Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Physics 270 – The Universe: Astrophysics, Gravity and Cosmology.

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Physics 270 – The Universe: Astrophysics, Gravity and Cosmology

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 The History of Cosmology Mythology vs the scientific methodMythology vs the scientific method Cosmos = Earth  solar system  Milky Way  Hubble sphereCosmos = Earth  solar system  Milky Way  Hubble sphere Copernicus, Brahe, Kepler, GalileoCopernicus, Brahe, Kepler, Galileo

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Newton: Cosmology as a Science Galileo: The Scientific method & the universality of scientific lawsGalileo: The Scientific method & the universality of scientific laws Newton’s lawsNewton’s laws Newton’s gravity: The heavens and the Earth follow the same scientific principlesNewton’s gravity: The heavens and the Earth follow the same scientific principles Galileo: Relativity before EinsteinGalileo: Relativity before Einstein

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Einstein’s Theories of Special and General Relativity Principle of RelativityPrinciple of Relativity Giving up absolute space and timeGiving up absolute space and time Space and time: where common sense makes no senseSpace and time: where common sense makes no sense what is here and there or now and then ?what is here and there or now and then ?

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Special Relativity All inertial frames of reference are equivalentAll inertial frames of reference are equivalent The speed of light is absolute (invariant)The speed of light is absolute (invariant) Maxwell’s equations are invariant under Lorentz transformationMaxwell’s equations are invariant under Lorentz transformation Newton’s laws, which are based on absolute space and time, need to be modifiedNewton’s laws, which are based on absolute space and time, need to be modified

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Some open problems How to treat accelerations ?How to treat accelerations ? How to deal with gravity ?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.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 ?Distance is relative, so which distance to use in computing the gravitational force ?

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Non-inertial reference frame Non-inertial frames  fictitious forcesNon-inertial frames  fictitious forces –centrifugal force –Coriolis force

Andris Skuja, May 9, 2006 -- Physics 270Andris 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 270Andris 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 270Andris Skuja, May 9, 2006 -- Physics 270 What effect does mass have? Gravity: tendency of massive bodies to attract each otherGravity: tendency of massive bodies to attract each other Inertia: resistance of a body against changes of its current state of motionInertia: resistance of a body against changes of its current state of motion

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Is gravity and inertia the same thing ? No. They are completely different physical concepts.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.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 identicalBut for gravity they appear to be identical  Equivalence Principle

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Eötvös experiment Coriolis Gravity

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Result of the Eötvös experiment Gravitational and inertial mass are identical to one part in a billionGravitational and inertial mass are identical to one part in a billion modern experiments: identical to one part in a hundred billionmodern experiments: identical to one part in a hundred billion

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 What effect does mass have? Source of gravitySource of gravity InertiaInertia

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Principle of Equivalence =1

Andris Skuja, May 9, 2006 -- Physics 270Andris 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 270Andris 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 270Andris Skuja, May 9, 2006 -- Physics 270 Consequences of the equivalence principle: mass bends light Outside Observer

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Examples for light bending

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Some effects predicted by the theory of general relativity gravity bends lightgravity bends light gravitational redshiftgravitational redshift gravitational time dilationgravitational time dilation gravitational length contractiongravitational length contraction

Andris Skuja, May 9, 2006 -- Physics 270Andris 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 linelight 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 geodesica path that minimizes the distance between two points is called a geodesic Examples for geodesicsExamples for geodesics –plane: straight line –sphere: great circle

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 What is the shortest way to Europe?

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Spacetime Fourth coordinate: ctFourth coordinate: ct time coordinate has different sign than spatial coordinatestime coordinate has different sign than spatial coordinates spacetime distance:spacetime distance: , ,  : metric coefficients , ,  : metric coefficients

Andris Skuja, May 9, 2006 -- Physics 270Andris 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 270Andris Skuja, May 9, 2006 -- Physics 270 General relativity Mass tells space how to curveMass tells space how to curve Space tells mass how to moveSpace tells mass how to move

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Why does space curvature result in attraction ?

Andris Skuja, May 9, 2006 -- Physics 270Andris 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 lineGiven 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  rThe circumference of a circle of radius r is 2  r The three angles of a triangle sum up to 180 The three angles of a triangle sum up to 180 

Andris Skuja, May 9, 2006 -- Physics 270Andris 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 lineGiven 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  rThe circumference of a circle of radius r is smaller than 2  r The three angles of a triangle sum up to more than 180 The three angles of a triangle sum up to more than 180 

Andris Skuja, May 9, 2006 -- Physics 270Andris 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 lineGiven 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  rThe circumference of a circle of radius r is larger than 2  r The three angles of a triangle sum up to less than 180 The three angles of a triangle sum up to less than 180 

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Tidal forces (I)

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Tidal forces (II)

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Tidal forces (III)

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Tidal forces (IV)

Andris Skuja, May 9, 2006 -- Physics 270Andris 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 globallythere is no freely falling frame of reference in which gravity vanishes globally there is a freely falling frame of reference in which gravity vanishes locallythere 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.equivalence principle holds for small labs, “small” in comparison to distances over which the gravitational field changes significantly. spacetime is locally flatspacetime is locally flat

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Towards a new theory for gravity... Requirements: it should locally fulfill the equivalence principleit should locally fulfill the equivalence principle it should relate geometry of space to the distribution of mass and energyit should relate geometry of space to the distribution of mass and energy it should be locally flatit should be locally flat it should reduce to Newtonian gravity for small velocities (compared to c) and for weak gravitational fieldsit should reduce to Newtonian gravity for small velocities (compared to c) and for weak gravitational fields

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 The entire Universe in one line Geometry of spacetime (Einstein tensor) Distribution of mass and energy in the universe (stress-energy tensor)

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Why is general relativity (GR) difficult ? conceptually difficult (relativity of space and time, curvature of spacetime)conceptually difficult (relativity of space and time, curvature of spacetime) set of 10 coupled partial differential equationsset of 10 coupled partial differential equations non linear (solutions do not superpose)non linear (solutions do not superpose) space and time are part of the solutionspace and time are part of the solution  exact solution known only for a very few simple cases

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Checklist How to deal with accelerations ?How to deal with accelerations ? How to deal with gravity ?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.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 ?Distance is relative, so which distance to use in computing the gravitational force ?

Andris Skuja, May 9, 2006 -- Physics 270Andris 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/observationShow that general relativity provides a consistent and accurate description of nature  test it by experiment/observation

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Some open problems How to deal with accelerations ?How to deal with accelerations ? How to deal with gravity ?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.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 ?Distance is relative, so which distance to use in computing the gravitational force ?

