 2006 -- Physics 270 First test: bending of light • Star light should be bend as it passes through the gravitational field of the Sun, i.e., it should be possible to see a star behind the Sun • General relativity predicts an angle of 1.75”, twice as big as that predicted by Newtonian gravity • measured by Arthur Eddington in 1919. Key event for Einstein’s elevation to a celebrity. •Andris Skuja, May 9, 2006 -- Physics 270 Test 2: Perihelion shift of Mercury • Planets do not move on perfect ellipses, but ellipses are precessing. This effect is due to the gravitational force exerted by the other planets •Andris Skuja, May 9, 2006 -- Physics 270 Test 2: Perihelion shift of Mercury • Planets do not move on perfect ellipses, but ellipses are precessing. This effects is caused by the perturbing effect of the other planets gravitational field. • Mercury’s precession amounts to 5600” per century, but only 5557” can be explained by Newtonian gravity, leaves a discrepancy of 43” per century. • General relativity predicts exactly this additional precession •Andris Skuja, May 9, 2006 -- Physics 270 Test 3: gravitational time dilation and redshift • Can be measured by experiments on Earth (challenging, but feasible) • Better: White Dwarfs (very compact objects; mass comparable to that of the Sun, radius comparable to that of the Earth), because they have a stronger gravitational field • Even better: Neutron Stars and Pulsars (very compact objects; mass comparable to that of the Sun, radius only 10-100 km), because they have a very strong gravitational field •Andris Skuja, May 9, 2006 -- Physics 270 Test 4: Binary pulsar PSR 1913+16 • Pulsar: a rapidly rotating highly magnetized neutron star that emits radio pulses at regular intervals • Discovered by Bell and Hewish in 1967 • Nobel Prize in physics (1974) •Andris Skuja, May 9, 2006 -- Physics 270 Test 4: Binary pulsar PSR 1913+16 • Pulsar: •Andris Skuja, May 9, 2006 -- Physics 270 Test 4: Binary pulsar PSR 1913+16 • Binary pulsar: two pulsars orbiting each other • Orbital time: 7.75h • Discovered by Hulse and Taylor in 1974 • Nobel Prize in physics (1993) •Andris Skuja, May 9, 2006 -- Physics 270 Test 4: Binary pulsar PSR 1913+16 • Precession: 4.2º per year •Andris Skuja, May 9, 2006 -- Physics 270 Test 4: Binary pulsar PSR 1913+16 • Time delay: Clocks tick slower in strong gravitational fields •Andris Skuja, May 9, 2006 -- Physics 270 Test 4: Binary pulsar PSR 1913+16 • Gravitational Waves: Orbital decay due to emission of gravitational radiation data points Prediction of GR •Andris Skuja, May 9, 2006 -- Physics 270 Tests to come: Gravity Probe B •Andris Skuja, May 9, 2006 -- Physics 270 Gravitational time dilation and redshift • Can be measured by experiments on Earth (challenging, but feasible) • Better: White Dwarfs (very compact objects; mass comparable to that of the Sun, radius comparable to that of the Earth), because they have a stronger gravitational field • Even better: Neutron Stars and Pulsars (very compact objects; mass comparable to that of the Sun, radius only 10-100 km), because they have a very strong gravitational field •Andris Skuja, May 9, 2006 -- Physics 270 Flash-back: Newtonian gravity • What velocity is required to leave the gravitational field of a planet or star? vesc 2G M R • Example: Earth – Radius: R = 6470 km = 6.47106 m – Mass: M = 5.97 1024 kg escape velocity: vesc = 11.1 km/s •Andris Skuja, May 9, 2006 -- Physics 270 Flash-back: Newtonian gravity • What velocity is required to leave the gravitational field of a planet or star? vesc • Example: Sun 2G M R – Radius: R = 700 000 km = 7108 m – Mass: M = 21030 kg escape velocity: vesc = 617 km/s •Andris Skuja, May 9, 2006 -- Physics 270 Flash-back: Newtonian gravity • What velocity is required to leave the gravitational field of a planet or star? vesc 2G M R • Example: a solar mass White Dwarf – Radius: R = 5000 km = 5106 m – Mass: M = 21030 kg escape velocity: vesc = 7300 km/s •Andris Skuja, May 9, 2006 -- Physics 270 Flash-back: Newtonian gravity • What velocity is required to leave the gravitational field of a planet or star? vesc 2G M R • Example: a solar mass neutron star – Radius: R = 10 km = 104 m – Mass: M = 21030 kg escape velocity: vesc = 163 000 km/s ½ c •Andris Skuja, May 9, 2006 -- Physics 270 Flash-back: Newtonian gravity • Can an object be so small that even light cannot escape ? Black Hole 2G M vescRS 2 cR RS: “Schwarzschild Radius” • Example: for a solar mass – Mass: M = 21030 kg Schwarzschild Radius: RS = 3 km •Andris Skuja, May 9, 2006 -- Physics 270 Some definitions ... and Black Holes • The Schwarzschild radius RS of an object of mass M is the radius, at which the escape speed is equal to the speed of light. • The event horizon is a sphere of radius RS. Nothing within the event horizon, not even light, can escape to the world outside the event horizon. • A Black Hole is an object whose radius is smaller than its event horizon. •Andris Skuja, May 9, 2006 -- Physics 270 Sizes of objects •Andris Skuja, May 9, 2006 -- Physics 270 Let’s do it within the context of general relativity — spacetime • spacetime distance (flat space): s c t R 2 2 2 time 2 space • Fourth coordinate: ct • time coordinate has different sign than spatial coordinates •Andris Skuja, May 9, 2006 -- Physics 270 Let’s do it within the context of general relativity — spacetime • spacetime distance (curved space of a point mass): RGM 11 2 2 S 2 2 2 2 ss 11 2 c ctt R 2GM 1 cR R 1 RS c/2 RR 22 time •Andris Skuja, May 9, 2006 -- Physics 270 space What happens if R RS 1 RS 2 2 2 s 1 c t R R 1 RS / R 2 time space • R > RS: everything o.k.: time: +, space: but gravitational time dilation and length contraction • R RS: time 0 space • R < RS: signs change!! time: , space: + “space passes”, everything falls to the center infinite density at the center, singularity •Andris Skuja, May 9, 2006 -- Physics 270 Structure of a Black Hole •Andris Skuja, May 9, 2006 -- Physics 270 What happens to an astronaut who falls into a black hole? • Far outside: nothing special • Falling in: long before the astronaut reaches the event horizon, he/she is torn apart by tidal forces • For an outside observer: – astronaut becomes more and more redshifted – The astronaut’s clock goes slower and slower – An outside observer never sees the astronaut crossing the event horizon. •Andris Skuja, May 9, 2006 -- Physics 270 What happens, if an astronaut falls into a black hole? • For the astronaut: – He/she reaches and crosses