Theory of Everything

Size: px

Start display at page:

Download "Theory of Everything"

Vivian Floyd
6 years ago
Views:

1 Theory of Everything The primordial theory of everything separated into gravity and a grand unified theory (GUT) at the Planck time This is referred to as spontaneous symmetry breaking

Inflation Alan Guth proposed in 1980 the idea of an inflationary period during the Big Bang At the very beginning, the Universe was in thermodynamic equilibrium The next step was

2 Inflation Alan Guth proposed in 1980 the idea of an inflationary period during the Big Bang At the very beginning, the Universe was in thermodynamic equilibrium The next step was sudden exponential expansion that smoothed out the Universe, leading to a flat Universe with Ω 0 = 1 This inflationary period lead to the smooth microwave background we observe today

3 History of the Universe

Hanny s Voorwerp Volunteer Hanny Van Arkel

stems from highly ionized oxygen Structure

5 Hanny s Voorwerp Volunteer Hanny Van Arkel described this photograph of spiral galaxy IC2497 as unusual The colour green (enhanced) is very unusual in astronomical pictures It stems from highly ionized oxygen Structure about 100,000 light years across and 650 million light years away

6 Astrophysics: Course Review

7 Interstellar Matter Giant molecular clouds of gas and dust contain regions of higher density and hot cores with temperature up to 300 K that can contain very young (proto-)stars The condition for a cloud of gas to collapse into a star was derived with simplifications by James Jeans (Jeans s Criterion) Time of collapse only depends on density and not on initial radius

8 Star Energy Sources The energy sources to power a stars luminosity are Chemical reactions to a very small amount Gravitation Not important for a star during the main part of it s life Very important for late stage Nuclear reactions The dominant source during the main part of a star s life Fusion of lighter nuclei into heavier nuclei is exothermic (up to 56 Fe) by releasing the excess binding energy Need to overcome repulsive Coulomb barrier by thermal energy

9 Nucleosynthesis Several basic reaction cycles can be found in stars that convert lighter elements into heavier elements The basic chain reaction converting hydrogen into helium is the proton-proton chain Other chains, like the CNO cycle contribute above a certain temperature The relative contribution of different chains depends critically on the temperature

10 Energy Transport Energy is transported mainly via radiation or convection The dominant transport mechanism depends critically on the opacity of the stellar material The opacity in turn depends on the interactions between photons and particles The two main sources out of five are Ionization κ λ bf Electron scattering off photons and Bremsstrahlung κ λ ff The total opacity is the sum of all contributions As a stars (or the solar) radius increases, the temperature gradient becomes steeper, because The temperature decreases The opacity increases towards a maximum The density decreases

11 The Eddington Luminosity Limit If the temperature is sufficiently high and the gas density low enough, radiation pressure can dominate over gas pressure This is not untypical for the outer layers of a very massive star and can be used to calculate the maximum luminosity astar can have and still remain in hydrostatic equilibrium L Ed = 4 π G c κ M

12 The Interior Structure of the Sun Data for one of many model calculations of the Sun center Temperature K Pressure N m -2 Density kg m -3 Hydrogen Helium

13 Summary of the Equations of Stellar Structure dp dr = G M r ρ r 2 Star in Hydrostatic Equilibrium dm r dr dl r dr = 4 π r 2 ρ = 4 π r 2 ρ ε Interior Mass Distribution of a Star Relation Luminosity Energy Generation Rate dt dr = 3 4 a c κ ρ T 3 L r 4 π r 2 Energy Transfer Through Radiation = 1 1 γ µ m H G M r k r 2 Energy Transfer Through Adiabatic Convection

14 Life Cycle of the Sun log ρ / g cm -3

15 The Vogt-Russel Theorem The mass and the composition structure throughout a star uniquely determine its radius, luminosity, and internal structure, as well as its subsequent evolution The change of a stars composition is the result of the change of the nuclear reactions during its lifetime

