Origin, Structure and Evolution of the Universe - Astronomy II | ASTR 1020, Study notes of Astronomy

Download Origin, Structure and Evolution of the Universe - Astronomy II | ASTR 1020 and more Study notes Astronomy in PDF only on Docsity! ASTR-1020: Astronomy II Course Lecture Notes Section XI Dr. Donald G. Luttermoser East Tennessee State University Edition 4.0 Abstract These class notes are designed for use of the instructor and students of the course ASTR-1020: Astronomy II at East Tennessee State University. Donald G. Luttermoser, ETSU XI–3 Figure XI–1: Cosmic Microwave Background as observed by COBE. This microwave image of the sky shows the variations in the Universe’s temperature at recombination time. Blue represents regions of cooler gas, and red represents regions of hotter gas. 3. In addition to these, two additional assumptions are typically included when describing the Big Bang: a) Universality — physical laws are the same everywhere in the Universe at all times. b) Cosmological Redshifts — redshifts are caused by the expansion of the Universe through the Doppler Effect. 4. We see the Big Bang fireball in every direction as microwave blackbody radiation =⇒ 3 K Cosmic Microwave Background (CMB) radiation. a) When this light was emitted, the Universe was very hot. b) As the Universe expanded, this light was redshifted until XI–4 ASTR-1020: Astronomy II today it is microwave light =⇒ the redshift of this light is z = 1100, whereas the farthest quasar is at z = 6.43. c) Penzias and Wilson discovered this CMB in the early 1960’s, confirming theoretical predictions of the Big Bang Theory made by Dicke and Peebles. Penzias and Wilson later won a Nobel Prize for their discovery. i) Penzias and Wilson made these observations from the ground and their instrument was not sensitive enough to see any variation in this background glow. ii) This presented a problem since the current Uni- verse has structure, how did this structure then arise? d) The COsmic Background Explorer (COBE) spacecraft was launch in the early 1990’s to investigate this back- ground radiation (see Figure XI-1). i) It found the Universe radiates as a perfect black- body (after the Solar System’s motion and Milky Way’s glow are subtracted) at a temp of 2.726 K. ii) COBE did detect small variations in the thermal distribution in the CMB on the order of 1 part in 100,000. iii) This variation is refereed to as the intrinsic anisotropy. iv) This intrinsic anisotropy shows that by the time this radiation was emitted (approximately 300,000 years Donald G. Luttermoser, ETSU XI–5 after the Big Bang), inhomogeneities in the mass- energy of the Universe had begun which would later form the galaxies. e) More recently, the Wilkinson Microwave Anisotropy Probe (WMAP) has observed this background at even higher spatial resolution (see Figure XI-2). i) WMAP has determined the most accurate value of Hubble’s constant (71 km/sec/Mpc) based on the pattern of the temperature variations. ii) This temperature variation also gives the age of the Universe (i.e., the time since the Big Bang) as 13.7 billion (1.37 × 1010) years. iii) Finally WMAP has shown that we live in a flat (in a 3-dimensional sense) space-time (discussed in detail shortly). 5. As the Universe expands, it should slow down due to the grav- itational pull of one galaxy on another. a) Are there enough galaxies (i.e., mass) to stop the expan- sion? i) If the Universe’s mass density, ρ, is less than a critical density, ρ < ρc, gravity will not halt the expansion =⇒ an Open Universe. ii) If ρ > ρc, gravity will halt the expansion and cause a contraction down to a Big Crunch ! =⇒ a Closed Universe. XI–8 ASTR-1020: Astronomy II Figure XI–3: Three possible shapes of the Universe as a function of Ω◦. Note that in these pictures, we represent our 3-dimensional space as a 2-dimensional surface. The top picture shows a positive curvature (i.e., spherical shape) with Ω◦ > 1 (ρ > ρc). The middle picture shows a universe with Ω◦ < 1 (ρ < ρc). This universe has a negative curvature — a hyperbolic (i.e., saddle) shape. The bottom picture shows a universe with Ω◦ = 1 (ρ = ρc) which is flat (zero curvature) space. Donald G. Luttermoser, ETSU XI–9 0 20 40 60 80 t (Gyr) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 R / R o to ρ > ρc ρ = ρc ρ < ρc Figure XI–4: Histories of three different curvature universes as a function of the density parameter. Note that the present size of the Universe (hence, present time) is indicated by R = 1. 