the event horizon in a finite time. – Nothing special happens while crossing the event horizon (except some highly distorted pictures of the local environment) – After crossing the event horizon, the astronaut has 10 microseconds to enjoy the view before he/she reaches the singularity at the center. •Andris Skuja, May 9, 2006 -- Physics 270 Cosmic censorship • Singularity: a point at which spacetime diverges – – – – infinite forces are acting laws of physics break down quantum gravity may help ? no problem as long as a singularity is shielded from the outside world by an event horizon • Hypothesis: Every singularity is surrounded by an event horizon. There are no naked singularities •Andris Skuja, May 9, 2006 -- Physics 270 Near a black hole: bending of light •Andris Skuja, May 9, 2006 -- Physics 270 The Photon sphere The photon sphere is a sphere of radius 1.5 RS. On the photon sphere, light orbits a black hole on a circular orbit. •Andris Skuja, May 9, 2006 -- Physics 270 Structure of a rotating black hole Within the ergosphere (or static sphere) nothing can remain at rest. Spacetime is dragged around the hole •Andris Skuja, May 9, 2006 -- Physics 270 No-Hair theorem • Properties of a black hole: – – – – it has a mass it has an electric charge it has a spin (angular momentum) that’s it. Like an elementary particle, but much more massive Black holes have no hair •Andris Skuja, May 9, 2006 -- Physics 270 Hawking Radiation • Heisenberg uncertainty principle: Et > h/2 Energy need not be conserved over short periods, only on average • Virtual particles: particle-antiparticle pairs created from vacuum energy fluctuations which quickly disappear • Virtual particles that can "steal" energy from elsewhere become real •Andris Skuja, May 9, 2006 -- Physics 270 Hawking Radiation • Virtual pairs near a black hole can steal energy from the gravitational field – Tidal stresses accelerate one particle outward, one drops into event horizon – Energy of new particle comes from gravitational energy of BH, so BH mass must decrease – Black hole evaporates! •Andris Skuja, May 9, 2006 -- Physics 270 Hawking Radiation • Energy for new particles comes from tidal stresses – Tidal effects must be large over short path lengths of virtual pairs – Smaller black holes have steeper gravitational gradients => Smaller black holes evaporate more quickly tevap = 1010(MBH /1012 kg)3 yr tevap(1Msolar) ~ 1065 yr •Andris Skuja, May 9, 2006 -- Physics 270 Hawking Radiation • Black holes emit as black bodies – Temperature of black hole proportional to rate of radiation – TBH = 10-7 (Msolar / MBH) – T(1 Msolar) ~ 10-7 K – T(106 Msolar) ~ 10-13 K •Andris Skuja, May 9, 2006 -- Physics 270 Exotica • White holes - a phenomenon analogous to a black hole from which light can only escape. No obvious way to make or power one • Wormholes - conduits between two points in spacetime. Unstable, difficult to avoid singularity without going faster than c, solutions with timelike paths only size of elementary particles. If they exist, probably not useful for travel since stable solutions require "exotic matter" •Andris Skuja, May 9, 2006 -- Physics 270 A Practical Perspective • Two main types of black hole in the universe – Stellar mass black holes: created by the collapse of a massive star at the end of its life, ~3-100? Msolar – Supermassive black holes (SMBH): found in the centers of galaxies, power quasars and AGN, ~a few times 106 - 109 M •Andris Skuja, May 9, 2006 -- Physics 270 Stellar Black Holes • Created from stars of more than ~30 Msolar • Detectable in binary systems – Normal or evolved star transfers mass to black hole via accretion disk – Measure orbital period and velocity of companion and use Kepler's laws to derive lower limits on mass – Neutron stars < 3 Msolar so any larger invisible companion must be black hole or unknown physics •Andris Skuja, May 9, 2006 -- Physics 270 Stellar Black Holes •Andris Skuja, May 9, 2006 -- Physics 270 Stellar Black Holes •Andris Skuja, May 9, 2006 -- Physics 270 Stellar Black Holes • X-Ray Binaries – Viscosity (friction) of gas in disk heats up disk – A few to 40% of gravitational potential energy (= rest mass energy) liberated – Temperatures of ~105-106 K in inner disk – Spectrum peaks in soft x-rays – Optically thin material in corona or inner disk at >107 K gives hard x-ray emission – Some with relativistic jets – Luminosities of order 105 Lsolar •Andris Skuja, May 9, 2006 -- Physics 270 Supermassive Black Holes • Active Galactic Nuclei (AGN) – Many types; most commonly discussed are radio galaxies, Seyferts, quasars, and QSOs – Large black holes at the centers of galaxies form at early epochs, possibly from collapse of dense stellar clusters, and grow by accretion over lifetime of universe – Luminosity from accretion disks as in X-ray binaries, but larger BH = lower temperature •Andris Skuja, May 9, 2006 -- Physics 270 Supermassive Black Holes • AGN structure – Accretion disk at a few x 104 K, peak emission in UV (R ~ 100AU ~100 RS) – Hot, rarefied gas in x-ray halo or corona (R ~ 110 AU ~ RS) – Broad emission line region (BLR); clouds with velocities of 104 kms-1, indicate strong gravitational field (R ~ 0.01pc) – Dusty molecular torus in plane of disk (R ~ 0.11pc) IR emission •Andris Skuja, May 9, 2006 -- Physics 270 Supermassive Black Holes • AGN structure continued – Narrow emission line region (NLR); clouds of ionized gas with widths of a few hundred kms-1 Seen in cones extending from ~50pc to 15kpc – Relativistic jets - accelerated by magnetic fields in disk to significant fraction of c. Looking headon into quasar jets, see OVVs and BL Lacs – Jets in radio galaxies may extend ~1 Mpc •Andris Skuja, May 9, 2006 -- Physics 270 Supermassive Black Holes •Andris Skuja, May 9, 2006 -- Physics 270 Supermassive Black Holes •Andris Skuja, May 9, 2006 -- Physics 270 Supermassive Black Holes •Andris Skuja, May 9, 2006 -- Physics 270 Supermassive Black Holes •Andris Skuja, May 9, 2006 -- Physics 270 Supermassive Black Holes • AGN characteristics – Emission over 21 orders of magnitude in frequency - from radio to -rays – Range of luminosities, from barely discernable to > 1015 Lsolar, 10,000 times the luminosity of a bright galaxy – Radio quiet and radio loud – Often associated with starbursts, interacting galaxies, Luminous Infrared Galaxies (LIRGs, ULIRGs, HLIRGs) •Andris Skuja, May 9, 2006 -- Physics 270 Supermassive Black Holes • Evidence – Kinematic evidence • • • • Stellar motions in