سمينار آقاي دکتر عباسي (دکتراي اختر شناسي از دانشگاه فردوسي مشهد) abasi@wali.um.ac.ir Introduction to Cosmology and Modern Astrophysics دريافت فايل پاور پونت به همراه عکس ها (3.8 مگابايت) Download Power Point File With Images >>> www.hamkelasy.com/solar/lecture.zip (3.8 MB) Text Only : Introduction to Cosmology and Modern Astrophysics The Story so far... 2005 is Einstein Year! (Most) Significant figure in Modern Physics 2005 100 years since the 3 “key papers” were published 50 years since his death Galileo Major contributions in many areas of physics Theories can be tested by conducting experiments. Also used thought experiments Isaac Newton “Nature and Nature s laws lay hid by night; God said, Let Newton be! And all was light.” Alexander Pope - intended Epitaph “Mortals, congratulate yourselves that so great a man has lived for the honour of the human race” Translation of the inscription on Newton s tombstone in Westminster Abbey “Nearer to gods no mortal may approach” Edmund Halley “Ode to Newton” “If I have seen further (than others) it is by standing upon the shoulders of Giants” Isaac Newton in a letter to Robert Hooke, 1675 Newton s Principia Isaac Newton Most famous for gravity but also: laid down 3 laws of motion much work on optics invented calculus independently of Leibniz First scientist to be knighted (in 1705 by Queen Anne) Albert Einstein Born in Ulm, Germany (1879) Well-documented that he was not a brilliant pupil! Managed to get into ETH in Zurich, graduated as a teacher in maths and physics in 1900 Became Swiss citizen in 1901 Employed in patent office 1902-1909 Einstein - 1905 Published `5 papers in Annalen der Physik Photoelectric effect (led to Nobel Prize in 1921) Brownian Motion (proved existence of atoms) Special Relativity Special Relativity 2 (E=mc2) Molecular dimensions (PhD) How to describe gravity: General Relativity Dynamics takes place in a four dimensional spacetime Mass induces warping or curvature of spacetime Spacetime curvature may also exist in the absence of mass (cosmological constant) A sermon on General Relativity In some contexts, spacetime curvature becomes pronounced, and space and time become inextricably linked or “coupled”. One example is black holes. Another is the universe as a whole. When we look on cosmological scales c/H0, you cannot view the universe as three dimensional, with time as a parameter. The universe exists as a 4D entity with strong curvature effects. You can t even qualitatively understand what is going on if you stick to a 3D view An analogy The surface of the Earth is a 2D surface embedded in a 3D space. Locally, the surface of the Earth looks purely 2D. On scales of the radius of the Earth, the curvature is unavoidable. Cosmology The study of the structure and evolution of the Universe as a whole. Seeks to answer questions such as: How big is the Universe? What shape is it? How old is it? How did it form? What will happen to it in the future? Distribution of Galaxies Galaxies appear to be distributed throughout the Universe Galaxies clump together into clusters and superclusters. Distant galaxies appear to be moving away from us. We know this from the redshifts in the spectrum of galaxies. Newton s Universe According to Newtonian cosmology, we live in a static, infinitely old and infinitely large universe with stars randomly scattered throughout the universe. In the early 1800s , the German astronomer Heinrich Olbers pointed out that something was wrong with this picture - Olbers s Paradox. Olbers s Paradox If the Universe is infinite, why isn t the sky bright at night? We should be able to have a line of sight to galaxy or star in any direction we look, if the line of sight extends far enough. But sky is dark, so there must be an end. End is due to expansion of Universe and resulting cosmic horizon - some of light from Universe has not reached us yet. Expansion of the Universe Einstein s relativity gave an entirely different picture of spacetime and gravity. His calculations showed that the universe must expand or contract, so he included a fudge factor into his equations - Cosmological Constant - so that his theory would support a static universe. Later, when it was established that the Universe is indeed expanding, he said that it was the biggest blunder in his life. Expansion of the Universe While some disagree about how the universe came into existence, no one argues that the Universe is expanding. The first person to discover this was Edwin Hubble. He observed that all remote galaxies are moving away from us. Hubble s Law - The further away something is from us, the faster it is receding from us. v = H0 * d v = recession velocity, H = Hubble s constant, d = distance Conceptualizing the expansion of the Universe What does it actually mean to say that the universe is expanding? Think of small coins representing the galaxies glued on a balloon as it is blown up. As the balloon expands, the the amount of space between the coins gets larger and large. Similarly,as the universe