6. If the Universe had gone through an Inflationary stage (see §XI.D.4), then the Universe is essentially flat and q◦ = 1/2. a) One of the key projects of the Hubble Space Telescope is to accurately measure Hubble’s constant (H◦). This project has determined that H◦ = 72 km/s/Mpc with an uncertainty of 10% (note that WMAP measures it more accurately at 71 km/s/Mpc with an uncertainty of 4%). b) Using these values of q◦ and H◦, we can ascertain the current mass-energy density of the Universe: ρ◦ = 3H2◦q◦ 8π G = 3 · ( 71 km/s ×103 m/km 106 pc ×3.0856×1016 m/pc )2 · (1/2) 8π (6.668 × 10−11 N m2/kg2) = 4.7 × 10−27 kg/m3 , or 6.6 times bigger than the baryonic matter we can mea- sure (and see). XI–10 ASTR-1020: Astronomy II c) As such, astronomers have introduced a term called dark matter — matter which is not made up of protons and neutrons and cannot easily be seen. d) So, 87% of the Universe seems to be composed of this dark matter! The race is on throughout the astrophysical community to try and find the identity of this hidden mass. e) Remember, galactic rotation curves also show that there is a large amount of matter in the vicinity of galaxies that cannot be seen. It is thought that this dark matter de- duced from cosmology is the same dark matter deduced from the rotation curve of our and other galaxies. 7. Recently, distance-redshift measurements of supernovae explo- sions in distant galaxies indicate, however, that the Universe may be accelerating instead of decelerating! a) The field equations from general relativity produce a con- stant term called the cosmological constant (Λ). i) Einstein’s field equations for the Universe pro- duce an equation of motion (like Newton’s 2nd law) of a(t) = (−4πGρ(t) − Λ) R(t) 3 , (XI-3) where a is the acceleration of the Universe’s ex- pansion, ρ is the mass-energy density, R is the size of the Universe, and t is the time since the Big Bang. ii) As can be seen, a, ρ, and R are all functions of time — they can change over time. Donald G. Luttermoser, ETSU XI–13 0 20 40 60 80 t (Gyr) 0 1 2 3 4 5 R / R o to Λ < 0 Λ = 0 Λ > 0 Figure XI–5: Histories of flat modified Friedmann model universes for various values of the cos- mological constant Λ. Note that the present size of the Universe (hence, present time) is indicated by R = 1. Example XI–1. What must the cosmological constant be for the best estimates of the parameters listed in Eq. (XI-4)? Λ = 4π(6.668 × 10−11 N m2/kg2) (4.7 × 10−27 kg/m3) − 3 ( 1 2 )   71 km/s × 10 3 m/km 106 pc × 3.0856 × 1016 m/pc   2 = −3.9 × 10−36 s−2 . From this, we can calculate what the acceleration of the Uni- verse is due to this cosmological constant term (use the best estimate of the radius of the Universe to be 14 billion light years = 1.3 × 1026 m): aΛ = Λ R 3 = (−3.9 × 10−36 s−2) · (1.3 × 1026 m) 3 = −1.7 × 10−10 m/s2 . XI–14 ASTR-1020: Astronomy II Now, since the acceleration due to gravity on the Earth’s sur- face is 9.80 m/s2, that’s 58 billion times larger than the accel- eration due to the cosmological constant — unmeasurable on the Earth’s surface (or by any large gravitating body). It only shows its presence on the very large scale! 8. This “antigravity” force caused by Λ > 0 and resulting in our Universe’s expansion to currently accelerate, has been affection- ately called dark energy by many astronomers. a) It was given this name due to the fact that there is ev- idence for “dark matter” in the Universe as previously described. b) Based on the WMAP observations and the standard model of cosmology, dark energy currently accounts for 74% of the total mass-energy of the Universe (see Figure XI-6). C. Particles and Forces 1. Before discussing the history of the Universe, we need to under- stand the 4 natural forces in nature and their effects on particles in the Universe. 2. There are 4 natural forces (i.e., those forces associated with force fields). In order of strength they are: a) Strong interactions: Force that binds nucleons to- gether — acts over a range of ∼10−13 cm. Hadrons participate in the strong force. The smallest component particle of a hadron is called a quark. This force is mediated by field particles called gluons. Donald G. Luttermoser, ETSU XI–15 Figure XI–6: Estimated distribution of dark matter and dark energy in the Universe. b) E/M interactions: Force between charged particles which has an infinite range that falls off as 1/r2. This force is 100 times weaker than the strong force, however it is what holds atoms and molecules together. This force is mediated by the photon field particle. c) Weak interactions: These are responsible for β-decay of nuclei (i.e., radioactivity) — 10−13 times as strong as strong interactions with a range  10−13 cm. The intermediate vector boson (often called weakons) mediates this force. d) Gravitational interactions: These are by far the weak- est of the interactions on the microscopic scale, typically about 10−40 times as strong as the strong interactions on nuclear scales. Gravity is another infinite, 1/r2 force, XI–18 ASTR-1020: Astronomy II 6. The theory on how quarks interact with each other is called quantum chromodynamics. One interesting result of this theory is that quarks cannot exist in isolation, they must always travel in groups of 2 to 3 quarks. 