center of Milky Way Stellar and gas motions in other galaxies OH masers in NGC 4258 All imply tremendous mass in a tiny area – Images of dusty torii and accretion disks – Only way of producing enough energy to make a quasar in so little space •Andris Skuja, May 9, 2006 -- Physics 270 Supermassive Black Holes •Andris Skuja, May 9, 2006 -- Physics 270 Supermassive Black Holes •Andris Skuja, May 9, 2006 -- Physics 270 Supermassive Black Holes •Andris Skuja, May 9, 2006 -- Physics 270 Supermassive Black Holes •Andris Skuja, May 9, 2006 -- Physics 270 Questions: • Do they really exist ? (Observe gravitational effects ) • How do we observe something that does not emit light? (Light bends around them) •Andris Skuja, May 9, 2006 -- Physics 270 The cosmic distance ladder • Parallax – solar neighborhood (< 1 kpc) • Main sequence fitting – distances within the Galaxy (<100 kpc) • Cepheids – nearby galaxies (< 20 Mpc) • Tully-Fisher relation – distant galaxies (< 500 Mpc) • Type 1a supernovae – cosmological distances (~ 1 Gpc) •Andris Skuja, May 9, 2006 -- Physics 270 Nature of spiral nebulae and the Milky Way (MW) Curtis • MW is 10 kpc across • Sun near center • spiral nebulae were other galaxies – high recession speed – apparent sizes of nebulae – did not believe van Maanen’s measurement Milky Way = one galaxy among many others Shapley • MW is 100 kpc across • Sun off center • spiral nebulae part of the Galaxy – apparent brightness of nova in the Andromeda galaxy – measured rotation of spirals (via proper motion) by van Maanen Milky Way = Universe •Andris Skuja, May 9, 2006 -- Physics 270 Solution • Role of dust – obscuration: Kapteyn/Curtis could only see a small fraction of the Milky Way disk – dimming: stars appear to be dimmer Shapley, ignoring dust, concluded that globular clusters are farther away than they actually are. Milky Way is 30 kpc across, Sun is 8.5 kpc off center. Spiral nebulae are galaxies like the Milky Way. Distance: millions of parsec. •Andris Skuja, May 9, 2006 -- Physics 270 •Andris Skuja, May 9, 2006 -- Physics 270 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 •Andris Skuja, May 9, 2006 -- Physics 270 The Hubble classification •Andris Skuja, May 9, 2006 -- Physics 270 The Hubble classification • Elliptical galaxies (E0-E7) – classified according to their flattening: 10(1-b/a) • Spiral galaxies (S0, Sa-Sd) – classified according to their bulge-to-disk ratio – Sa: large bulge, Sd: small bulge – S0: transition spiral to elliptical • Barred spiral galaxies (SB0, SBa-SBd) – classified according to their bulge to disk ratio • Irregular galaxies (Irr) •Andris Skuja, May 9, 2006 -- Physics 270 THE EXPANDING UNIVERSE: Using the Doppler Effect to Measure Velocity T4 T3 T2 T1 Redshift Blueshift •Andris Skuja, May 9, 2006 -- Physics 270 Galaxy Spectroscopy Spectra of a nearby star and a distant galaxy Star is nearby, approximately at rest Galaxy is distant, traveling away from us at 12,000 km/s Stellar Spectrum Sodium Magnesium The larger the redshift: the greater the distance from us Galaxy Spectrum Calcium •Andris Skuja, May 9, 2006 -- Physics 270 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 •Andris Skuja, May 9, 2006 -- Physics 270 red shift Doppler effect redshift: 1 v / c 1 z 1 v / c z=0: not moving z=2: v=0.8c z=: v=c •Andris Skuja, May 9, 2006 -- Physics 270 The redshift-distance relation •Andris Skuja, May 9, 2006 -- Physics 270 The redshift-distance relation •Andris Skuja, May 9, 2006 -- Physics 270 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 = 70 km/s/Mpc •Andris Skuja, May 9, 2006 -- Physics 270 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. If the velocity of recession is proportional to distance, then any point is at the center of the expansion •Andris Skuja, May 9, 2006 -- Physics 270 The great synthesis (1930) • Meeting by Einstein, Hubble and Lemaître – Einstein: theory of general relativity – Friedmann and Lemaître: expanding universe as a solution to Einstein’s equation – Hubble: observational evidence that the universe is indeed expanding • Consequence: – Universe started from a point The Big Bang Model •Andris Skuja, May 9, 2006 -- Physics 270 History of the Universe (with Inflation) •Andris Skuja, May 9, 2006 -- Physics 270 Let’s apply Einstein’s equation to the Universe • What is the solution of Einstein’s equation for a homogeneous, isotropic mass distribution? – As in Newtonian dynamics, gravity is always attractive – a homogeneous, isotropic and initially static universe is going to collapse under its own gravity – Alternative: expanding universe (Friedmann) •Andris Skuja, May 9, 2006 -- Physics 270 Einstein’s proposal: cosmological constant • There is a repulsive force in the universe vacuum exerts a pressure empty space is curved rather than flat • The repulsive force compensates the attractive gravity static universe is possible • but: such a universe turns out to be unstable: one can set up a static universe, but it simply does not remain static • Einstein: “greatest blunder of his life”, but is it really … ? •Andris Skuja, May 9, 2006 -- Physics 270 initial distance: 1 length unit final distance: 2 length units recess velocity: 1 length unit per time unit initial distance: 2 length units final distance: 4 length units recess velocity: 2 length units per time unit •Andris Skuja, May 9, 2006 -- Physics 270 A metric of an expanding Universe • Recall: flat space s ct x y z 2 2 2 2 2 • better: using spherical coordinates (r,,) s ct r r r sin 2 2 2 2 •Andris Skuja, May 9, 2006 -- Physics 270 2 2 2 2 A metric of an expanding Universe • But, this was for a static space. How does this expression change if we consider an expanding space ? s ct R 2 (t ) r 2 r 2 2 r 2 sin 2 2 2 2 • R(t) is the so-called scale factor •Andris Skuja, May 9, 2006 -- Physics 270 Example: static universe R(t) t •Andris Skuja, May 9, 2006 -- Physics 270 Example: expanding at a constant rate R(t) t •Andris Skuja, May 9, 2006 -- Physics 270 Example: expansion is slowing down R(t) t •Andris Skuja, May 9, 2006 -- Physics 270 Example: expansion is accelerating R(t) t •Andris Skuja, May 9, 2006 -- Physics 270 Example: collapsing R(t) t •Andris Skuja, May 9, 2006 -- Physics 270 How old is the universe? • A galaxy at distance d recedes at velocity v=H0 d. • When was the position of this galaxy identical to that of our galaxy? Answer: d 1 t Hubble v H0 • tHubble: Hubble time. For H0 = 65 km/s/Mpc: tHubble = 15 Gyr •Andris Skuja, May 9, 2006 -- Physics 270 How big is the universe? • We can’t tell. We can only see (and are affected by) that part of the universe that is closer than the distance that light can travel in a time corresponding to the age of the Universe • But we can estimate, how big the observable universe is: c d Hubble ct Hubble H0 • dHubble: Hubble radius. For H0 = 65 km/s/Mpc: dHubble = 4.6 Gpc •Andris Skuja, May 9, 2006 -- Physics 270 A metric of an expanding Universe • But, so far, we only considered a flat space. What, if there is curvature ? 