expands, the amount of space between the widely separated galaxies increases. The Expansion of the Universe The motion of galaxies away from us is due to the expansion of the Universe. Like buttons on a balloon which when inflated all move away from one another, so too are all the galaxies moving apart. The buttons are not moving it is the balloon itself that carries the buttons away. Space itself is expanding and simply carrying the galaxies with it. The scientific basis of modern cosmology Hubble s Law V = H0d The universe is expanding Red Shift and Distance Hubble - 1929 Creating space What is the universe expanding into? NOTE! The Universe is not expanding into pre-existing space - it “creates” space as it goes (!?), just as the surface of a balloon gets bigger as it is blown up. There is nothing “beyond” the universe, because there is no beyond. Asking what is beyond the universe is a meaningless question. The Big Bang Since the Universe is expanding it must have been smaller in the past. At some point in the past the entire Universe must have been packed into some very small size. In 1927, Abbé George Lemaitre, a Belgian cosmologist and priest proposed that the Universe began as a “Primeval Atom” and estimated its age. To estimate the age you need to know the expansion rate - in other words Hubble s Constant, H. H is 71 +/- 4 km/sec/Mpc giving an age to the Universe of 13.7 +/- 0.2 Billion years. The Cosmic Horizon There is a limit to how deep in the Universe we can peer. We are at the center of the limits of our vision (a.k.a. the Cosmic Particle Horizon) limit set by how old Universe is and speed of light: light from distant galaxies must have had time to reach us our cosmic horizon is different from other galaxies - they are at their own center This solves the Olbers s Paradox. We do not receive light from galaxies beyond our horizon. The cosmic horizon The Cosmic Singularity At the moment of the Big Bang: A state of infinite density filled the universe A condition of infinite curvature existed, giving rise to a situation where space and time were jumbled. Therefore, we cannot apply laws of physics to describe the moment of the Big bang. This is very similar to the condition at the center of a black hole - i.e. at the black hole singularity For this reason we refer to the black hole as the Cosmic Singularity. Plank Time Due to the state of the universe during the BB, we cannot use laws of physics to describe this event. Nor can science answer what existed before the BB - these are fundamentally unknowable things. In fact, from the beginning of the BB until 10-43 seconds after The BB, space & time was so jumbled-up that laws of Physics fails us This time interval tP = 10-43 sec. is referred to as the Plank time. Arno Penzias & Robert Wilson Skip Forward to 1964 Cosmic microwave background radiation (CMB) This radiation is blackbody radiation and depends on the temperature, just like the radiation from the Sun. This radiation which fills all space is referred to as the Cosmic Microwave background radiation (CMB). It was discovered by Arno Penzias & Robert Wilson in the early 60s. Why 2.7 K? Original temperature about 1013 Kelvin and density 1010 g/cm3, but expansion has cooled it. Cooling occurs as space is stretched by expansion, and wavelengths get longer - redshift. The redshift caused by the expansion of the universe is called the cosmological redshift. The Big Bang happened EVERYWHERE in space - right here included!! Will the universe expand forever? What is the shape of the Universe? The density of the Universe Hard question to answer - requires knowing how much matter and radiation is in the Universe (equivalently: Energy density) Which plays a more important role in the Universe; Matter or energy? Depends on when! At present the matter & radiation densities: Radiation density r rad= 4.6 x 10-31 kg/m3 Matter density r m = 2 to 4 x 10-27 kg/m3 ( 1 to 2 H atoms in 1 m3) The density of the Universe Today, mater prevails over radiation in the Universe - matter-dominated Universe However, as you go back in time towards the BB, as the universe was more compressed, both densities were higher, but in addition photons were not so redshifted => higher energy. Early universe was a radiation-dominated Universe The transition from radiation dominated to matter dominated universe happened about 2500 yrs. after the BB History of the Universe Very exciting in the beginning, very dull now. Hot early, cool later. Radiation dominated: At first, Universe very hot. Exotic forms of matter present, but were quickly destroyed. Mostly EM radiation like gamma rays present. Would see brightness everywhere. Matter dominated: (Like now) Universe dark, cooler. Matter forms and stays formed. Transition between two eras is where CMB came from What shape is the Universe? Open Universe: Will expand forever. Negative curvature. Parallel lines always diverge. Closed Universe: Stops expanding and collapses again. Positive curvature. Parallel lines always converge. Flat