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Boost factor special relativity:special relativity: general relativity:general relativity:

Andris Skuja, May 9, 2006 -- Physics 270Andris 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 SunStar 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 270Andris 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 SunStar 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 gravityGeneral 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.measured by Arthur Eddington in 1919. Key event for Einstein’s elevation to a celebrity.

Andris Skuja, May 9, 2006 -- Physics 270Andris 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 planetsPlanets 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 270Andris 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.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.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 precessionGeneral relativity predicts exactly this additional precession

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Test 3: gravitational time dilation and redshift Can be measured by experiments on Earth (challenging, but feasible)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 fieldBetter: 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 fieldEven 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 270Andris 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 intervalsPulsar: a rapidly rotating highly magnetized neutron star that emits radio pulses at regular intervals Discovered by Bell and Hewish in 1967Discovered by Bell and Hewish in 1967 Nobel Prize in physics (1974)Nobel Prize in physics (1974)

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Test 4: Binary pulsar PSR 1913+16 Pulsar:Pulsar:

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Test 4: Binary pulsar PSR 1913+16 Binary pulsar: two pulsars orbiting each otherBinary pulsar: two pulsars orbiting each other Orbital time: 7.75hOrbital time: 7.75h Discovered by Hulse and Taylor in 1974Discovered by Hulse and Taylor in 1974 Nobel Prize in physics (1993)Nobel Prize in physics (1993)

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Test 4: Binary pulsar PSR 1913+16 Precession: 4.2º per yearPrecession: 4.2º per year

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Test 4: Binary pulsar PSR 1913+16 Time delay: Clocks tick slower in strong gravitational fieldsTime delay: Clocks tick slower in strong gravitational fields

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Test 4: Binary pulsar PSR 1913+16 Gravitational Waves: Orbital decay due to emission of gravitational radiationGravitational Waves: Orbital decay due to emission of gravitational radiation data points Prediction of GR

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Tests to come: Gravity Probe B

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Gravitational time dilation and redshift Can be measured by experiments on Earth (challenging, but feasible)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 fieldBetter: 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 fieldEven 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 270Andris Skuja, May 9, 2006 -- Physics 270 Flash-back: Newtonian gravity What velocity is required to leave the gravitational field of a planet or star?What velocity is required to leave the gravitational field of a planet or star? Example: EarthExample: Earth –Radius: R = 6470 km = 6.47  10 6 m –Mass: M = 5.97  10 24 kg  escape velocity: v esc = 11.1 km/s

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Flash-back: Newtonian gravity What velocity is required to leave the gravitational field of a planet or star?What velocity is required to leave the gravitational field of a planet or star? Example: SunExample: Sun –Radius: R = 700 000 km = 7  10 8 m –Mass: M = 2  10 30 kg  escape velocity: v esc = 617 km/s

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Flash-back: Newtonian gravity What velocity is required to leave the gravitational field of a planet or star?What velocity is required to leave the gravitational field of a planet or star? Example: a solar mass White DwarfExample: a solar mass White Dwarf –Radius: R = 5000 km = 5  10 6 m –Mass: M = 2  10 30 kg  escape velocity: v esc = 7300 km/s

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Flash-back: Newtonian gravity What velocity is required to leave the gravitational field of a planet or star?What velocity is required to leave the gravitational field of a planet or star? Example: a solar mass neutron starExample: a solar mass neutron star –Radius: R = 10 km = 10 4 m –Mass: M = 2  10 30 kg  escape velocity: v esc = 163 000 km/s  ½ c

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Flash-back: Newtonian gravity Can an object be so small that even light cannot escape ?  Black HoleCan an object be so small that even light cannot escape ?  Black Hole R S : “Schwarzschild Radius” R S : “Schwarzschild Radius” Example: for a solar massExample: for a solar mass –Mass: M = 2  10 30 kg  Schwarzschild Radius: R S = 3 km

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Some definitions... and Black Holes The Schwarzschild radius R S of an object of mass M is the radius, at which the escape speed is equal to the speed of light.The Schwarzschild radius R S 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 R S. Nothing within the event horizon, not even light, can escape to the world outside the event horizon.The event horizon is a sphere of radius R S. 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.A Black Hole is an object whose radius is smaller than its event horizon.

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Sizes of objects

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Let’s do it within the context of general relativity — spacetime spacetime distance (flat space):spacetime distance (flat space): space time Fourth coordinate: ctFourth coordinate: ct time coordinate has different sign than spatial coordinatestime coordinate has different sign than spatial coordinates

Andris Skuja, May 9, 2006 -- Physics 270Andris 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):spacetime distance (curved space of a point mass): time space

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 What happens if R  R S R > R S : everything o.k.: time: +, space:  but gravitational time dilation and length contractionR > R S : everything o.k.: time: +, space:  but gravitational time dilation and length contraction R  R S : time  0 space  R  R S : time  0 space   R < R S : signs change!! time: , space: +  “space passes”, everything falls to the center  infinite density at the center, singularityR < R S : signs change!! time: , space: +  “space passes”, everything falls to the center  infinite density at the center, singularity time space

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Structure of a Black Hole

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 What happens to an astronaut who falls into a black hole? Far outside: nothing specialFar outside: nothing special Falling in: long before the astronaut reaches the event horizon, he/she is torn apart by tidal forcesFalling in: long before the astronaut reaches the event horizon, he/she is torn apart by tidal forces For an outside observer: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 270Andris Skuja, May 9, 2006 -- Physics 270 What happens, if an astronaut falls into a black hole? For the astronaut: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 270Andris Skuja, May 9, 2006 -- Physics 270 Cosmic censorship Singularity: a point at which spacetime divergesSingularity: 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.Hypothesis: Every singularity is surrounded by an event horizon. There are no naked singularities There are no naked singularities

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Near a black hole: bending of light

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 The Photon sphere The photon sphere is a sphere of radius 1.5 R S. On the photon sphere, light orbits a black hole on a circular orbit. The photon sphere is a sphere of radius 1.5 R S. On the photon sphere, light orbits a black hole on a circular orbit.

