Astroparticle Physics

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372 17 Solutions4.( ) 2R 0 t0 3= ,R mr t mrwhere R mr is the size of the universe at the time of matter–radiation equality t mr =50 000 a. With t 0 = 14 billion years, one hasR 0≈ 4280 .R mrThe size of the universe at that time wasR mr ≈ R 04280 ≈ 3.27 × 106 light-years ≈ 3.09 × 10 22 m .Extrapolating to earlier times requires to assume R ∼ √ t, since for times t
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Astroparticle Physics
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Prof. Dr. Claus GrupenUniversity of
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VIPrefaceand M.Sc. Mehmet T. Kurt (
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VIIIPrefaceOn top of that, the basi
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XTable of Contents5 Acceleration Me
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XIITable of Contents11 The Cosmic M
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11 Historical Introduction“Look i
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1.1 Discoveries in the 20th Century
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1.2 Discoveries of New Elementary P
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1.3 Start of the Satellite Era 11ex
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1.3 Start of the Satellite Era 13CO
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1.3 Start of the Satellite Era 1519
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1.4 Open Questions 171989) and at e
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1.5 Problems 191.5 Problems1. Work
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22 2 The Standard Model of Elementa
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}28 2 The Standard Model of Element
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353 Kinematics and Cross Sections
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3.1 Threshold Energies 373.1 Thresh
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3.2 Four-Vectors 39Example 3: Consi
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3.2 Four-Vectors 41Example 6: Muon
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3.2 Four-Vectors 43Because of E γ2
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3.3 Lorentz Transformation 45energi
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3.5 Problems 47If j is the particle
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494 Physics of Particleand Radiatio
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4.2 Interaction Processes Used for
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4.2 Interaction Processes Used for
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4.3 Principles of the Atmospheric A
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4.4 Special Aspects of Photon Detec
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4.6 Propagation and Interactions of
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4.8 Problems 61board of a satellite
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635 Acceleration Mechanisms“Physi
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5.2 Acceleration by Sunspot Pairs 6
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5.3 Shock Acceleration 67The ejecte
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5.5 Pulsars 69Since this accelerati
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5.6 Binaries 71one obtains, using E
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5.7 Energy Spectra of Primary Parti
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5.7 Energy Spectra of Primary Parti
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776 Primary Cosmic Rays“It will b
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6.1 Charged Component of Primary Co
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6.2 Neutrino Astronomy 87is only co
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6.2 Neutrino Astronomy 89ν e + e
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6.2 Neutrino Astronomy 91For an ass
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6.2 Neutrino Astronomy 93upward-goi
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6.2 Neutrino Astronomy 957 Be + p
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6.2 Neutrino Astronomy 97A reconstr
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6.2 Neutrino Astronomy 99nos (or in
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6.2 Neutrino Astronomy 101In the ho
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6.2 Neutrino Astronomy 103The exper
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6.2 Neutrino Astronomy 105muon spec
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6.2 Neutrino Astronomy 107The setup
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6.3 Gamma Astronomy 109All parts of
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6.3 Gamma Astronomy 111The energy s
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6.3 Gamma Astronomy 1136.3.3 Measur
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6.3 Gamma Astronomy 115v = c n = 29
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6.3 Gamma Astronomy 117The relation
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6.3 Gamma Astronomy 119Future space
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6.3 Gamma Astronomy 121γ -ray burs
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6.4 X-Ray Astronomy 123bursters all
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6.4 X-Ray Astronomy 125synchrotron
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6.4 X-Ray Astronomy 127In 1952 Wolt
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6.4 X-Ray Astronomy 129In 1959 the
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6.4 X-Ray Astronomy 131Measurements
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6.5 Gravitational-Wave Astronomy 13
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6.5 Gravitational-Wave Astronomy 13
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6.6 Problems 1373. Radiation exposu
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6.6 Problems 139the star and its te
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1417 Secondary Cosmic Rays“There
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7.1 Propagation in the Atmosphere 1
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7.1 Propagation in the Atmosphere 1
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7.2 Cosmic Rays at Sea Level 1477.2
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7.2 Cosmic Rays at Sea Level 149muo
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7.3 Cosmic Rays Underground 151N(ν
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7.3 Cosmic Rays Underground 153[ a
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7.3 Cosmic Rays Underground 155Fig.