2 r 2 2 2 2 2 2 2 2 s ct R (t ) r r sin 2 1 kr • k is the curvature constant – k=0: flat space – k>0: spherical geometry – k<0: hyperbolic geometry •Andris Skuja, May 9, 2006 -- Physics 270 A metric of an expanding Universe • But, so far, we only considered a flat space. What, if there is curvature ? k>0 k=0 • k is the curvature constant – k=0: flat space – k>0: spherical geometry – k<0: hyperbolic geometry •Andris Skuja, May 9, 2006 -- Physics 270 k<0 Cosmological redshift • While a photon travels from a distance 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 changes. received Rnow emitted Rthen •Andris Skuja, May 9, 2006 -- Physics 270 Cosmological redshift • General definition of redshift: received emitted z emitted for cosmological redshift: 1 z received emitted Rnow Rthen •Andris Skuja, May 9, 2006 -- Physics 270 Cosmological redshift • Examples: – z=1 Rthen/Rnow = 0.5 • at z=1, the universe had 50% of its present day size • emitted blue light (400 nm) is shifted all the way through the optical spectrum and is received as red light (800 nm) – z=4 Rthen/Rnow = 0.2 • at z=4, the universe had 20% of its present day size • emitted blue light (400 nm) is shifted deep into the infrared and is received at 2000 nm – most distant astrophysical object discovered so far: z=5.8 •Andris Skuja, May 9, 2006 -- Physics 270 Let’s switch to general relativity • Friedmann equation 8 G 2 2 v R kc 3 2 • k is the curvature constant •Andris Skuja, May 9, 2006 -- Physics 270 Let’s switch to general relativity • Friedmann equation 8 G 2 2 v R kc 3 2 • k is the curvature constant – k=0: flat space, forever expanding – k>0: spherical geometry, eventually recollapsing – k<0: hyperbolic geometry, forever expanding •Andris Skuja, May 9, 2006 -- Physics 270 k>0 k=0 •Andris Skuja, May 9, 2006 -- Physics 270 k<0 Can we predict the fate of the Universe ? • Friedmann equation: v8 G8 G2 kc 2 H v 2 R kc 2 R 3 3 R 2 2 22 0 • k=0: crit 2 0 3H 8 G •Andris Skuja, May 9, 2006 -- Physics 270 Can we predict the fate of the Universe ? • If the density of the Universe – =crit: flat space, forever expanding – >crit: spherical geometry, recollapsing – < crit: hyperbolic geometry, forever expanding • so what is the density of the universe? – We don’t know precisely – >crit very unlikely – currently favored model: 0.3crit •Andris Skuja, May 9, 2006 -- Physics 270 How big is crit ? • crit = 810-30 g/cm3 1 atom per 200 liter • density parameter 0 3H 0 crit 8 G 2 0 – 0 =1: flat space, forever expanding (open) – 0 >1: spherical geometry, recollapsing (closed) – 0 <1: hyperbolic geometry, forever expanding • currently favored model: 0 = 0.3 •Andris Skuja, May 9, 2006 -- Physics 270 How can we measure 0 ? • Count all the mass we can “see” – tricky, some of the mass may be hidden … • Measure the rate at which the expansion of the universe is slowing down – a more massive universe will slow down faster • Measure the geometry of the universe – is it spherical, hyperbolic or flat ? •Andris Skuja, May 9, 2006 -- Physics 270 Let’s try to measure the deceleration • Acceleration according to Newton: M 4 G a G 2 R R 3 • deceleration parameter aR 0 q0 2 v 2 •Andris Skuja, May 9, 2006 -- Physics 270 So what’s the meaning of q0 ? • deceleration parameter q0 – q0>0.5: – 0<q0<0.5: deceleration is so strong that eventually the universe stops expanding and starts collapsing deceleration is too weak to stop expansion • What’s the difference between q0, 0 and k ? – k: – 0: – q0: curvature of the universe mass content of the universe kinematics of the universe •Andris Skuja, May 9, 2006 -- Physics 270 So let’s measure q0 ! • How do we do that? – Measure the rate of expansion at different times, i.e. measure and compare the expansion based on nearby galaxies and based on high redshift galaxies • Gravity is slowing down expansion expansion rate should be higher at high redshift. •Andris Skuja, May 9, 2006 -- Physics 270 So let’s measure q0 ! q0 = 0 q0 = 0.5 fainter Data indicates: q0 < 0 Expansion is accelerating more distant •Andris Skuja, May 9, 2006 -- Physics 270 Science discovery of the year 1998 • The expansion of the universe is accelerating !!! • But gravity is always attractive, so it only can decelerate Revival of the cosmological constant •Andris Skuja, May 9, 2006 -- Physics 270 Friedmann’s equation for >0 8 G R 2 2 v R kc 3 3 2 2 • k is the curvature constant – k=0: flat space space, flat universe – k>0: spherical geometry geometry, closed universe – k<0: hyperbolic geometry, geometry open universe • but for sufficiently large a spherically curved universe may expand forever •Andris Skuja, May 9, 2006 -- Physics 270 Deceleration parameter q for >0 • Acceleration according to Newton: 4 G a R R 3 3 • deceleration parameter with aR 0 q0 2 v 2 2 3H 0 •Andris Skuja, May 9, 2006 -- Physics 270 The fate of the Universe for >0 k=+1 >0 =0 •Andris Skuja, May 9, 2006 -- Physics 270 Is the fate of the Universe well determined ? • deceleration: – ½0 – > 0: decelerating – ½0 – < 0: accelerating • curvature – 0 + = 1: flat – 0 + < 1: hyperbolic – 0 + > 1: spherical • two equations for two variables well posed problem •Andris Skuja, May 9, 2006 -- Physics 270 Cosmology: the quest for three numbers • The Hubble constant H0 how fast is the universe expanding • The density parameter 0 how much mass is in the universe • The cosmological constant the vacuum energy of the universe • current observational situation: • H0 = 65 km/s/Mpc • 0 = 0.3; = 0.7 flat space •Andris Skuja, May 9, 2006 -- Physics 270 How old is the Universe? • A galaxy at distance d recedes at velocity v=H0 d. • When was the position of this galaxy identical to that of our galaxy? Answer: d 1 t Hubble v H0 • tHubble: Hubble time. For H0 = 65 km/s/Mpc: tHubble = 15 Gyr •Andris Skuja, May 9, 2006 -- Physics 270 The age of the Universe revisited • So far, we have assumed that the expansion velocity is not changing (q0=0, empty universe) • How does this estimate change, if the expansion