Andris Skuja, May 9, 2006 -- Physics 270Andris 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 Within the ergosphere (or static sphere) nothing can remain at rest. Spacetime is dragged around the hole

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 No-Hair theorem Properties of a black hole: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 Black holes have no hair

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Hawking Radiation Heisenberg uncertainty principle:Heisenberg uncertainty principle:  E  t > 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 disappearVirtual particles: particle-antiparticle pairs created from vacuum energy fluctuations which quickly disappear Virtual particles that can "steal" energy from elsewhere become realVirtual particles that can "steal" energy from elsewhere become real

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Hawking Radiation Virtual pairs near a black hole can steal energy from the gravitational fieldVirtual 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 270Andris Skuja, May 9, 2006 -- Physics 270 Hawking Radiation Energy for new particles comes from tidal stressesEnergy 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 t evap = 10 10 (M BH /10 12 kg) 3 yr t evap = 10 10 (M BH /10 12 kg) 3 yr t evap (1M solar ) ~ 10 65 yr t evap (1M solar ) ~ 10 65 yr

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Hawking Radiation Black holes emit as black bodiesBlack holes emit as black bodies –Temperature of black hole proportional to rate of radiation –T BH = 10 -7 (M solar / M BH ) –T(1 M solar ) ~ 10 -7 K –T(10 6 M solar ) ~ 10 -13 K

Andris Skuja, May 9, 2006 -- Physics 270Andris 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 oneWhite 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"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 270Andris Skuja, May 9, 2006 -- Physics 270 A Practical Perspective Two main types of black hole in the universeTwo 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? M solar ~3-100? M solar –Supermassive black holes (SMBH): found in the centers of galaxies, power quasars and AGN, ~a few times 10 6 - 10 9 M ~a few times 10 6 - 10 9 M

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Stellar Black Holes Created from stars of more than ~30 M solarCreated from stars of more than ~30 M solar Detectable in binary systemsDetectable 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 M solar so any larger invisible companion must be black hole or unknown physics

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Stellar Black Holes

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Stellar Black Holes X-Ray BinariesX-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 ~10 5 -10 6 K in inner disk –Spectrum peaks in soft x-rays –Optically thin material in corona or inner disk at >10 7 K gives hard x-ray emission –Some with relativistic jets –Luminosities of order 10 5 L solar

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Supermassive Black Holes Active Galactic Nuclei (AGN)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 270Andris Skuja, May 9, 2006 -- Physics 270 Supermassive Black Holes AGN structureAGN structure –Accretion disk at a few x 10 4 K, peak emission in UV (R ~ 100AU ~100 R S ) –Hot, rarefied gas in x-ray halo or corona (R ~ 1- 10 AU ~ R S ) –Broad emission line region (BLR); clouds with velocities of 10 4 kms -1, indicate strong gravitational field (R ~ 0.01pc) –Dusty molecular torus in plane of disk (R ~ 0.1- 1pc) IR emission

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Supermassive Black Holes AGN structure continuedAGN 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 head- on into quasar jets, see OVVs and BL Lacs –Jets in radio galaxies may extend ~1 Mpc

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Supermassive Black Holes

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Supermassive Black Holes AGN characteristicsAGN characteristics –Emission over 21 orders of magnitude in frequency - from radio to  -rays –Range of luminosities, from barely discernable to > 10 15 L solar, 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 270Andris Skuja, May 9, 2006 -- Physics 270 Supermassive Black Holes EvidenceEvidence –Kinematic evidence Stellar motions in center of Milky WayStellar motions in center of Milky Way Stellar and gas motions in other galaxiesStellar and gas motions in other galaxies OH masers in NGC 4258OH masers in NGC 4258 All imply tremendous mass in a tiny areaAll 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 270Andris Skuja, May 9, 2006 -- Physics 270 Supermassive Black Holes

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Questions: Do they really exist ? (Observe gravitational effects )Do they really exist ? (Observe gravitational effects ) How do we observe something that does not emit light? (Light bends around them)How do we observe something that does not emit light? (Light bends around them)

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 The cosmic distance ladder ParallaxParallax –solar neighborhood (< 1 kpc) Main sequence fittingMain sequence fitting –distances within the Galaxy (<100 kpc) CepheidsCepheids –nearby galaxies (< 20 Mpc) Tully-Fisher relationTully-Fisher relation –distant galaxies (< 500 Mpc) Type 1a supernovaeType 1a supernovae –cosmological distances (~ 1 Gpc)

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Nature of spiral nebulae and the Milky Way (MW) Curtis MW is 10 kpc acrossMW is 10 kpc across Sun near centerSun near center spiral nebulae were other galaxiesspiral 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 acrossMW is 100 kpc across Sun off centerSun off center spiral nebulae part of the Galaxyspiral 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 270Andris Skuja, May 9, 2006 -- Physics 270 Solution Role of dustRole 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 270Andris Skuja, May 9, 2006 -- Physics 270

Edwin Hubble (1889-1953) Four major accomplishments in extragalactic astronomy The establishment of the Hubble classification scheme of galaxiesThe establishment of the Hubble classification scheme of galaxies The convincing proof that galaxies are island “universes”The convincing proof that galaxies are island “universes” The distribution of galaxies in spaceThe distribution of galaxies in space The discovery that the universe is expandingThe discovery that the universe is expanding

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 The Hubble classification

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 The Hubble classification Elliptical galaxies (E0-E7)Elliptical galaxies (E0-E7) –classified according to their flattening: 10  (1-b/a) Spiral galaxies (S0, Sa-Sd)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)Barred spiral galaxies (SB0, SBa-SBd) –classified according to their bulge to disk ratio Irregular galaxies (Irr)Irregular galaxies (Irr)

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 THE EXPANDING UNIVERSE: Using the Doppler Effect to Measure Velocity Blueshift Redshift T1T1 T2T2 T3T3 T4T4

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Calcium Magnesium Sodium Galaxy Spectrum Stellar Spectrum 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 Galaxy Spectroscopy The larger the redshift: the greater the distance from us

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Doppler effect red shift blue shift The light of an approaching source is shifted to the blue, the light of a receding source is shifted to the red.

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Doppler effect redshift: z=0: not moving z=2: v=0.8c z=  : v=c

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 The redshift-distance relation

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Key results Most galaxies are moving away from usMost 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 = H 0  dThe recession speed v is larger for more distant galaxies. The relation between recess velocity v and distance d fulfills a linear relation: v = H 0  d Hubble’s measurement of the constant H 0 : H 0 = 500 km/s/MpcHubble’s measurement of the constant H 0 : H 0 = 500 km/s/Mpc today’s best fit value of the constant: H 0 = 70 km/s/Mpctoday’s best fit value of the constant: H 0 = 70 km/s/Mpc

Andris Skuja, May 9, 2006 -- Physics 270Andris 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 270Andris Skuja, May 9, 2006 -- Physics 270 The great synthesis (1930) Meeting by Einstein, Hubble and LemaîtreMeeting 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:Consequence: –Universe started from a point  The Big Bang Model

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 History of the Universe (with Inflation)

Andris Skuja, May 9, 2006 -- Physics 270Andris 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?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 270Andris Skuja, May 9, 2006 -- Physics 270 Einstein’s proposal: cosmological constant  There is a repulsive force in the universeThere 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 possibleThe 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 staticbut: 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 … ?Einstein: “greatest blunder of his life”, but is it really … ?