7. There are 2 addition terms that are used to describe particles — terms that describe the spin of a particle: a) In quantum mechanics, a system of identical particles 1, 2, 3, ... is described by a wave function, which describes the spin of the particle. b) A wave function must be either symmetrical (even) or antisymmetrical (odd) with respect to the interchange of coordinates of any pair of identical particles. c) If symmetrical, the particles are called bosons and have zero or integer (i.e., 0, 1, 2, 3, ...) spins. d) If antisymmetrical, the particles are called fermions and have half-integer (i.e., 12, 3 2 , 5 2 , ...) spins. e) An antisymmetrical wave function must vanish as 2 iden- tical particles approach each other. As a result, 2 fermions in the same quantum state exhibit a strong mutual re- pulsion =⇒ Pauli Exclusion Principle. f) No such restrictions exist for bosons. g) Leptons and baryons are fermions. h) Mesons and field particles (i.e., photons) are bosons. Donald G. Luttermoser, ETSU XI–19 The Standard Model of Particle Physics MATTER & ENERGY FORCES CONSTITUENTS Strong E/M Weak Gravity Gluons Photons W & Z Bosons Gravitons Quarks u c t d s b Leptons e µ τ νe νµ ντ Figure XI–7: The Standard Model is the current best description of the subatomic world. D. History of the Universe 1. Singularity, the Big Bang Itself! t = 0, D = 0, ρ = ρrad → ∞, T = Trad → ∞ . a) If the Universe is closed, then a finite amount of mass- energy is located in a zero volume (like a black hole sin- gularity). b) If the Universe is open or flat, then the Universe has an infinite total amount of mass-energy located in an infinite volume at this stage. c) We currently have no physics that can describe the his- tory and events occurring in the Universe at this point. Perhaps if quantum mechanics and general relativity are ever combined (i.e., quantum gravity) (see Figure XI- XI–20 ASTR-1020: Astronomy II h+ G c Classical Mechanics Quantum Mechanics Newtonian Gravity Quantum Gravity Special Relativity General Relativity Quantum Field Theory Theory of Everything Figure XI–8: The relationship of the various theories of the natural force with respect to the fundamental physical constants of the Universe. Note that those “theories” (actually hypotheses) in italics have not yet been confirmed. 8), we will have a physical theory that can describe the Universe here and explain why the Big Bang ever oc- curred. d) In the header lists for each of these eras, t represents time since the Big Bang, D the diameter of the Universe at time t, ρ is the mass-energy density, T is the tem- perature, and later, z corresponds to the redshift. Each of these values are listed at the beginning and ending of each era. 2. Quantum Era 0 < t < 10−43 sec = tP = Planck Time, 0 < D < 10−33 cm = `P = Planck Length, ρ = ρrad > 10 90 gm/cm3, T = Trad > 10 32 K . Donald G. Luttermoser, ETSU XI–23 gravititational force weak force electromagnetic force strong force electroweak force Grand Unified Theory (GUT) Force Supergravity (quantum gravity) more energy st ro n ge r fo rc e Figure XI–9: The ‘Theory’ of Everything will describe the four natural forces as one force at very high energies (that is, early in the Universe). The four combined forces are called unification and are said to have symmetry. As it expands, the Universe cools (i.e., looses energy) and at certain temperatures, forces start to decouple. Each symmetry breaking of the natural forces of the Universe, shown as ‘dots’ in this figure, correspond to the Universe changing its state. The decoupling of the GUT Force causes the Universe to expand exponentially instead of the standard linear expansion seen during the other epochs. XI–24 ASTR-1020: Astronomy II b) During this time, all baryonic matter is created from the primeval soup of field particles =⇒ individual quarks and antiquarks are made =⇒ matter (and antimatter) arise from the field energy particles via E = mc2. i) Field particles all have integer spins =⇒ they are bosons. ii) The GUT predicts that baryon number conser- vation and charge & parity (CP) conservation can be violated occasionally. In particle physics, par- ity is defined as the symmetry of behavior in an interaction of a subatomic particle with that of its mirror image. iii) These CP violations can cause slight asymme- tries in decay rates of a given boson decaying to