16 Pre Main-Sequence Evolution

17 Post-Main-Sequence Existence The maximum fraction of the star s mass that can still support the outer lying mass was derived by Schönberg and Chandrasekhar Bahcall et al, Ap. J. 555 (2001) M ic 0.37 M µ env µ ic 2 When the limit is reached, the core will start to collapse (4) µ ic = mean molecular weight of isothermal core

18 Australian Telescope and Education Outreach

Period-Luminosity Relation Two types of variable Cepheid stars show a relation between their pulse period and luminosity The more luminous stars have longer

19 Period-Luminosity Relation Two types of variable Cepheid stars show a relation between their pulse period and luminosity The more luminous stars have longer pulse periods The measurement of period directly relates to the absolute luminosity The comparison between apparent and absolute luminosity gives the distance

20 Classification of Supernovae Type I do not contain any hydrogen lines Ia contain strong Si II line at 615 nm Ib no Si lines, strong helium lines Ic no Si lines, no helium lines Type II contain hydrogen lines II-P plateau 30 to 80 days after maximum luminosity II-L linear light curve

21 Core-Collapse Supernovae Type Ia supernovae are different from the other types Involve binary star system with a white dwarf Type Ib, Ic and II are core-collapse supernovae Involve stars of more than eight solar masses Carbon-oxygen core will burn Depending on mass of star a shell structure of fusion zones of heavier elements (towards the core) will develop

22 Light Curves of Supernovae The shape of the light curve, in particular after the initial stage, is defined by the contributions of the different decay channels Model of SN 1987a snlite.shtml

23 Electron Degeneracy Pressure and White Dwarf Stars A degenerate electron gas exerts pressure, because only one Fermion can occupy any given state, including ground states This pressure opposes the gravitational force in a white dwarf star This gives for the condition for a degenerate electron gas T ħ < 2 3 π 2 Z ⅔ ρ ⅔ = D 3 m k m H A Chandrasekhar realized, that there has to be a maximum mass for a white dwarf M Ch = 1.44 M The mass of a white dwarf is inverse proportional to its volume Larger mass white dwarfs are smaller

Neutron Degeneracy Like electrons, neutrons obey Fermi-Dirac statistics Stars consisting of neutrons at very high density are called neutron stars, supported by neutron degeneracy pressure The radius

24 Neutron Degeneracy Like electrons, neutrons obey Fermi-Dirac statistics Stars consisting of neutrons at very high density are called neutron stars, supported by neutron degeneracy pressure The radius for a 1.4 solar mass neutron star is 10 to15 km Outer crust contains heavy nuclei Inner crust contains mixture of heavy nuclei, superfluid neutrons Interior contains dissolved nuclei There may be a core containing pions, for example Very unclear at the moment

Pulsars Pulsating stars were discovered in 1967 via radio dipole antennae by Jocelyn Bell and Anthony Hewish Pulse period of PSR 1919+21 is 1.337 s Most pulsars have periods between 0.

25 Pulsars Pulsating stars were discovered in 1967 via radio dipole antennae by Jocelyn Bell and Anthony Hewish Pulse period of PSR is s Most pulsars have periods between 0.25 s and 2 s The periods are exceptionally well defined Periods slow down at a rate of about Only spinning neutron stars can produce periods in this range Orbiting or pulsating stars are ruled out as are white dwarfs

26 Crab Pulsar Simplified sketch of the Crab pulsar Hester et al., Ap. J. 448, 240 (1985)

Equivalence Principle Motion in a gravitational field cannot be distinguished from forcefree motion in an accelerated coordinate system S These reference frames are referred to as

27 Equivalence Principle Motion in a gravitational field cannot be distinguished from forcefree motion in an accelerated coordinate system S These reference frames are referred to as local inertial reference frames All physical experiments carried out in these reference frames will have an identical outcome Examples are Free fall in an elevator Curved spacetime