decelerates, i.e. q0>0 ? now • An 0>0, =0 universe is younger than 15 Gyr •Andris Skuja, May 9, 2006 -- Physics 270 The age of the Universe revisited • So far, we only have considered decelerating universes now • How does this estimate change, if the expansion accelerates, i.e. q0<0 ? • An >0 universe can be older than 15 Gyr •Andris Skuja, May 9, 2006 -- Physics 270 The age of the Universe revisited • 0=0, =0: tHubble =1/H0 = 15 Gyr • 0=1, =0: tHubble =2/(3H0)= 10 Gyr • open universes with 0<0<1, =0 are between 10 and 15 Gyr old • closed universes with 0>1, =0 are less than 10 Gyr old • >0 increases, <0 decreases the age of the universe • 0=0.3, =0.7: tHubble =0.96/H0 = 14.5 Gyr •Andris Skuja, May 9, 2006 -- Physics 270 Can we measure the age of the Universe ? • not directly • but we can constrain the age of the Universe. It must not be younger than the oldest star in the Universe. • How do we measure the age of stars? – radioactive dating – stellar evolution models • Result: age of the oldest star ~12-14 Gyr • 0>~1 strongly disfavored •Andris Skuja, May 9, 2006 -- Physics 270 The life of a universe – key facts • Unless is sufficiently large (which is inconsistent with observations) all cosmological models start with a big bang. • An universe doesn’t change its geometry. A flat universe has always been and will always be flat, a spherical universe is always spherical and so on. • Two basic solutions: – eventual collapse for large 0 or negative – eternal expansion otherwise •Andris Skuja, May 9, 2006 -- Physics 270 Some common misconceptions • The picture that the Universe expands into a preexisting space like an explosion • The question “what was before the big bang?” • Remember: spacetime is part of the solution to Einstein’s equation • Space and time are created in the big bang •Andris Skuja, May 9, 2006 -- Physics 270 So is the big crunch the same as the big bang run in reverse ? • No. The Universe has meanwhile formed stars, black holes, galaxies etc. • Second law of thermodynamics: The entropy (disorder) of a system at best stays the same but usually increases with time, in any process. There is no perpetual motion machine. • Second law of thermodynamics defines an arrow of time. •Andris Skuja, May 9, 2006 -- Physics 270 Friedmann’s equation for =0, 0<1 8 G kc H 2 3 R 2 Expansion rate Falls off like Falls off like of the Universe the cube of R the square of R • At early epochs, the first term dominates the early universe appears to be almost flat • At late epochs, the second term dominates the late universe appears to be almost empty •Andris Skuja, May 9, 2006 -- Physics 270 Friedmann’s equation for >0, 0<1 8 G kc H 2 3 R 3 2 Expansion rate of the Universe Falls off like Falls off like the cube of R the square of R constant • At early epochs, the first term dominates the early universe appears to be almost flat • At late epochs, the third term dominates the late universe appears to be exponentially expanding •Andris Skuja, May 9, 2006 -- Physics 270 A puzzling detail • =0: for most of its age, the universe looks either to be flat or to be empty • >0: for most of its age, the universe looks either to be flat or to be exponentially expanding • Isn’t it strange that we appear to live in that short period between those two extremes ? Flatness problem •Andris Skuja, May 9, 2006 -- Physics 270 The life of a universe – key facts • Unless is sufficiently large (which is inconsistent with observations) all cosmological models start with a big bang. • An universe doesn’t change its geometry. A flat universe has always been and will always be flat, a spherical universe is always spherical and so on. • Two basic solutions: – eventual collapse for large 0 or negative – eternal expansion otherwise •Andris Skuja, May 9, 2006 -- Physics 270 General acceptance of the big bang model • Until mid 60ies: big bang model very controversial, many alternative models • After mid 60ies: little doubt on validity of the big bang model • Four pillars on which the big bang theory is resting: – – – – Hubble’s law Cosmic microwave background radiation The origin of the elements Structure formation in the universe •Andris Skuja, May 9, 2006 -- Physics 270 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) •Andris Skuja, May 9, 2006 -- Physics 270 Hoyle’s ”Big Bang” •Andris Skuja, May 9, 2006 -- Physics 270 What are the consequences (Gamow)? • In order to form hydrogen and helium at the right proportions, the following conditions are required: – density: 10-5 g/cm-3 – temperature: T 109 K • Radiation from this epoch should be observable as an isotropic background radiation • Due to the expansion of the universe to 310-30 g/cm3, the temperature should have dropped to T 5 K (-450 F) • Can we observe this radiation ? •Andris Skuja, May 9, 2006 -- Physics 270 The discovery of the relic radiation • Gamov’s result on the background radiation was not well recognized by the scientific community • Result was rediscovered by Dicke and Peebles in the early sixties. They started developing an antenna to search for the background radiation • T 5 K microwaves • but … •Andris Skuja, May 9, 2006 -- Physics 270 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 •Andris Skuja, May 9, 2006 -- Physics 270 A quote ... • John Bahcall: "The discovery of the cosmic microwave background radiation changed forever the nature of cosmology, from a subject that had many elements in common with theology to a fantastically exciting empirical study of the origins and evolution of the things that populate the physical universe." •Andris Skuja, May 9, 2006 -- Physics 270 The Big Bang and the Creation of the elements (Hoyle + Saltpeter) • Atoms are mostly empty space • Atoms consist of protons (+), neutrons (o) and electrons (-) • protons and neutrons form the atomic nucleus • # of protons determines the element • electrons in the outskirts determine chemistry •Andris Skuja, May 9, 2006 -- Physics 270 The structure of matter • Neutrons and protons are very similar, but – Protons are electrically charged, neutrons are not – Neutrons have a slightly higher mass • Electrons are much less massive than nucleons most of the mass of an atom is in its nucleus • If charges of the same sign repel, and the nucleus is made of protons, why don’t the protons fly apart ? •Andris Skuja, May 9, 2006 -- Physics 270 The four forces of nature • gravity • electromagnetism • strong nuclear force – keeps atomic nuclei together • weak nuclear force – decay of free