Andris Skuja, May 9, 2006 -- Physics 270Andris 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 270Andris Skuja, May 9, 2006 -- Physics 270 A metric of an expanding Universe Recall: flat spaceRecall: flat space better: using spherical coordinates (r, ,  )better: using spherical coordinates (r, ,  )

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 A metric of an expanding Universe But, this was for a static space. How does this expression change if we consider an expanding space ?But, this was for a static space. How does this expression change if we consider an expanding space ? R(t) is the so-called scale factorR(t) is the so-called scale factor

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Example: static universe R(t) t

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Example: expanding at a constant rate R(t) t

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Example: expansion is slowing down R(t) t

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Example: expansion is accelerating R(t) t

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Example: collapsing R(t) t

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 How old is the universe? A galaxy at distance d recedes at velocity v=H 0  d.A galaxy at distance d recedes at velocity v=H 0  d. When was the position of this galaxy identical to that of our galaxy? Answer:When was the position of this galaxy identical to that of our galaxy? Answer: t Hubble : Hubble time. For H 0 = 65 km/s/Mpc: t Hubble = 15 Gyrt Hubble : Hubble time. For H 0 = 65 km/s/Mpc: t Hubble = 15 Gyr

Andris Skuja, May 9, 2006 -- Physics 270Andris 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 UniverseWe 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:But we can estimate, how big the observable universe is: d Hubble : Hubble radius. For H 0 = 65 km/s/Mpc: d Hubble = 4.6 Gpcd Hubble : Hubble radius. For H 0 = 65 km/s/Mpc: d Hubble = 4.6 Gpc

Andris Skuja, May 9, 2006 -- Physics 270Andris 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 ?But, so far, we only considered a flat space. What, if there is curvature ? k is the curvature constantk is the curvature constant –k=0: flat space –k>0: spherical geometry –k<0: hyperbolic geometry

Andris Skuja, May 9, 2006 -- Physics 270Andris 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 ?But, so far, we only considered a flat space. What, if there is curvature ? k is the curvature constantk is the curvature constant –k=0: flat space –k>0: spherical geometry –k<0: hyperbolic geometry k>0 k<0k=0

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Cosmological redshift While a photon travels from a distance source to an observer on Earth, the Universe expands in size from R then to R now.While a photon travels from a distance source to an observer on Earth, the Universe expands in size from R then to R now. Not only the Universe itself expands, but also the wavelength of the photon changes.Not only the Universe itself expands, but also the wavelength of the photon changes.

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Cosmological redshift General definition of redshift:  for cosmological redshift:General definition of redshift:  for cosmological redshift:

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Cosmological redshift Examples:Examples: –z=1  R then /R now = 0.5 at z=1, the universe had 50% of its present day sizeat 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)emitted blue light (400 nm) is shifted all the way through the optical spectrum and is received as red light (800 nm) –z=4  R then /R now = 0.2 at z=4, the universe had 20% of its present day sizeat 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 nmemitted 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 270Andris Skuja, May 9, 2006 -- Physics 270 Friedmann equationFriedmann equation k is the curvature constantk is the curvature constant Let’s switch to general relativity

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Friedmann equationFriedmann equation k is the curvature constantk is the curvature constant –k=0: flat space, forever expanding –k>0: spherical geometry, eventually recollapsing –k<0: hyperbolic geometry, forever expanding Let’s switch to general relativity

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 k>0 k<0k=0

Can we predict the fate of the Universe ? Friedmann equation:Friedmann equation: k=0:k=0:

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 If the density  of the UniverseIf 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?so what is the density of the universe? –We don’t know precisely –  >  crit very unlikely –currently favored model:   0.3  crit Can we predict the fate of the Universe ?

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 How big is  crit ?  crit = 8  10 -30 g/cm 3  1 atom per 200 liter  crit = 8  10 -30 g/cm 3  1 atom per 200 liter density parameter  0density parameter  0 –  0 =1: flat space, forever expanding (open) –  0 >1: spherical geometry, recollapsing (closed) –  0 <1: hyperbolic geometry, forever expanding currently favored model:  0 = 0.3currently favored model:  0 = 0.3

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 How can we measure  0 ? Count all the mass we can “see”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 downMeasure 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 universeMeasure the geometry of the universe –is it spherical, hyperbolic or flat ?

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Let’s try to measure the deceleration Acceleration according to Newton:Acceleration according to Newton: deceleration parameterdeceleration parameter

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 So what’s the meaning of q 0 ? deceleration parameter q 0deceleration parameter q 0 –q 0 >0.5:deceleration is so strong that eventually the universe stops expanding and starts collapsing –0<q 0 <0.5: deceleration is too weak to stop expansion What’s the difference between q 0,  0 and k ?What’s the difference between q 0,  0 and k ? –k: curvature of the universe –  0 :mass content of the universe –q 0 : kinematics of the universe

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 So let’s measure q 0 ! How do we do that?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.Gravity is slowing down expansion  expansion rate should be higher at high redshift.

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 So let’s measure q 0 ! q 0 = 0 q 0 = 0.5 more distant fainter Data indicates: q 0 < 0  Expansion is accelerating

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Science discovery of the year 1998 The expansion of the universe is accelerating !!!The expansion of the universe is accelerating !!! But gravity is always attractive, so it only can decelerateBut gravity is always attractive, so it only can decelerate  Revival of the cosmological constant 

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 k is the curvature constantk is the curvature constant –k=0: flat space, flat universe –k>0: spherical geometry, closed universe –k<0: hyperbolic geometry, open universe Friedmann’s equation for  >0 k is the curvature constantk is the curvature constant –k=0: flat space –k>0: spherical geometry –k<0: hyperbolic geometry but for sufficiently large  a spherically curved universe may expand foreverbut for sufficiently large  a spherically curved universe may expand forever

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Deceleration parameter q for  >0 Acceleration according to Newton:Acceleration according to Newton: deceleration parameterdeceleration parameter Acceleration according to Newton:Acceleration according to Newton: deceleration parameter withdeceleration parameter with

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 k=+1  =0  >0 The fate of the Universe for  >0

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Is the fate of the Universe well determined ? deceleration:deceleration: –½  0 –   > 0: decelerating –½  0 –   < 0: accelerating curvaturecurvature –  0 +   = 1: flat –  0 +   < 1: hyperbolic –  0 +   > 1: spherical two equations for two variables  well posed problemtwo equations for two variables  well posed problem