Schwarzschild Metric Spacetime is curved in the vicinity of mass Assume spherical mass M with radius R Karl Schwarzschild solved in 1916 the field equations Einstein published in his general

28 Schwarzschild Metric Spacetime is curved in the vicinity of mass Assume spherical mass M with radius R Karl Schwarzschild solved in 1916 the field equations Einstein published in his general relativity article He obtained this metric for curved spacetime inside the vacuum Karl Schwarzschild ( ) (ds ) 2 = ( 1 R s / r ) (c dt ) 2 ( 1 R s / r ) 1 (dr ) 2 (r dθ ) 2 (r sin θ dϕ ) 2 Here the Schwarzschild Radius is given by R s = 2 G M c 2

29 Black Holes In 1783 the English amateur astronomer John Michell advanced the idea of photons as particles being subject to gravitation A star 500 times larger than the Sun with it s average density would be strong enough to prevent light from leaving The escape velocity is given by v = Solving for the radius with the speed of light as the escape velocity 2 G M r ½ R = 2 G M c 2 = 2.95 ( M / M ) km This radius is very small and was considered unrealistic Compare to Schwarzschild Radius

30 Black Holes d r dt = c ( 1 R s / r ) In case r R S the coordinate speed of light = c, as expected in flat spacetime For r = R S the coordinate speed of light is zero Any information from within the Schwarzschild radius cannot reach us Any star collapsed to within the Schwarzschild radius is called a black hole A black hole is enclosed by the event horizon, the spherical surface given by the Schwarzschild radius

31 Mass Ranges of Black Holes Stellar-mass black holes 3 15 solar masses Formed through core collapse Intermediate-mass black holes IMBH solar masses Evidence in detection of ultraluminous X-ray sources Might form through mergers of stellar-mass black holes Found in the center of globular clusters and low-mass galaxies Supermassive black holes SMBH 10 5 to 10 9 solar masses Exist at the center of (probably) most galaxies Maybe formed through collisions of galaxies Maybe formed through continuation of IMBH formation

Stellar-Mass Black Hole Candidates Easiest way to find a black hole would probably be in a close binary system The black hole would pull gas from the companion star The angular momentum of their

32 Stellar-Mass Black Hole Candidates Easiest way to find a black hole would probably be in a close binary system The black hole would pull gas from the companion star The angular momentum of their orbital motion would lead to a gas disk around the black hole The gas would spiral down towards the black hole, heating up to very high temperatures and emit X-rays Only the gravity of a neutron star of black hole can produce X-rays If the invisible star exceeds 3 solar masses, it probably is a black hole

33 The Milky Way Structure The Milky Way consists of Galactic disk about 50 kpc in diameter Galactic bulge near the center Stellar Halo with globular clusters The Sun is 8 kpc away from the center Difference to earlier calculations basically due to interstellar extinction

The Milky Way Disk The Milky Way disk contains young to medium aged stars, a total of about 100 to 400 billion The disk also contains most of the gas and dust of the galaxy The disk is about 30 kpc

34 The Milky Way Disk The Milky Way disk contains young to medium aged stars, a total of about 100 to 400 billion The disk also contains most of the gas and dust of the galaxy The disk is about 30 kpc in diameter and 0.3 kpc thick The Sun is about 8 kpc away from the center of the galaxy Measured rotational speed of about 220 km/s = 225 pc / Myr For the rotational speed we get ω = rad / Myr One revolution takes about 224 million years

35 Rotation Curve of the Milky Way For comparison, the Triassic period extended from 200 to 250 million years ago First mammals developing on Pangaea Measuring the rotational speed as a function of the radius shows an almost flat distribution For very small distances from the galactic center, the rotational speed increases rapidly, typical for a rigid body For larger radii, the rotational speed is almost flat around 220 km/s

36 The Milky Way Center Radio image at 1 m wavelength of the region around Sagittarius

37 Morphological Classification Edwin Hubble classified galaxies according to appearance into Elliptical Galaxies E Spiral Galaxies Normal Spiral Galaxies S Barred Spiral Galaxies SB Irregular Galaxies Irr

