The physics of interstellar dust

584 Pages·2003·6.33 MB·English

by  E. Krugel

The Physics of Interstellar Dust
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
theoretical and experimental astronomy and astrophysics. Books in the series
range in level from textbooks and handbooks to more advanced expositions of
currentresearch.
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Series in Astronomy and Astrophysics
The Physics of Interstellar Dust
Endrik Kru¨gel
Max-Planck-Institutfu¨r Radioastronomie,
Bonn,Germany
Institute of Physics Publishing
Bristol and Philadelphia
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SeriesEditors: MBirkinshaw,UniversityofBristol,UK
MElvis,Harvard–SmithsonianCenterforAstrophysics,USA
JSilk,UniversityofOxford,UK
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Contents
Preface xix
1 Thedielectricpermeability 1
1.1 Maxwell’sequations 1
1.1.1 Electricfieldandmagneticinduction 1
1.1.2 Electricpolarizationofthemedium 2
1.1.3 Thedependenceofthedielectricpermeabilityon
directionandfrequency 3
1.1.4 Thephysicalmeaningoftheelectricsusceptibilityχ 4
1.1.5 Magneticpolarizationofthemedium 6
1.1.6 Themagneticsusceptibility 7
1.1.7 Dielectricsandmetals 7
1.1.8 Freechargesandpolarizationcharges 8
1.1.9 Thefieldequations 9
1.2 Wavesinadielectricmedium 10
1.2.1 Thewaveequation 10
1.2.2 Thewavenumber 11
1.2.3 Theopticalconstantorrefractiveindex 12
1.2.4 Energydissipationofagraininavariablefield 13
1.3 Theharmonicoscillator 15
1.3.1 TheLorentzmodel 15
1.3.2 Freeoscillations 16
1.3.3 Thegeneralsolutiontotheoscillatorequation 17
1.3.4 Dissipationofenergyinaforcedoscillation 18
1.3.5 Dissipationofenergyinafreeoscillation 19
1.3.6 Theplasmafrequency 20
1.3.7 Dispersionrelationofthedielectricpermeability 20
1.4 Theharmonicoscillatorandlight 22
1.4.1 Attenuationandrefractionoflight 23
1.4.2 Retardedpotentialsofamovingcharge 24
1.4.3 Emissionofanharmonicoscillator 26
1.4.4 Radiationofhigherorder 27
1.4.5 Radiationdamping 28
viii Contents
1.4.6 Thecrosssectionofanharmonicoscillator 29
1.4.7 Theoscillatorstrength 30
1.4.8 Thenaturallinewidth 31
1.5 Wavesinaconductingmedium 32
1.5.1 Thedielectricpermeabilityofaconductor 33
1.5.2 ConductivityandtheDrudeprofile 34
1.5.3 Electromagneticwavesinaplasmawithamagneticfield 36
1.5.4 Groupvelocityofelectromagneticwavesinaplasma 37
1.6 Polarizationthroughorientation 38
1.6.1 Polarizationinaconstantfield 38
1.6.2 Polarizationinatime-variablefield 39
1.6.3 Relaxationafterswitchingoffthefield 40
1.6.4 ThedielectricpermeabilityinDebyerelaxation 41
2 Howtoevaluategraincrosssections 44
2.1 Definingcrosssections 44
2.1.1 Crosssectionforscattering,absorptionandextinction 44
2.1.2 Crosssectionforradiationpressure 46
2.1.3 Efficiencies,massandvolumecoefficients 47
2.2 Theopticaltheorem 47
2.2.1 Theintensityofforwardscatteredlight 47
2.2.2 Therefractiveindexofadustymedium 50
2.3 Mietheoryforasphere 51
2.3.1 Thegeneratingfunction 52
2.3.2 Separationofvariables 52
2.3.3 Seriesexpansionofwaves 54
2.3.4 Expansioncoefficients 54
2.3.5 Scatteredandabsorbedpower 56
2.3.6 Absorptionandscatteringefficiencies 57
2.4 Polarizationandscattering 57
2.4.1 Theamplitudescatteringmatrix 57
2.4.2 Angle-dependenceofscattering 58
2.4.3 Thepolarizationellipse 60
2.4.4 Stokesparameters 61
2.4.5 Stokesparametersofscatteredlightforasphere 62
2.5 TheKramers–Kronigrelations 64
2.5.1 Mathematicalformulationoftherelations 64
2.5.2 Theelectricsusceptibilityandcausality 66
2.5.3 TheKramers–Kronigrelationforthedielectricpermeability 67
2.5.4 Extensiontometals 67
2.5.5 Dispersionofthemagneticsusceptibility 68
2.5.6 ThreecorollariesoftheKKrelation 69
2.6 Compositegrains 71
2.6.1 Effectivemediumtheories 72
Contents ix
2.6.2 Garnett’smixingrule 73
2.6.3 ThemixingruleofBruggeman 74
2.6.4 Compositionofgrainsinprotostellarcores 74
2.6.5 Howsize,iceandporositychangetheabsorptioncoefficient 76
3 Verysmallandverybigparticles 80
3.1 Tinyspheres 80
3.1.1 WhenisaparticleintheRayleighlimit? 80
3.1.2 EfficienciesofsmallspheresfromMietheory 81
3.1.3 Adielectricsphereinaconstantelectricfield 82
3.1.4 Scatteringandabsorptionintheelectrostaticapproximation 84
3.1.5 Polarizationandangle-dependentscattering 85
3.1.6 Small-sizeeffectsbeyondMietheory 86
3.2 Asmallmetallicsphereinamagneticfield 87
3.2.1 Slowlyvaryingfield 87
3.2.2 Themagneticpolarizability 89
3.2.3 Thepenetrationdepth 89
3.2.4 Limitingvaluesofthemagneticpolarizability 90
3.3 Tinyellipsoids 90
3.3.1 Ellipticalcoordinates 91
3.3.2 Anellipsoidinaconstantelectricfield 92
3.3.3 Crosssectionandshapefactor 93
3.3.4 Randomlyorientedellipsoids 95
3.3.5 Pancakesandcigars 95
3.3.6 Rotationabouttheaxisofgreatestmomentofinertia 97
3.4 Thefieldsinsideadielectricparticle 99
3.4.1 Internalfieldanddepolarizationfield 99
3.4.2 Depolarizationfieldandthedistributionofsurfacecharges 100
3.4.3 Thelocalfieldatanatom 101
3.4.4 TheClausius–Mossottirelation 101
3.5 Verylargeparticles 103
3.5.1 Babinet’stheorem 103
3.5.2 Reflectionandtransmissionataplanesurface 104
3.5.3 Huygens’principle 106
3.5.4 FresnelzonesandacheckonHuygens’principle 109
3.5.5 Thereciprocitytheorem 111
3.5.6 Diffractionbyacircularholeorasphere 111
3.5.7 Diffractionbehindahalf-plane 113
3.5.8 Particlesofsmallrefractiveindex 116
3.5.9 X-rayscattering 117