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Cosmology: the quest for three numbers The Hubble constant H 0The Hubble constant H 0  how fast is the universe expanding The density parameter  0The density parameter  0  how much mass is in the universe The cosmological constant  The cosmological constant    the vacuum energy of the universe current observational situation:current observational situation: H 0 = 65 km/s/MpcH 0 = 65 km/s/Mpc  0 = 0.3;   = 0.7  flat space  0 = 0.3;   = 0.7  flat space

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 How old is the Universe? A galaxy at distance d recedes at velocity v=H 0  d.A galaxy at distance d recedes at velocity v=H 0  d. When was the position of this galaxy identical to that of our galaxy? Answer:When was the position of this galaxy identical to that of our galaxy? Answer: t Hubble : Hubble time. For H 0 = 65 km/s/Mpc: t Hubble = 15 Gyrt Hubble : Hubble time. For H 0 = 65 km/s/Mpc: t Hubble = 15 Gyr

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 The age of the Universe revisited So far, we have assumed that the expansion velocity is not changing ( q 0 =0, empty universe)So far, we have assumed that the expansion velocity is not changing ( q 0 =0, empty universe) How does this estimate change, if the expansion decelerates, i.e. q 0 >0 ?How does this estimate change, if the expansion decelerates, i.e. q 0 >0 ? An  0 >0,  =0 universe is younger than 15 GyrAn  0 >0,  =0 universe is younger than 15 Gyr now

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 now So far, we only have considered decelerating universesSo far, we only have considered decelerating universes How does this estimate change, if the expansion accelerates, i.e. q 0 <0 ?How does this estimate change, if the expansion accelerates, i.e. q 0 <0 ? The age of the Universe revisited An  >0 universe can be older than 15 GyrAn  >0 universe can be older than 15 Gyr

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270  0 =0,  =0: t Hubble =1/H 0 = 15 Gyr  0 =0,  =0: t Hubble =1/H 0 = 15 Gyr  0 =1,  =0: t Hubble =2/(3H 0 )= 10 Gyr  0 =1,  =0: t Hubble =2/(3H 0 )= 10 Gyr open universes with 0<  0 <1,  =0 are between 10 and 15 Gyr oldopen universes with 0<  0 <1,  =0 are between 10 and 15 Gyr old closed universes with  0 >1,  =0 are less than 10 Gyr oldclosed universes with  0 >1,  =0 are less than 10 Gyr old  >0 increases,  0 increases,  <0 decreases the age of the universe  0 =0.3,  =0.7: t Hubble =0.96/H 0 = 14.5 Gyr  0 =0.3,  =0.7: t Hubble =0.96/H 0 = 14.5 Gyr The age of the Universe revisited

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 not directlynot directly but we can constrain the age of the Universe. It must not be younger than the oldest star in the Universe.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?How do we measure the age of stars? –radioactive dating –stellar evolution models Result: age of the oldest star ~12-14 GyrResult: age of the oldest star ~12-14 Gyr  0 >~1 strongly disfavored  0 >~1 strongly disfavored Can we measure the age of the Universe ?

Andris Skuja, May 9, 2006 -- Physics 270Andris 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.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.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:Two basic solutions: –eventual collapse for large  0 or negative  –eternal expansion otherwise

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Some common misconceptions The picture that the Universe expands into a preexisting space like an explosionThe picture that the Universe expands into a preexisting space like an explosion The question “what was before the big bang?”The question “what was before the big bang?” Remember: spacetime is part of the solution to Einstein’s equationRemember: spacetime is part of the solution to Einstein’s equation Space and time are created in the big bangSpace and time are created in the big bang

Andris Skuja, May 9, 2006 -- Physics 270Andris 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.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: 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.Second law of thermodynamics defines an arrow of time.

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 At early epochs, the first term dominatesAt early epochs, the first term dominates  the early universe appears to be almost flat At late epochs, the second term dominatesAt late epochs, the second term dominates  the late universe appears to be almost empty Friedmann’s equation for  =0,  0 <1 Expansion rate of the Universe Falls off like the cube of R Falls off like the square of R

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 At early epochs, the first term dominatesAt early epochs, the first term dominates  the early universe appears to be almost flat At late epochs, the third term dominatesAt late epochs, the third term dominates  the late universe appears to be exponentially expanding Friedmann’s equation for  >0,  0 0,  0 <1 Expansion rate of the Universe Falls off like the cube of R Falls off like the square of R constant

Andris Skuja, May 9, 2006 -- Physics 270Andris 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 empty  >0: for most of its age, the universe looks either to be flat or to be exponentially expanding  >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 ?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 270Andris 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.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.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:Two basic solutions: –eventual collapse for large  0 or negative  –eternal expansion otherwise

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 General acceptance of the big bang model Until mid 60ies: big bang model very controversial, many alternative modelsUntil mid 60ies: big bang model very controversial, many alternative models After mid 60ies: little doubt on validity of the big bang modelAfter mid 60ies: little doubt on validity of the big bang model Four pillars on which the big bang theory is resting:Four pillars on which the big bang theory is resting: –Hubble’s law –Hubble’s law –Cosmic microwave background radiation –The origin of the elements –Structure formation in the universe

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Georgy Gamov (1904-1968) If the universe is expanding, then there has been a big bangIf the universe is expanding, then there has been a big bang Therefore, the early universe must have been very dense and hotTherefore, the early universe must have been very dense and hot Optimum environment to breed the elements by nuclear fusion (Alpher, Bethe & Gamow, 1948)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 270Andris Skuja, May 9, 2006 -- Physics 270 Hoyle’s ”Big Bang”

Andris Skuja, May 9, 2006 -- Physics 270Andris 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:In order to form hydrogen and helium at the right proportions, the following conditions are required: –density:   10 -5 g/cm -3 –temperature:T  10 9 K Radiation from this epoch should be observable as an isotropic background radiationRadiation from this epoch should be observable as an isotropic background radiation Due to the expansion of the universe to   3  10 -30 g/cm 3, the temperature should have dropped to T  5 K (-450 F)Due to the expansion of the universe to   3  10 -30 g/cm 3, the temperature should have dropped to T  5 K (-450 F) Can we observe this radiation ?Can we observe this radiation ?