38 Radio Galaxies Cyg A appears to be about 240 Mpc away and receding with a velocity of about 16,600 km/s Cyg A is still the brightest radio source besides the Sun Two lobes extending in opposite directions are visible The lobes are connected via jets to the cd galaxy

Quasars In 1960 Thomas Matthews and Allan Sandage were searching for the optical counterpart to the radio source 3C 48 They found a 16 th magnitude star-like object displaying broad emission lines

39 Quasars In 1960 Thomas Matthews and Allan Sandage were searching for the optical counterpart to the radio source 3C 48 They found a 16 th magnitude star-like object displaying broad emission lines not associated to any known atom or molecule This and similar objects, like 3C 273 shown below, are classified as quasi-stellar radio sources (quasars) The spectra s appearance is due to their very large redshift Some of the recessional velocities are up to 30% of the speed of light This makes them also some of the most distant objects measured

40 Quasars Large cosmological redshifts are caused by the expansion of space through which the light travels The rate of expansion is changing with the energy density of the Universe as it evolves The fractional change in wavelength is the same as the fractional change in the size of the Universe, R λ observed - λ emitted z = = λ emitted R observed - R emitted R emitted or 1 + z = R observed R emitted For z = 3, the Universe is now four times larger than when the light was emitted

41 Unified Model for AGN Both mass estimates are about the same order of magnitude The different types of AGN discussed so far can then be explained within a model assuming a supermassive black hole at the center and an accretion disk around it The source for the produced energy is accretion of matter through a disk around a rotating black hole by release of gravitational potential energy The accretion luminosity generated by a mass rate Ṁ through a disk can be written as L disk = η Ṁ c 2 with < η < the efficiency of the process Taking the quasar luminosity of W and an efficiency of 0.1, we obtain for the mass accretion Ṁ 8 M / yr

42 Tully-Fisher Relation We saw that there exists a relation between the luminosity of a spiral galaxy and its maximum rotation velocity The relation was determined first in 1977 by Tully and Fisher by measuring the Dopplerbroadened 21 cm radio emission line from neutral hydrogen in a sample of spiral galaxies

Cosmic Expansion Comparison of red-shifts for different astronomical objects The more the spectral lines are shifted towards the red end of the

43 Cosmic Expansion Comparison of red-shifts for different astronomical objects The more the spectral lines are shifted towards the red end of the spectrum, the more far away the object is and the larger its recessional velocity v = H 0 d = c (z + 1) 2 1 (z + 1) MPc = 3.26 million light years

44 Hubble Constant The Hubble constant is often expressed as H 0 = 100 h km s -1 Mpc -1 = h s -1 To estimate how long ago the Big Bang occurred, calculate the time t H needed for a galaxy to travel to it s present distance d, assuming incorrectly a constant velocity v d = v t H = H 0 d t H t H = H -1 0 = h -1 s Using h = 0.71 t H = yr

45 Clusters of Galaxies The Cosmological Principle states that on the largest scale, the Universe is homogeneous and isotropic This is not true at smaller scales Groups of galaxies usually have less than 50 members The typical galaxy group is about 1.4 h -1 Mpc across and contains about h -1 solar masses Clusters of galaxies contain 50 to thousands of galaxies The typical galaxy cluster is about 6 h -1 Mpc across and contains about h -1 solar masses Clusters of galaxy clusters are referred to as superclusters

46 Galaxy Distribution in the Universe Local distribution of galaxies compiled by the 2dF Galaxy Redshift Survey using the 3.9 m Anglo-Australian Telescope (AAO)

AST-1002 Section 0459 Review for Final Exam Please do not forget about doing the evaluation!

AST-1002 Section 0459 Review for Final Exam Please do not forget about doing the evaluation! Bring pencil #2 with eraser No use of calculator or any electronic device during the exam We provide the scantrons