neutrons into protons + n p+ + e•Andris Skuja, May 9, 2006 -- Physics 270 The structure of matter •Andris Skuja, May 9, 2006 -- Physics 270 Abundance of elements • Hydrogen and helium most abundant • gap around Li, Be, B •Andris Skuja, May 9, 2006 -- Physics 270 Thermal history of the universe • When the universe was younger than 300 000 yrs, it was so hot that neutral atoms separated into nuclei and electrons. It was too hot to bind atomic nuclei and electrons to atoms by the electromagnetic force • When the universe was younger than ~1 sec, it was so hot that atom nuclei separated into neutrons and protons. It was too hot to bind protons and neutrons to atomic nuclei by the strong nuclear force •Andris Skuja, May 9, 2006 -- Physics 270 Formation of helium in the big bang • Hydrogen: 1 nucleon (proton) • Helium: 4 nucleons (2 protons, 2 neutrons) • In order to from helium from hydrogen one has to – bring 2 protons and 2 neutrons close together, so the strong nuclear force can act and hold them together – close together: Coulomb repulsion has to be overcome high velocities high temperatures • but: 4 body collisions are highly unlikely •Andris Skuja, May 9, 2006 -- Physics 270 Transforming hydrogen into helium • Hot big bang: neutrons and protons • Use a multi step procedure: – – – – p + n 2H p + 2H 3He n + 2H 3H 3He + 3He 4He + 2 p • some side reactions: – 3He + 3H 7Li – 3He + 3He 7Be •Andris Skuja, May 9, 2006 -- Physics 270 Mass gap/stability gap at A=5 and 8 • There is no stable atomic nucleus with 5 or with 8 nucleons • Reaction chain stops at 7Li • So how to form the more massive elements? • There exist a meta-stable nucleus (8B*). If this nucleus is hit by another 4He during its lifetime, 12C and other elements can be formed •Andris Skuja, May 9, 2006 -- Physics 270 Mass gap/stability gap at A=5 and 8 • Reaction chain: – 4He + 4He 8B* – 8B* + 4He 12C • so-called 3-body reaction (Saltpeter) • in order to have 3-body reactions, high particle densities are required – densities are not high enough in the big-bang – but they are in the center of evolved stars • Conclusion: big bang synthesizes elements up to 7Li. Higher elements are formed in stars •Andris Skuja, May 9, 2006 -- Physics 270 Primordial nucleosynthesis Consistent with abundance of H, He and Li Result: • abundance of H,He and Li is consistent • but: b ~0.04 •Andris Skuja, May 9, 2006 -- Physics 270 How far can we see ? • Naked eye: 2 million Light years (Andromeda galaxy) • Large telescopes: 14 billion Lyr (z=5.8) • What are the limiting factors ? – there are no bright sources at high z – light is redshifted into the infrared – absorption • The universe appears to be fairly transparent out to z=5.8 •Andris Skuja, May 9, 2006 -- Physics 270 When does a gas become opaque? • A gas appears opaque (e.g. fog) if light is efficiently scattered by the atoms/molecules of the gas The three important factors are thus – the density of the gas (denser more particles more scattering) – the efficiency with which each individual particle can scatter light – wavelength of the light •Andris Skuja, May 9, 2006 -- Physics 270 The transition from a transparent to an opaque universe • At z=0 the universe is fairly transparent • At higher z, the universe becomes denser ( = 0(1+z)3) and hotter (T=T0(1+z)) • At z=1100, the universe is so dense that its temperature exceeds 3000K. In a fairly sharp transition, the universe becomes completely ionized and opaque to visible light. (last scattering surface) • At z=1100, the universe is ~300 000 yrs old •Andris Skuja, May 9, 2006 -- Physics 270 Black body radiation • A hot a body is brighter than a cool one (LT4, Stefan-Boltzmann’s law) • A hot body’s spectrum is bluer than that of a cool one (max1/T, Wien’s law) •Andris Skuja, May 9, 2006 -- Physics 270 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 •Andris Skuja, May 9, 2006 -- Physics 270 Should the CMB be perfectly smooth ? • No. Today’s Universe is homogeneous and isotropic on the largest scales, but there is a fair amount of structure on small scales, such as galaxies, clusters of galaxies etc. •Andris Skuja, May 9, 2006 -- Physics 270 Should the CMB be perfectly smooth ? • We expect some wriggles in the CMB radiation, corresponding to the seeds from which later on galaxies grow •Andris Skuja, May 9, 2006 -- Physics 270 The Cosmic Background Explorer (COBE) Main objectives: • To accurately measure the temperature of the CMB • To find the expected fluctuations in the CMB •Andris Skuja, May 9, 2006 -- Physics 270 Main results from COBE •Andris Skuja, May 9, 2006 -- Physics 270 More results from the CMB • The Earth is moving with respect to the CMB Doppler shift – Earth’s motion around the Sun – Sun’s motion around the Galaxy – Motion of the Galaxy with respect to other galaxies (large scale flows) •Andris Skuja, May 9, 2006 -- Physics 270 More results from the CMB • The Earth is moving with respect to the CMB Doppler shift • The emission of the Galaxy •Andris Skuja, May 9, 2006 -- Physics 270 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 •Andris Skuja, May 9, 2006 -- Physics 270 The BOOMERANG mission • COBE was a satellite mission, why ? – Measure at mm and sub-mm wavelengths – Earth atmosphere almost opaque at those wavelengths due to water vapor – satellite missions take a long time and are expensive • What can be done from the ground ? – Balloon experiment – desert South Pole •Andris Skuja, May 9, 2006 -- Physics 270 The BOOMERANG mission •Andris Skuja, May 9, 2006 -- Physics 270 The BOOMERANG mission •Andris Skuja, May 9, 2006 -- Physics 270 How can we measure the geometry of the universe • We need a yard stick on the CMB • For different curvatures, a yard stick of given length appears under different angles •Andris Skuja, May 9, 2006 -- Physics 270 Measuring the Curvature of the Universe Using the CMB •Andris Skuja, May 9, 2006 -- Physics 270 Measuring the Curvature of the Universe Using the CMB • Recall: with supernovae, one measures q0 =½0 – • CMB fluctuations measure curvature 0 + • two equations for two variables problem solved •Andris Skuja, May 9, 2006 -- Physics 270 What comes next ? WMAP •Andris Skuja, May 9, 2006 -- Physics 270 Planck Can we see the sound of the universe ? • Compressed gas heats up temperature fluctuations •Andris Skuja, May 9, 2006 -- Physics 270 Acoustic Oscillations in the CMB • Although there are fluctuations on all scales, there is a characteristic angular scale. •Andris Skuja, May 9, 2006 -- Physics 