Andris Skuja, May 9, 2006 -- Physics 270Andris 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 communityGamov’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 radiationResult was rediscovered by Dicke and Peebles in the early sixties. They started developing an antenna to search for the background radiation T  5 K  microwavesT  5 K  microwaves but …but …

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Penzias and Wilson 1965 Working at Bell labsWorking at Bell labs Used a satellite dish to measure radio emission of the Milky WayUsed 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 radiationThey found some extra noise in the receiver, but couldn’t explain it  discovery of the background radiation Most significant cosmological observation since HubbleMost significant cosmological observation since Hubble Nobel prize for physics 1978Nobel prize for physics 1978

Andris Skuja, May 9, 2006 -- Physics 270Andris 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."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 270Andris Skuja, May 9, 2006 -- Physics 270 The Big Bang and the Creation of the elements (Hoyle + Saltpeter) Atoms are mostly empty spaceAtoms are mostly empty space Atoms consist of protons (+), neutrons (o) and electrons (-)Atoms consist of protons (+), neutrons (o) and electrons (-) protons and neutrons form the atomic nucleusprotons and neutrons form the atomic nucleus # of protons deter- mines the element# of protons deter- mines the element electrons in the outskirts determine chemistryelectrons in the outskirts determine chemistry

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 The structure of matter Neutrons and protons are very similar, butNeutrons 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 nucleusElectrons 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 ?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 270Andris Skuja, May 9, 2006 -- Physics 270 n  p + n  p + + e - + n  p + + e - + n  p + + e - The four forces of nature gravitygravity electromagnetismelectromagnetism strong nuclear forcestrong nuclear force –keeps atomic nuclei together weak nuclear forceweak nuclear force –decay of free neutrons into protons

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 The structure of matter

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Abundance of elements Hydrogen and helium most abundantHydrogen and helium most abundant gap around Li, Be, Bgap around Li, Be, B

Andris Skuja, May 9, 2006 -- Physics 270Andris 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 forceWhen 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 forceWhen 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 270Andris Skuja, May 9, 2006 -- Physics 270 Formation of helium in the big bang Hydrogen: 1 nucleon (proton)Hydrogen: 1 nucleon (proton) Helium: 4 nucleons (2 protons, 2 neutrons)Helium: 4 nucleons (2 protons, 2 neutrons) In order to from helium from hydrogen one has toIn 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 unlikelybut: 4 body collisions are highly unlikely

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Transforming hydrogen into helium Hot big bang: neutrons and protonsHot big bang: neutrons and protons Use a multi step procedure:Use a multi step procedure: – p + n  2 H – p + 2 H  3 He – n + 2 H  3 H – 3 He + 3 He  4 He + 2 p some side reactions:some side reactions: – 3 He + 3 H  7 Li – 3 He + 3 He  7 Be

Andris Skuja, May 9, 2006 -- Physics 270Andris 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 nucleonsThere is no stable atomic nucleus with 5 or with 8 nucleons Reaction chain stops at 7 LiReaction chain stops at 7 Li So how to form the more massive elements?So how to form the more massive elements? There exist a meta-stable nucleus ( 8 B*). If this nucleus is hit by another 4 He during its lifetime, 12 C and other elements can be formedThere exist a meta-stable nucleus ( 8 B*). If this nucleus is hit by another 4 He during its lifetime, 12 C and other elements can be formed

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Mass gap/stability gap at A=5 and 8 Reaction chain:Reaction chain: – 4 He + 4 He  8 B* – 8 B* + 4 He  12 C so-called 3-body reaction (Saltpeter)so-called 3-body reaction (Saltpeter) in order to have 3-body reactions, high particle densities are requiredin 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 7 Li. Higher elements are formed in starsConclusion: big bang synthesizes elements up to 7 Li. Higher elements are formed in stars

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Primordial nucleosynthesis Result: abundance of H,He and Li is consistentabundance of H,He and Li is consistent but:  b ~0.04but:  b ~0.04 Consistent with abundance of H, He and Li

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 How far can we see ? Naked eye: 2 million Light years (Andromeda galaxy)Naked eye: 2 million Light years (Andromeda galaxy) Large telescopes: 14 billion Lyr (z=5.8)Large telescopes: 14 billion Lyr (z=5.8) What are the limiting factors ?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=5.8The universe appears to be fairly transparent out to z=5.8

Andris Skuja, May 9, 2006 -- Physics 270Andris 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 thusA 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 270Andris Skuja, May 9, 2006 -- Physics 270 The transition from a transparent to an opaque universe At z=0 the universe is fairly transparentAt z=0 the universe is fairly transparent At higher z, the universe becomes denser (  =  0  (1+z) 3 ) and hotter (T=T 0  (1+z))At higher z, the universe becomes denser (  =  0  (1+z) 3 ) and hotter (T=T 0  (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 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 oldAt z=1100, the universe is ~300 000 yrs old

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Black body radiation A hot a body is brighter than a cool one (L  T 4, Stefan-Boltzmann’s law)A hot a body is brighter than a cool one (L  T 4, Stefan-Boltzmann’s law) A hot body’s spectrum is bluer than that of a cool one ( max  1/T, Wien’s law)A hot body’s spectrum is bluer than that of a cool one ( max  1/T, Wien’s law)

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 The cosmic microwave background radiation (CMB) Temperature of 2.728±0.004 KTemperature of 2.728±0.004 K isotropic to 1 part in 100 000isotropic to 1 part in 100 000 perfect black bodyperfect black body 1990ies: CMB is one of the major tools to study cosmology1990ies: CMB is one of the major tools to study cosmology Note: ~1% of the noise in your TV is from the big bangNote: ~1% of the noise in your TV is from the big bang

Andris Skuja, May 9, 2006 -- Physics 270Andris 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.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 270Andris 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 growWe expect some wriggles in the CMB radiation, corresponding to the seeds from which later on galaxies grow

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 The Cosmic Background Explorer (COBE) Main objectives: To accurately measure the temperature of the CMBTo accurately measure the temperature of the CMB To find the expected fluctuations in the CMBTo find the expected fluctuations in the CMB

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Main results from COBE

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 More results from the CMB The Earth is moving with respect to the CMB  Doppler shiftThe 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 270Andris Skuja, May 9, 2006 -- Physics 270 More results from the CMB The Earth is moving with respect to the CMB  Doppler shiftThe Earth is moving with respect to the CMB  Doppler shift The emission of the GalaxyThe emission of the Galaxy

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 More results from the CMB The Earth is moving with respect to the CMB  Doppler shiftThe Earth is moving with respect to the CMB  Doppler shift The emission of the GalaxyThe emission of the Galaxy Fluctuations in the CMBFluctuations in the CMB

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 The BOOMERANG mission COBE was a satellite mission, why ?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 ?What can be done from the ground ? –Balloon experiment –desert  South Pole

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 The BOOMERANG mission

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 How can we measure the geometry of the universe We need a yard stick on the CMBWe need a yard stick on the CMB For different curvatures, a yard stick of given length appears under different anglesFor different curvatures, a yard stick of given length appears under different angles

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Measuring the Curvature of the Universe Using the CMB

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Measuring the Curvature of the Universe Using the CMB Recall: with supernovae, one measures q 0 =½  0 –  Recall: with supernovae, one measures q 0 =½  0 –   CMB fluctuations measure curvature   0 +  CMB fluctuations measure curvature   0 +   two equations for two variables  problem solvedtwo equations for two variables  problem solved

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 What comes next ? WMAPPlanck

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Can we see the sound of the universe ? Compressed gas heats up  temperature fluctuationsCompressed gas heats up  temperature fluctuations

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Acoustic Oscillations in the CMB Although there are fluctuations on all scales, there is a characteristic angular scale.Although there are fluctuations on all scales, there is a characteristic angular scale.