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7.4 Extensive Air Showers 157hadron
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7.4 Extensive Air Showers 159precis
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7.4 Extensive Air Showers 161primar
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7.5 Nature and Origin of the Highes
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7.6 Problems 169‘Milky Way’ of
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1718 Cosmology“As far as the laws
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8.1 The Hubble Expansion 173isotrop
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8.2 The Isotropic and Homogeneous U
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8.3 The Friedmann Equation from New
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8.4 The Friedmann Equation from Gen
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8.4 The Friedmann Equation from Gen
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8.7 Nature of Solutions to the Frie
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8.7 Nature of Solutions to the Frie
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8.8 Experimental Evidence for the V
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8.9 Problems 189where E max is the
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1919 The Early Universe“Who cares
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9.2 Thermodynamics of the Early Uni
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9.3 Solving the Friedmann Equation
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9.3 Solving the Friedmann Equation
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9.4 Thermal History of the First Te
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9.5 The Baryon Asymmetry of the Uni
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9.6 Problems 211investigation of CP
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21310 Big Bang Nucleosynthesis“In
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10.2 Start of the BBN Era 215these
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10.3 The Neutron-to-Proton Ratio 21
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10.4 Neutrino Decoupling, Positron
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10.5 Synthesis of Light Nuclei 221i
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10.6 Detailed BBN 223Fig. 10.4Evolu
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10.6 Detailed BBN 225prediction for
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10.7 Constraints on the Number of N
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22911 The Cosmic MicrowaveBackgroun
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11.2 Discovery and Basic Properties
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11.3 Formation of the CMB 23311.3 F
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11.4 CMB Anisotropies 235Once the p
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11.5 The Monopole and Dipole Terms
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11.6 Determination of Cosmological
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24512 Inflation“Inflation hasn’
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12.2 The Flatness Problem 247Althou
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12.3 The Monopole Problem 249place
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12.4 How Inflation Works 251the pre
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12.5 Mechanisms for Inflation 253On
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12.5 Mechanisms for Inflation 255th
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12.6 Solution to the Flatness Probl
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12.8 Solution to the Monopole Probl
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12.9 Inflation and the Growth of St
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12.10 Outlook on Inflation 263years
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26513 Dark Matter“There is a theo
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13.2 Motivation for Dark Matter 267
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13.3 Problems 285map of about 1 ◦
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28714 Astrobiology“In the beginni
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14 Astrobiology 289on the chances t
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14.1 Problems 2913. What determines
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294 15 OutlookTheory of Everythingo
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296 15 Outlookmatter dominanceprimo
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29916 Glossary“A good notation ha
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16 Glossary 301The antiparticle of
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16 Glossary 303The Big Rip is a cos
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16 Glossary 305Stars which have rap
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16 Glossary 307A quantity is conser
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16 Glossary 309X-ray binary consist
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16 Glossary 311The electron and its
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16 Glossary 313Particle detector fo
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16 Glossary 315The interaction of p
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16 Glossary 317High Resolution Imag
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16 Glossary 319Short for Large Elec
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16 Glossary 321Distant galaxies wit
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16 Glossary 323Transmutation of a n
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16 Glossary 325See fermion.The poin
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16 Glossary 327Quantum anomalies ca
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16 Glossary 329The metric describin
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16 Glossary 331This theory refers t
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16 Glossary 333Particles whose spin
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16 Glossary 335(c) The value of the
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33717 Solutions“The precise state
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17.1 Chapter 1 3394. By definition
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17.2 Chapter 2 3412. For any unstab
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17.4 Chapter 4 3434.p b❅■ ✒
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17.4 Chapter 4 3455. From the expre
Page 722: 17.5 Chapter 5 347Consequences:The
Page 726: 17.6 Chapter 6 3493. a) The average
Page 730: 17.6 Chapter 6 351b) On both sides
Page 734: 17.6 Chapter 6 353This gives the sc
Page 738: 17.6 Chapter 6 3555. Measured flux
Page 742: 17.7 Chapter 7 3574. N(> E,R) = A(a
Page 746: 17.8 Chapter 8 359Since E = hν = h
Page 750: 17.8 Chapter 8 3615. Photon mass m
Page 754: 17.9 Chapter 9 3639. Schwarzschild
Page 758: 17.9 Chapter 9 365which is the Schw
Page 762: 17.10 Chapter 10 367whereσ√hadr
Page 766: 17.11 Chapter 11 3694. Planck distr
Page 770: 17.12 Chapter 12 371The related mas
Page 776: 374 17 SolutionsThe axion mass does
Page 780: 376 17 Solutions100 kg kgW 0 = = 50
Page 784: 378 17 SolutionsThis results inM pl
Page 790: 381A Mathematical AppendixA.1 Selec
Page 794: A.1 Selected Formulae 383∫e x dx
Page 798: A.2 Mathematics for Angular Variati
Page 802: A.2 Mathematics for Angular Variati
Page 806: 389B Results from Statistical Physi
Page 810: B.1 Statistical Mechanics Review 39
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B.2 Number and Energy Densities 397
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B.3 Equations of State 399which rel
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401C Definition of Equatorialand Ga
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403D Important Constants for Astrop
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405References“References are like
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407Further Reading“Education is t
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Further Reading 409Ulf Borgeest, Ka
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Further Reading 411M. A. Bucher, D.
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414 Photo Credits{20} ESA/XMM-Newto
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416 Indexanisotropy, 85, 86- cosmic
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418 Index- of hydrogen, 94, 222, 22
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420 Index- parameters, 243- - deter
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422 Indexeffective number of degree
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424 IndexFeynman diagram, 26, 98, 2
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426 IndexHarrison-Zel’dovich spec
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428 IndexKoshiba, M., 13kpc, 318, s
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430 Index- standard, see StandardMo
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432 Index- primary, energy spectrum
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434 Indexplanet, extrasolar, 18plan
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436 Indexrange- relation, energy-,
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438 Index- dark, 269- double, see b
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440 Indexuncertainty- principle, se
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