270 Acoustic Oscillations in the CMB WMAP team (Bennett et al. 2003) •Andris Skuja, May 9, 2006 -- Physics 270 Last scattering surface transparent opaque •Andris Skuja, May 9, 2006 -- Physics 270 Sound Waves in the Early Universe After recombination: Before recombination: Ionized – Universe is neutral. – Photons can travel freely past the baryons. – Phase of oscillation at trec affects late-time amplitude. Recombination z ~ 1000 ~400,000 years Time •Andris Skuja, May 9, 2006 -- Physics 270 Neutral Today Big Bang – Universe is ionized. – Photons provide enormous pressure and restoring force. – Perturbations oscillate as acoustic waves. Sound Waves • Each initial overdensity (in DM & gas) is an overpressure that launches a spherical sound wave. • This wave travels outwards at 57% of the speed of light. • Pressure-providing photons decouple at recombination. CMB travels to us from these spheres. • Sound speed plummets. Wave stalls at a radius of 150 Mpc. • Overdensity in shell (gas) and in the original center (DM) both seed the formation of galaxies. Preferred separation of 150 Mpc. •Andris Skuja, May 9, 2006 -- Physics 270 QuickTime™ and a GIF decompressor are needed to see this picture. A Statistical Signal • The Universe is a superposition of these shells. • The shell is weaker than displayed. • Hence, you do not expect to see bullseyes in the galaxy distribution. • Instead, we get a 1% bump in the correlation function. •Andris Skuja, May 9, 2006 -- Physics 270 Cosmological Constraints Pure CDM degeneracy 2s 1s Acoustic scale alone WMAP 1s range •Andris Skuja, May 9, 2006 -- Physics 270 The History of the Universe The “Concordance” Model (not yet the “Standard Model”) of Cosmology: The Universe is homogeneous and flat (horizon problem and flatness problem) The Universe evolved from a quantum fluctuation no bigger than 10-35 m in diameter. Since gravitational energy is negative and the energy of a massive object is positive, the total energy of the quantum fluctuation can be zero If the fluctuation now expands it may become the entire universe The “Concordance” Model postulates that the initial expansion was very rapid indeed (cosmic inflation) •Andris Skuja, May 9, 2006 -- Physics 270 History of the Universe (with Inflation) •Andris Skuja, May 9, 2006 -- Physics 270 Inflation (potential) •Andris Skuja, May 9, 2006 -- Physics 270 Matter era • The energy of matter is nowadays ~10000 times higher than that of radiation • but temperature rises like (1+z) • 2.7K < T < 10000K: matter era • dominate particles (in order of decreasing contribution: – baryons, photons, neutrinos • dominant forces: – gravity •Andris Skuja, May 9, 2006 -- Physics 270 Radiation era • As the temperature exceeds ~ 10000K, radiation starts dominating • 10000K < T < 1010K: radiation era • dominate particles (in order of decreasing contribution: – photons, neutrinos, baryons • dominant forces: – electromagnetism, gravity •Andris Skuja, May 9, 2006 -- Physics 270 Electron-positron annihilation • As the temperature exceeds ~ 1010K, creation of electron-positron pairs – T > 1010K: equilibrium between electronpositron pair creation and annihilation – T < 1010K: freeze-out. Remaining pairs annihilate •Andris Skuja, May 9, 2006 -- Physics 270 Lepton era • 1010K < T < 1012K • dominate particles (in order of decreasing contribution: – electrons, positrons, photons, neutrinos, antineutrinos, baryons • dominant forces: – electromagnetism, weak nuclear, gravity •Andris Skuja, May 9, 2006 -- Physics 270 Hadron annihilation • As the temperature exceeds ~ 1012K, creation of hadron-antihadron pairs (e.g. proton-antiproton) – T > 1012K: equilibrium between hadron pair creation and annihilation – T < 1012K: freeze-out. Remaining pairs annihilate •Andris Skuja, May 9, 2006 -- Physics 270 Hadron era • 1012K < T < 1013K • dominate particles (in order of decreasing contribution: – baryons+antiparticles, mesons+antiparticles, electrons, positrons, photons, neutrinos, antineutrinos • dominant forces: – electromagnetism, strong nuclear, weak nuclear, gravity •Andris Skuja, May 9, 2006 -- Physics 270 Still quark era • 1013K < T < 1015K • hadrons (baryons, mesons) break into quarks • dominate particles (in order of decreasing contribution: – quarks, antiquarks, electrons, positrons, photons, neutrinos, antineutrinos • dominant forces: – electromagnetism, strong nuclear, weak nuclear, gravity •Andris Skuja, May 9, 2006 -- Physics 270 Electroweak phase transition • As the temperature exceeds ~ 1015K, electromagnetism and weak nuclear force join to form the electroweak force – T > 1015K: electroweak force – T < 1015K: electromagnetism, weak nuclear force • Limit of what we can test in particle accelerators. • Nobel prizes 1979 (theory) and 1984 (experiment) •Andris Skuja, May 9, 2006 -- Physics 270 Quark era • 1015K < T < 1029K • dominate particles (in order of decreasing contribution: – quarks, antiquarks, electrons, positrons, photons, neutrinos, antineutrinos • dominant forces: – electroweak, strong nuclear, gravity •Andris Skuja, May 9, 2006 -- Physics 270 GUT phase transition • As the temperature exceeds ~ 1029K, electroweak force and strong nuclear force join to form the GUT (grand unified theories) – T > 1029K: GUT – T < 1029K: electroweak force, strong nuclear force • relatively solid theoretical framework (but may be wrong), but pretty much no constraint by experiments •Andris Skuja, May 9, 2006 -- Physics 270 GUT era • 1029K < T < 1032K • dominate particles (in order of decreasing contribution: – Zillions of particles, most of them not detected yet • dominant forces: – GUT, gravity •Andris Skuja, May 9, 2006 -- Physics 270 Planck epoch • T > 1032K unification of GUT and gravity • Particles: – ??? • Forces: – TOE (theory of everything) • The last frontier ... •Andris Skuja, May 9, 2006 -- Physics 270 Structure formation in the Big-Bang model •Andris Skuja, May 9, 2006 -- Physics 270 The Hubble sequence of galaxies •Andris Skuja, May 9, 2006 -- Physics 270 A galaxy census: spiral galaxies • Most common type among the luminous galaxies (~75%) • two major classes, S and SB – regular spirals (S) – barred spirals (SB) • further classified from a to d according to the bulge-to-disk ratio – a: very large, prominent bulge – d: essentially no bulge at all • The Milky Way is a Sbc or a SBbc galaxy •Andris Skuja, May 9, 2006 -- Physics 270 A galaxy census: spiral galaxies • Spiral galaxies are disk like and in centrifugal equilibrium • The are “cold”, i.e. the velocity dispersion (random motion of individual stars) s is much smaller than the rotation velocity vrot (Milky Way: s=20 km/s; vrot=220 km/s) • They mainly consist of stars, but ~10% of the mass is gas and dust • They actively form stars (Milky Way: ~ 1 star per year) •Andris Skuja, May 9, 2006 -- Physics 270 A galaxy census: elliptical galaxies • ~20% of the luminous galaxies are ellipticals • classified according to the flattening E0-E7: n=10(1b/a) – E0: circular – E7: minor axis only 30% of major axis • They are “hot”, i.e. the velocity dispersion s is much larger than the rotation velocity vrot • flattened by an anisotropic velocity dispersion • little gas, no recent star formation • predominantly in clusters of galaxies •Andris Skuja, May 9, 2006 -- Physics 270 A galaxy census: other galaxies • Irregular galaxies (~ 5% of the luminous galaxies) • dwarf galaxies – – – – – dwarf irregulars dwarf spheroidals dwarf ellipticals blue compact dwarfs ... •Andris Skuja, May 9, 2006 -- Physics 270 Toomre & Toomre (mid 70s) • 11 out of the 4000 galaxies in the New General Catalog (NGC) show indications of recent interactions (e.g. tails) • Those tidal features last a few 108 years • Over the age of the universe, several hundred of those interactions must have taken place • There are several hundred elliptical galaxies in the NGC •Andris Skuja, May 9, 2006 -- Physics 270 Do ellipticals form by merging spirals ? •Andris Skuja, May 9, 2006 -- Physics 270 Younger galaxies should be smaller ... •Andris Skuja, May 9, 2006 -- Physics 270 How good is the assumption of isotropy? • CMB: almost perfect • but what about the closer neighborhood ? •Andris Skuja, May 9, 2006 -- Physics 270 How good is the assumption of isotropy? • CMB: almost perfect • but what about the closer neighborhood ? The great wall •Andris Skuja, May 9, 2006 -- Physics 270 The spatial distribution of galaxies • Galaxies are not randomly distributed but correlated • Network of structures (filaments, sheets, walls) “cosmic web” Courtesy: Huan Lin •Andris Skuja, May 9, 2006 -- Physics 270 65 Mpc z=9.00 50 million particle N-body simulation •Andris Skuja, May 9, 2006 -- Physics 270 65 Mpc z=4.00 50 million particle N-body simulation •Andris Skuja, May 9, 2006 -- Physics 270 65 Mpc z=2.33 50 million particle N-body simulation •Andris Skuja, May 9, 2006 -- Physics 270 65 Mpc z=1.00 50 million particle N-body simulation •Andris Skuja, May 9, 2006 -- Physics 270 65 Mpc z=0.00 50 million particle N-body simulation •Andris Skuja, May 9, 2006 -- Physics 270 Does a picture like this look familiar ? •Andris Skuja, May 9, 2006 -- Physics 270 Counting all the mass ... • Obstacle: we want mass, but we see light • Procedure: – count all the stars you see and multiply them with there luminosity total visible luminosity – correct for dust absorption total luminosity – convert luminosity into mass using a mass-tolight ratio M / M sun L / Lsun – The sun has =1 by definition. •Andris Skuja, May 9, 2006 -- Physics 270 Overall result: 0.01 Implications: • less than the nucleosynthesis constraint of =0.04 in baryons consistent • Most of the baryons in the universe (~75%) do not shine [are too dim to be detected] – gas and dust – stellar remnants (white dwarfs, neutron stars, black holes) – brown dwarfs [failed stars] •Andris Skuja, May 9, 2006 -- Physics 270 •Andris Skuja, May 9, 2006 -- Physics 270 Evidence of dark matter: rotation curves of spiral galaxies •Andris Skuja, May 9, 2006 -- Physics 270 Fritz Zwicky He measured the velocities of galaxies in galaxy clusters and concluded that most of the cluster’s mass must be dark •Andris Skuja, May 9, 2006 -- Physics 270 Evidence of dark matter: X-ray clusters •Andris Skuja, May 9, 2006 -- Physics 270 Evidence of dark matter: clusters of galaxies •Andris Skuja, May 9, 2006 -- Physics 270 Evidence of dark matter: large scale flows •Andris Skuja, May 9, 2006 -- Physics 270 Overall result: 0.3 Implications: • most of the mass in the Universe is dark • most of it is even of non-baryonic origin • the perfect Copernican principle – – – – The Earth is not at the center of the solar system The Sun is not at the center of the Milky Way The Milky Way is not at the center of the Universe We may not even be made from the most abundant type of matter in the Universe •Andris Skuja, May 9, 2006 -- Physics 270 Is the claim that dark matter exist really so embarrassing ? • When Leverrier was proposing in the 1840s that there maybe an 8th planet in the solar system, Neptune, a planet that can explain the irregularities of Uranus’ orbit, this planet was also “dark matter” • But it was a clear prediction that eventually could be tested observationally • The discovery of Neptune by Galle was one of the finest moments of science •Andris Skuja, May 9, 2006 -- Physics 270 MACHOs ? • MAssive Compact Halo Objects • Brown dwarfs (stars not massive enough to shine) • Dim white dwarfs (relics of stars like the Sun) • Massive black holes (stars that massive that even light cannot escape) • but: if the DM is really in MACHOs, something with the nucleosynthesis constraint must be wrong •Andris Skuja, May 9, 2006 -- Physics 270 How can we see MACHOs ? • Gravitational lensing: • If foreground object has only little mass, the image split is too small to be observed • But the amplification (brightening) is observable •Andris Skuja, May 9, 2006 -- Physics 270 How can we see MACHOs ? • How likely is it for a star in the Milky Way to get amplified ? • Once every 10 million years •Andris Skuja, May 9, 2006 -- Physics 270 How can we see MACHOs ? • Solution: monitor 10 million stars simultaneously •Andris Skuja, May 9, 2006 -- Physics 270 How can we see MACHOs ? Magnification due to gravitational lensing There are not enough brown dwarfs to account for the dark matter in the Milky Way. Alcock et al. 1993 •Andris Skuja, May 9, 2006 -- Physics 270 WIMPs ? • Weakly Interacting Massive Particles • Massive neutrino – at least we know that it exists – we don’t know whether it has mass or not – hot dark matter (hot: moving at speeds near the speed of light) • Another (yet undiscovered) particle predicted by some particle physicists – cold dark matter (cold: moving much slower than the speed of light) •Andris Skuja, May 9, 2006 -- Physics 270 Summary • The Universe is stranger than Alice’s Wonderland • We have only scratched the surface of what is know • Many insights and observations still to come •Andris Skuja, May 9, 2006 -- Physics 270