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Acoustic Oscillations in the CMB WMAP team (Bennett et al. 2003)

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Last scattering surface transparent opaque

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Sound Waves in the Early Universe Before recombination: Before recombination: –Universe is ionized. –Photons provide enormous pressure and restoring force. –Perturbations oscillate as acoustic waves. After recombination: After recombination: –Universe is neutral. –Photons can travel freely past the baryons. –Phase of oscillation at t rec affects late-time amplitude. Big Bang Today Recombination z ~ 1000 ~400,000 years Ionized Neutral Time

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Sound Waves Each initial overdensity (in DM & gas) is an overpressure that launches a spherical sound wave.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.This wave travels outwards at 57% of the speed of light. Pressure-providing photons decouple at recombination. CMB travels to us from these spheres.Pressure-providing photons decouple at recombination. CMB travels to us from these spheres. Sound speed plummets. Wave stalls at a radius of 150 Mpc.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.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 270Andris Skuja, May 9, 2006 -- Physics 270 A Statistical Signal The Universe is a super- position of these shells.The Universe is a super- position of these shells. The shell is weaker than displayed.The shell is weaker than displayed. Hence, you do not expect to see bullseyes in the galaxy distribution.Hence, you do not expect to see bullseyes in the galaxy distribution. Instead, we get a 1% bump in the correlation function.Instead, we get a 1% bump in the correlation function.

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Cosmological Constraints 1  2  WMAP 1  range Pure CDM degeneracy Acoustic scale alone

Andris Skuja, May 9, 2006 -- Physics 270Andris 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 270Andris Skuja, May 9, 2006 -- Physics 270 History of the Universe (with Inflation)

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Inflation (potential)

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Matter era The energy of matter is nowadays ~10000 times higher than that of radiationThe energy of matter is nowadays ~10000 times higher than that of radiation but temperature rises like (1+z)but temperature rises like (1+z) 2.7K < T < 10000K: matter era2.7K < T < 10000K: matter era dominate particles (in order of decreasing contribution:dominate particles (in order of decreasing contribution: –baryons, photons, neutrinos dominant forces:dominant forces: –gravity

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Radiation era As the temperature exceeds ~ 10000K, radiation starts dominatingAs the temperature exceeds ~ 10000K, radiation starts dominating 10000K < T < 10 10 K: radiation era10000K < T < 10 10 K: radiation era dominate particles (in order of decreasing contribution:dominate particles (in order of decreasing contribution: –photons, neutrinos, baryons dominant forces:dominant forces: –electromagnetism, gravity

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Electron-positron annihilation As the temperature exceeds ~ 10 10 K, creation of electron-positron pairsAs the temperature exceeds ~ 10 10 K, creation of electron-positron pairs –T > 10 10 K: equilibrium between electron- positron pair creation and annihilation –T < 10 10 K: freeze-out. Remaining pairs annihilate

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Lepton era 10 10 K < T < 10 12 K10 10 K < T < 10 12 K dominate particles (in order of decreasing contribution:dominate particles (in order of decreasing contribution: –electrons, positrons, photons, neutrinos, antineutrinos, baryons dominant forces:dominant forces: –electromagnetism, weak nuclear, gravity

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Hadron annihilation As the temperature exceeds ~ 10 12 K, creation of hadron-antihadron pairs (e.g. proton-antiproton)As the temperature exceeds ~ 10 12 K, creation of hadron-antihadron pairs (e.g. proton-antiproton) –T > 10 12 K: equilibrium between hadron pair creation and annihilation –T < 10 12 K: freeze-out. Remaining pairs annihilate

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Hadron era 10 12 K < T < 10 13 K10 12 K < T < 10 13 K dominate particles (in order of decreasing contribution:dominate particles (in order of decreasing contribution: –baryons+antiparticles, mesons+antiparticles, electrons, positrons, photons, neutrinos, antineutrinos dominant forces:dominant forces: –electromagnetism, strong nuclear, weak nuclear, gravity

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Still quark era 10 13 K < T < 10 15 K10 13 K < T < 10 15 K hadrons (baryons, mesons) break into quarkshadrons (baryons, mesons) break into quarks dominate particles (in order of decreasing contribution:dominate particles (in order of decreasing contribution: –quarks, antiquarks, electrons, positrons, photons, neutrinos, antineutrinos dominant forces:dominant forces: –electromagnetism, strong nuclear, weak nuclear, gravity

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Electroweak phase transition As the temperature exceeds ~ 10 15 K, electromagnetism and weak nuclear force join to form the electroweak forceAs the temperature exceeds ~ 10 15 K, electromagnetism and weak nuclear force join to form the electroweak force –T > 10 15 K: electroweak force –T < 10 15 K: electromagnetism, weak nuclear force Limit of what we can test in particle accelerators.Limit of what we can test in particle accelerators. Nobel prizes 1979 (theory) and 1984 (experiment)Nobel prizes 1979 (theory) and 1984 (experiment)

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Quark era 10 15 K < T < 10 29 K10 15 K < T < 10 29 K dominate particles (in order of decreasing contribution:dominate particles (in order of decreasing contribution: –quarks, antiquarks, electrons, positrons, photons, neutrinos, antineutrinos dominant forces:dominant forces: –electroweak, strong nuclear, gravity

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 GUT phase transition As the temperature exceeds ~ 10 29 K, electroweak force and strong nuclear force join to form the GUT (grand unified theories)As the temperature exceeds ~ 10 29 K, electroweak force and strong nuclear force join to form the GUT (grand unified theories) –T > 10 29 K: GUT –T < 10 29 K: electroweak force, strong nuclear force relatively solid theoretical framework (but may be wrong), but pretty much no constraint by experimentsrelatively solid theoretical framework (but may be wrong), but pretty much no constraint by experiments

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 GUT era 10 29 K < T < 10 32 K10 29 K < T < 10 32 K dominate particles (in order of decreasing contribution:dominate particles (in order of decreasing contribution: –Zillions of particles, most of them not detected yet dominant forces:dominant forces: –GUT, gravity

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Planck epoch T > 10 32 K unification of GUT and gravityT > 10 32 K unification of GUT and gravity Particles:Particles: –??? Forces:Forces: –TOE (theory of everything) The last frontier...The last frontier...

