Dark Sky, Dark Matter

227 Pages·2002·2.14 MB·English

by  J.M Overduin

Dark Sky, Dark Matter
Series in Astronomy and Astrophysics
SeriesEditors: MBirkinshaw,UniversityofBristol,UK
MElvis,Harvard–SmithsonianCenterforAstrophysics,USA
JSilk,UniversityofOxford,UK
The Series in Astronomy and Astrophysics includes books on all aspects of
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Series in Astronomy and Astrophysics
Dark Sky, Dark Matter
J M Overduin
Universita¨t Bonn, Bonn, Germany and
Waseda University, Tokyo, Japan
P S Wesson
University of Waterloo, Waterloo, Canada
Institute of Physics Publishing
Bristol and Philadelphia
(cid:1)c IOPPublishingLtd2003
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SeriesEditors: MBirkinshaw,UniversityofBristol,UK
MElvis,Harvard–SmithsonianCenterforAstrophysics,USA
JSilk,UniversityofOxford,UK
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Contents
Preface ix
1 Thedarknightsky 1
1.1 Olbers’paradox 1
1.2 AshorthistoryofOlbers’paradox 2
1.3 Theparadoxnow:stars,galaxiesandUniverse 5
1.4 Theresolution:ageversusexpansion 9
1.5 Thedata: opticalandotherwise 10
1.6 Conclusion 13
2 Themodernresolutionandenergy 16
2.1 Big-bangcosmology 16
2.2 Thebolometricbackground 16
2.3 Fromtimetoredshift 20
2.4 Matterandenergy 22
2.5 Theexpansionrate 24
2.6 Thestaticanalogue 27
2.7 Aquantitativeresolution 29
2.8 LightattheendoftheUniverse? 35
3 Themodernresolutionandspectra 41
3.1 Thespectralbackground 41
3.2 Frombolometrictospectralintensity 42
3.3 Thedelta-functionspectrum 44
3.4 Gaussianspectra 50
3.5 Blackbodyspectra 51
3.6 Normalandstarburstgalaxies 54
3.7 BacktoOlbers 61
4 Thedarkmatter 66
4.1 Fromlighttodarkmatter 66
4.2 Thefourelementsofmoderncosmology 67
4.3 Baryons 68
4.4 Colddarkmatter 73
4.5 Neutrinos 76
vi Contents
4.6 Vacuumenergy 78
4.7 ThecoincidentalUniverse 85
5 Thevacuum 90
5.1 Vacuumdecay 90
5.2 Thevariablecosmological‘constant’ 91
5.3 Energydensity 95
5.4 Sourceregionsandluminosity 101
5.5 Bolometricintensity 105
5.6 Spectralenergydistribution 106
5.7 Themicrowavebackground 108
6 Axions 113
6.1 Lightaxions 113
6.2 Restmass 114
6.3 Axionhalos 117
6.4 Intensity 119
6.5 Theinfraredandopticalbackgrounds 120
7 Neutrinos 127
7.1 Thedecaying-neutrinohypothesis 127
7.2 Boundneutrinos 128
7.3 Luminosity 130
7.4 Free-streamingneutrinos 133
7.5 Intergalacticabsorption 135
7.6 Theultravioletbackground 139
8 Supersymmetricweaklyinteractingparticles 146
8.1 Thelightestsupersymmetricparticle 146
8.2 Neutralinos 147
8.3 Pairannihilation 149
8.4 One-loopdecays 154
8.5 Tree-leveldecays 157
8.6 Gravitinos 161
8.7 Thex-rayandγ-raybackgrounds 163
9 Blackholes 170
9.1 Primordialblackholes 170
9.2 Initialmassdistribution 171
9.3 Evolutionandnumberdensity 173
9.4 Cosmologicaldensity 175
9.5 Spectralenergydistribution 177
9.6 Luminosity 179
9.7 Bolometricintensity 179
9.8 Spectralintensity 183
9.9 Higher-dimensional‘blackholes’ 186
Contents vii
10 Conclusions 192
A Bolometricintensityintegrals 196
A.1 Radiation-dominatedmodels 196
A.2 Matter-dominatedmodels 197
A.3 Vacuum-dominatedmodels 199
B Dynamicswithadecayingvacuum 202
B.1 Radiation-dominatedregime 202
B.2 Matter-dominatedregime 203
B.3 Vacuum-dominatedregime 204
C Absorptionbygalactichydrogen 206
Index 209
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Preface
The darkness of the night sky awed our ancestors and fascinates modern
astronomers.Itisafundamentalproblem:whyisthenightskydark,andjusthow
darkisit? Thisbookexaminestheseoverlappingproblemsfromtheviewpoints
ofbothhistoryandmoderncosmology.
Olbers’ paradox is a vintage conundrum that was known to other thinkers
prior to its formulation by the Prussian astronomer in 1823. Given that the
Universeisunbounded,governedbythestandardlawsofphysics,andpopulated
by light sources of constant intensity, the simple cube law of volumes and
numbersimpliesthattheskyshouldbeablazewithlight.Obviouslythisisnotso.
However,theparadoxdoesnotlieinnaturebutinourunderstandingofphysics.
A Universewith a finite age, such as followsfrom big-bangtheory, necessarily
hasgalaxiesoffiniteage.Thereisthereforeakindofimaginarysphericalsurface
arounduswhichdependsontheageandthespeedoflight. Thatis,wecanonly
seesomeofthegalaxiesintheUniverse,andthisisthemainreasonwhythenight
sky is dark. Just how dark can be calculated using the astrophysics of galaxies
andtheirstars,andthedynamicsofrelativisticcosmology.
We knowfromthedynamicsofindividualgalaxiesandclustersofgalaxies
thatthemajorityofthematterwhichexertsgravitationalforcesisnotdetectable
by conventional telescopes. This dark matter could, in principle, have many
forms, and candidates include various types of elementary particles as well as
vacuumfluctuations,blackholesandothers.Mostofthesecandidatesareunstable
todecayandproducephotons. Sodarkmatterdoesnotonlyaffectthedynamics
oftheUniverse,buttheintensityofintergalacticradiationaswell.Conversely,we
canuseobservationsofbackgroundradiationtoconstrainthenatureanddensity
ofdarkmatter. ThusdoesOlbers’problemgainnewimportance.
Modern cosmology is a cooperative endeavour, and we would like to
acknowledge some of the people who have helped to shape our ideas about
the Universe and what it may contain. It is a pleasure to thank H-J Fahr and
K-IMaeda for hospitality at the Institut fu¨r Astrophysik und Extraterrestrische
Forschung in Bonn and at Waseda University in Tokyo, where much of this
book was written with support from the Alexander von Humboldt Foundation
and the Japan Society for the Promotion of Science. Many of the results we
will present on astrophysics, general relativity and particle physics have been
ix