more stable particles: • The kaon K can decay to a pion π via either K → π− + e+ + νe K → π+ + e− + νe . • The first of these two reactions occurs slightly (but measurably) more frequently than the sec- ond. • As such, it is possible to get slight asymme- tries between matter and antimatter over time as these particles are made out of the field par- ticle soup. Donald G. Luttermoser, ETSU XI–25 c) During this time, the temperatures are too high for the strong force to connect the quarks together to make baryons and anti-baryons. d) Due to CP violation, for every 30 million antiquarks, there are 30 million + 1 quarks by the end of this era. e) The Universe resumes a linear expansion at the end of this era. 5. Quark Era 10−32 sec < t < 10−6 sec 330 cm < D < 109 cm = 4D⊕ 1037 gm/cm3 < ρrad < 10 17 gm/cm3 1018 K < T < 1013 K . a) Forces between quarks act strangely: The farther away they get from each other, the stronger the force exerted (opposite of the direction of gravity). At the beginning of this era, the temperature is so high that quark motions can overcome this force and hence are not bound with each other. b) At t = 10−12 sec, T = 1015 K, ρ = 1024 gm/cm3, the electromagnetic and weak forces decouple =⇒ when this occurs, leptons start to form. c) This era ends when the temperature is cool enough for quarks to form bound states (T = 1013 K, ρ = 1017 gm/cm3) and become hadrons. XI–28 ASTR-1020: Astronomy II e) The future of the Universe is now set =⇒ all within the first 3 minutes! 9. Radiation Era 3 min < t < 10, 000 yr 109 < z < 2200 1019 cm < D < 1021 cm = 1000 ly = 300 pc 10−8 gm/cm3 < ρ < 10−15 gm/cm3 107 K < T < 105 K . a) In this era, ρrad > ρmatter. b) The temperature is still greater than 105 K which keeps hydrogen ionized. c) Since H is ionized, there are an abundance of free elec- trons which effectively blocks the flow of radiation (i.e., photons) =⇒ Compton scattering and Thompson scat- tering. d) The Universe is completely opaque during this time. e) At the end of this era, ρm = ρrad. 10. Matter Era 1000 yr < t < present = 13.7 Gyr 2200 < z < 0 1021 cm < D < 1028 cm = 13.7 Gly = 4.2 Gpc 10−15 gm/cm3 < ρ < 3 × 10−30 gm/cm3 105 K < T < 2.7 K . a) Here we are assuming that present is at t = 13.7 × 109 (13.7 billion) years. Donald G. Luttermoser, ETSU XI–29 Age of the Universe T em p er at u re ( K ) 10-43 sec 10-35 sec 10-12 sec 10-6 sec 1 sec 15 sec 1 min 3x105 yrs 13x109 yrs 3 3000 106 109 1010 1013 1015 1027 1034 spacetime forms quarks & leptons created inflation 4 forces established leptons split into neutrinos & electrons gravity governs expansion quarks make protons/neutrons CP violation causes matter < antimatter neutrinos decouple electrons/positron annihilation ends leaving small number of unmatched electrons fusion of H into He photons decouple = CMB galaxies, stars, planets form Figure XI–10: Graphical representation of the history of the Universe. b) Matter begins to dominate radiation in this era: ρmatter > ρrad. c) H (hydrogen) becomes completely neutral when T < 3000 K (t = 300, 000 years, z = 1100) =⇒ the Universe becomes transparent to light since the opacity from elec- tron scattering drops to zero! i) We see this epoch today as the 2.7 K background radiation =⇒ visible light when emitted at z = 1100, redshifted today (z = 0) to microwave radi- ation. ii) This time is called the recombination time of the Universe. iii) This is what we are seeing when we observe the 2.7 K background. XI–30 ASTR-1020: Astronomy II d) Inhomogeneities in the matter begin to grow due to grav- itational instabilities just after recombination. i) The densest parts of these inhomogeneities quickly collapse down to form supermassive black holes. ii) Hydrogen and helium created in the Big Bang start to accumulate in the vicinity of these super- massive black holes forming protogalaxies. iii) During this time after the recombination but before the first stars light up, the Universe is dark at visible wavelengths. e) Galaxies begin to “light-up” as this accumulating hy- drogen and helium reach high enough densities for star formation to begin. i) It is at this time that the Population III stars (i.e., no metalicity) begin to form in earnest from the IGM (intergalactic medium) and ISM (inter- stellar medium). ii) This occurs at approximately z = 20, t = 1 × 108 years after the Big Bang. f) Galaxies begin to cluster at z ≈ 10, t = 3 × 108 years. g) The first Population II (low metalicity) stars form in our Galaxy out of material expelled from the Population III stars at z ≈ 9, t = 4 × 108 years after the Big Bang. h) Quasars become active and Population II stellar forma- tion rates begin to drop in the Milky Way at z ≈ 6, t = 6 × 108 years.