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Structure formation in the Big-Bang model

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 The Hubble sequence of galaxies

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 A galaxy census: spiral galaxies Most common type among the luminous galaxies (~75%)Most common type among the luminous galaxies (~75%) two major classes, S and SBtwo major classes, S and SB –regular spirals (S) –barred spirals (SB) further classified from a to d according to the bulge-to-disk ratiofurther 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 galaxyThe Milky Way is a Sbc or a SBbc galaxy

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 A galaxy census: spiral galaxies Spiral galaxies are disk like and in centrifugal equilibriumSpiral galaxies are disk like and in centrifugal equilibrium The are “cold”, i.e. the velocity dispersion (random motion of individual stars)  is much smaller than the rotation velocity v rot (Milky Way:  =20 km/s; v rot =220 km/s)The are “cold”, i.e. the velocity dispersion (random motion of individual stars)  is much smaller than the rotation velocity v rot (Milky Way:  =20 km/s; v rot =220 km/s) They mainly consist of stars, but ~10% of the mass is gas and dustThey mainly consist of stars, but ~10% of the mass is gas and dust They actively form stars (Milky Way: ~ 1 star per year)They actively form stars (Milky Way: ~ 1 star per year)

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 A galaxy census: elliptical galaxies ~20% of the luminous galaxies are ellipticals~20% of the luminous galaxies are ellipticals classified according to the flattening E0-E7: n=10  (1- b/a)classified according to the flattening E0-E7: n=10  (1- b/a) –E0: circular –E7: minor axis only 30% of major axis They are “hot”, i.e. the velocity dispersion  is much larger than the rotation velocity v rotThey are “hot”, i.e. the velocity dispersion  is much larger than the rotation velocity v rot flattened by an anisotropic velocity dispersionflattened by an anisotropic velocity dispersion little gas, no recent star formationlittle gas, no recent star formation predominantly in clusters of galaxiespredominantly in clusters of galaxies

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 A galaxy census: other galaxies Irregular galaxies (~ 5% of the luminous galaxies)Irregular galaxies (~ 5% of the luminous galaxies) dwarf galaxiesdwarf galaxies –dwarf irregulars –dwarf spheroidals –dwarf ellipticals –blue compact dwarfs –...

Andris Skuja, May 9, 2006 -- Physics 270Andris 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)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 10 8 yearsThose tidal features last a few 10 8 years Over the age of the universe, several hundred of those interactions must have taken placeOver the age of the universe, several hundred of those interactions must have taken place There are several hundred elliptical galaxies in the NGCThere are several hundred elliptical galaxies in the NGC

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Do ellipticals form by merging spirals ?

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Younger galaxies should be smaller...

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 How good is the assumption of isotropy? CMB: almost perfectCMB: almost perfect but what about the closer neighborhood ?but what about the closer neighborhood ?

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 How good is the assumption of isotropy? CMB: almost perfectCMB: almost perfect but what about the closer neighborhood ?but what about the closer neighborhood ? The great wall

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Galaxies are not randomly distributed but correlatedGalaxies are not randomly distributed but correlated Network of structures (filaments, sheets, walls)  “cosmic web”Network of structures (filaments, sheets, walls)  “cosmic web” The spatial distribution of galaxies Courtesy: Huan Lin

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 z=9.00 65 Mpc 50 million particle N-body simulation

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Does a picture like this look familiar ?

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Counting all the mass... Obstacle: we want mass, but we see lightObstacle: we want mass, but we see light Procedure: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-to- light ratio –The sun has  =1 by definition.

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Overall result: Implications: less than the nucleosynthesis constraint of  =0.04 in baryons  consistentless 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]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 270Andris Skuja, May 9, 2006 -- Physics 270

Evidence of dark matter: rotation curves of spiral galaxies

Andris Skuja, May 9, 2006 -- Physics 270Andris 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 270Andris Skuja, May 9, 2006 -- Physics 270 Evidence of dark matter: X-ray clusters

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Evidence of dark matter: clusters of galaxies

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Evidence of dark matter: large scale flows

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Overall result: Implications: most of the mass in the Universe is darkmost of the mass in the Universe is dark most of it is even of non-baryonic originmost of it is even of non-baryonic origin the perfect Copernican principlethe 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 270Andris 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”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 observationallyBut it was a clear prediction that eventually could be tested observationally The discovery of Neptune by Galle was one of the finest moments of scienceThe discovery of Neptune by Galle was one of the finest moments of science

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 MACHOs ? MAssive Compact Halo ObjectsMAssive Compact Halo Objects Brown dwarfs (stars not massive enough to shine)Brown dwarfs (stars not massive enough to shine) Dim white dwarfs (relics of stars like the Sun)Dim white dwarfs (relics of stars like the Sun) Massive black holes (stars that massive that even light cannot escape)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 wrongbut: if the DM is really in MACHOs, something with the nucleosynthesis constraint must be wrong

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 How can we see MACHOs ? Gravitational lensing:Gravitational lensing: If foreground object has only little mass, the image split is too small to be observedIf foreground object has only little mass, the image split is too small to be observed But the amplification (brightening) is observableBut the amplification (brightening) is observable

Andris Skuja, May 9, 2006 -- Physics 270Andris 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 ?How likely is it for a star in the Milky Way to get amplified ? Once every 10 million yearsOnce every 10 million years

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 How can we see MACHOs ? Solution: monitor 10 million stars simultaneouslySolution: monitor 10 million stars simultaneously

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 How can we see MACHOs ? Alcock et al. 1993 Magnification due to gravitational lensing There are not enough brown dwarfs to account for the dark matter in the Milky Way.

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 WIMPs ? Weakly Interacting Massive ParticlesWeakly Interacting Massive Particles Massive neutrinoMassive 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 physicistsAnother (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 270Andris Skuja, May 9, 2006 -- Physics 270 Summary The Universe is stranger than Alice’s WonderlandThe Universe is stranger than Alice’s Wonderland We have only scratched the surface of what is knowWe have only scratched the surface of what is know Many insights and observations still to comeMany insights and observations still to come

Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Physics 270 – The Universe: Astrophysics, Gravity and Cosmology.

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Andris Skuja, May 9, 2006 -- Physics 270Andris Skuja, May 9, 2006 -- Physics 270 Physics 270 – The Universe: Astrophysics, Gravity and Cosmology.

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