Universe: exactly stops expanding but doesn t collapse (really doesn t exactly stop until infinite time). Zero curvature. Parallel lines remain parallel What shape is the Universe? The curvature (Shape) of the universe depends on the combined matter + radiation density - r 0 Critical Density r C : If r 0 = r C the universe is flat If r 0 > r C the universe is closed If r 0 < r C the universe is open Using H0 = 70 km/s/Mpc we get r C = 9.2 x 10-27 kg/m3 5.5 hydrogen atoms per cubic meter What shape is the Universe? Astronomers prefer to use the Density parameter instead of density: W 0 = r 0 / r C Therefore, the shape of the universe can be understood in terms of W 0 . Critical Density r C : If W 0 = 1 the universe is flat If W 0 > 1 the universe is closed If W 0 < 1 the universe is open Flat space Curved space Measurements of open vs. closed universe These measurements are underway with a new generation of telescopes From current observations astrophysicists find that W 0 = 1.0 with an uncertainty of 10%. This means that the universe is flat. The flatness of the universe presents a major dilemma. Dark Energy The matter & Radiation density parameter W m/R lies between 0.2 - 0.4. But W 0 = 1.0 and if there is only matter & radiation in the Universe then W 0 = W m/R !! The source of the missing density must be some form of energy that we cannot detect from its gravitational effects (like astronomers do with dark matter) nor does it emit any radiation. This mysterious energy is called Dark Energy Dark Energy Therefore, the density parameter of the universe has two components: W 0 = W m/R + W L , where W L is the dark energy density parameter. W L should be between 0.6 & 0.8 (since W m/R = 0.2 to 0.4 and W 0 = 1.0). That is dark energy accounts for 60% to 80% of the contents of the universe!! It is believed that this dark energy to be a form of energy that provides an anti-gravity like effect that cause the universe to accelerate mare rapidly. This concept goes back to Einstein and his cosmological constant. Dark Matter Recent measurements: Is the expansion speeding up? Recently published measurements of velocity vs. distance using supernovae as distance indicators suggest that the rate of expansion is increasing. Where is the energy driving this rate of increase coming from? Dark Energy? The First Few Moments Initially the Universe was incredibly hot. Matter and energy were freely transforming into one another through Einstein s Mass-Energy relation. The mass formed were in matter anti-matter pairs. Matter and anti-matter destroy one another when they come into contact but just enough matter existed to survive. This remaining matter is what fills the Universe. Composition of the Early Universe As the Universe cooled Hydrogen nuclei began to form. Conditions were still hot enough for fusion reactions to occur forming Helium. Nearly all elements heavier than Helium however were formed later by stars. We notice that the oldest stars have much less heavy elements than the Sun. This is further evidence for the Big Bang theory. After neutral atoms formed the radiation that filled the Universe was allowed to freely propagate. Steady State Theory Bondi, Gold, Hoyle - 1948 The same laws of physics are valid at all times The Universe does not change in time Continuous creation of matter balances the expansion of the Universe There are more bright radio sources at greater distances => the Universe is changing The discovery of CMBR killed the idea of a static Universe Steady State Universe Bondi, Gold, Hoyle - 1948 NEUTRON STARS AND BLACK HOLES NEUTRON STAR Mass is between 1.4 and 3 solar masses A star about the size of a city Smallest, densest star known in the Universe Density is about 1014 gm/cm3 One teaspoon of material would weigh 109 tons. Surface gravity is 7 x 109 Earth s Magnetic field is 1012 Earth s. Rotation period ranges from 0.001 to 100 seconds. Electrons are crushed into protons forming neutrons (inverse beta decay). INVERSE BETA DECAY PULSARS Pulsars are rapidly rotating neutron stars detected by radio pulses. Pulsars are like cosmic lighthouses beaming their radiation toward Earth. PULSAR MODEL CRAB NEBULA IN X-RAYS STELLAR BLACK HOLES For stars greater than about 3 solar masses, neutron pressure (nuclear force) will not stop the core s gravitational collapse. Gravity wins the final battle. No known force in the Universe can stop the contraction. A black hole in space-time is formed, where the force of gravity is so great that not even light can escape from this bottomless gravitational well. When escape velocity reaches the speed of light on a collapsing neutron star, a black hole is formed. SCHWARTZCHILD RADIUS A LEAP INTO A BLACK HOLE Time dilation Length contraction Gravitational red shift Strong tidal forces JETS AND ACCRETION DISKS Bipolar flows are seen ejecting matter perpendicular to the accretion disk. High speed jets have matter moving near the speed of light. SS 433 The End
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