Astronomical Spectroscopy: An Introduction To The Atomic And Molecular Physics Of Astronomical Spectra

203 Pages·2005·3.655 MB·English

by  Jonathan Tennyson

ASTRONOMICAL
SPECTROSCOPY
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Imperial College Press Advanced Physics Texts – Vol. 2
ASTRONOMICAL
SPECTROSCOPY
An Introduction to the Atomic and
Molecular Physics of Astronomical Spectra
by
JONATHAN TENNYSON
University College Londomn, UK
PressImperial College
Published by
Imperial College Press
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Covent Garden
London WC2H 9HE
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World Scientific Publishing Co. Pte. Ltd.
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British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
ASTRONOMICAL SPECTROSCOPY
An Introduction to the Atomic and Molecular Physics of Astronomical Spectra
Copyright © 2005 by Imperial College Press
All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means,
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May18,2005 12:24 WSPC/SPI-B267:AstronomicalSpectroscopy fm
PREFACE
This book follows closely a lecture course I gave entitled ‘Astronomical
Spectroscopy’tothird-yearundergraduatestudentsatUniversityCollege
London between 1998 and 2003. The students who attended had done
a prior introductory course on Quantum Mechanics which covered the
hydrogen atom but no further atomic physics or spectroscopy. A similar
levelofpriorknowledgeisassumedinthecurrentwork.
Therearemanypeoplewhosehelphavebeenessentialforthecomple-
tion of this book. First I must thank BillSomerville who inaugurated the
courseAstronomicalSpectroscopyandtaughtitfortwoyearsbeforeme.
Heselflesslysharedhislecturenotesandothermaterialswithme.Iwould
like to thank Ceinwen Sanderson for turning my hand-scrawled lecture
A
notesintoLTEX,andmycolleaguesTonyLynas-Gray,BillSomerville,Peter
Storeyand JeremyYatesfor their extensivecomments on the draftof the
book. I owe a debtof gratitude to my graduatestudents Bob Barberand
Natasha Doss who checked all the problems and found many errors. I
thankallofthemforthecorrections;anyerrorsthatremainareallmine.
I must alsothankthe studentswho attendedmyAstronomicalSpec-
troscopy course. It was great fun to teach, not least because the latest
developments in astrophysics often fed straight into the lectures. Partic-
ular thanks are due to the class of 2003 who made a number of helpful
commentsandsuggestionsonthecontentsofthebook.
A book on spectroscopy thrives on good illustrations and I have
shamelesslyplunderedtheliteratureandothersourcesforspectratoillus-
trate this one. I must thank Xiaowei Liu for help with digitising many
of the published spectra, my student Iryna Rozum, my son Matthew,
and especially David Rage for their help with the other illustrations.
v
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vi AstronomicalSpectroscopy
I thank the journal publishers and the many authors who greeted my
requests to reproduce their work with prompt enthusiasm, especially
thoseauthorswhoadaptedfiguresatmyrequest.Eachjournalandauthor
isindividuallyacknowledgedinthefigurecaptions.
Finally I must acknowledge the UCL astronomers of the past and
present who have answered my many questions on astrophysics with a
patience their frequent stupidity probably did not deserve. Particularly
highonthislistarePeteStoreyandMikeBarlow,buttherestofthevaried
lunchcrewshouldnotbeforgotten.Withoutyoumyknowledgeofthings
astronomical would be the same as it was the day I arrived at UCL —
nothing.
JonathanTennyson
London,
July2004
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CONTENTS
Preface v
1. WhyRecordSpectraofAstronomicalObjects? 1
1.1 AHistoricalIntroduction . . . . . . . . . . . . . . . . . . . . 1
1.2 WhatOneCanLearnfromStudyingSpectra . . . . . . . . . 3
2. TheNatureofSpectra 7
2.1 Transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 AbsorptionandEmission . . . . . . . . . . . . . . . . . . . . 8
2.3 OtherMeasuresofTransitionProbabilities . . . . . . . . . . 10
2.4 StimulatedEmission . . . . . . . . . . . . . . . . . . . . . . . 10
2.5 OpticalDepth . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.6 CriticalDensity. . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.7 WavelengthorFrequency? . . . . . . . . . . . . . . . . . . . 13
2.8 TheElectromagneticSpectrum . . . . . . . . . . . . . . . . . 14
3. AtomicHydrogen 17
3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2 TheSchro¨dingerEquationofHydrogen-LikeAtoms . . . . 17
3.3 ReducedMass . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.4 AtomicUnits . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.5 WavefunctionsforHydrogen. . . . . . . . . . . . . . . . . . 20
3.6 EnergyLevelsandQuantumNumbers . . . . . . . . . . . . 21
3.7 H-AtomDiscreteSpectra . . . . . . . . . . . . . . . . . . . . 23
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viii AstronomicalSpectroscopy
3.8 H-AtomSpectrainDifferentLocations . . . . . . . . . . . . 30
3.8.1 Balmerseries . . . . . . . . . . . . . . . . . . . . . . . 30
3.8.2 Lymanseries . . . . . . . . . . . . . . . . . . . . . . . 33
3.8.3 Infraredlines . . . . . . . . . . . . . . . . . . . . . . . 34
3.9 H-AtomContinuumSpectra . . . . . . . . . . . . . . . . . . 35
3.9.1 Processes . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.9.2 H-atomemissioninHIIregions . . . . . . . . . . . . 36
3.10 RadioRecombinationLines. . . . . . . . . . . . . . . . . . . 38
3.11 RadioRecombinationLinesforOtherAtoms . . . . . . . . 40
3.12 AngularMomentumCouplingintheHydrogenAtom . . . 43
3.13 TheFineStructureofHydrogen . . . . . . . . . . . . . . . . 44
3.14 HyperfineStructureintheHAtom . . . . . . . . . . . . . . 46
3.15 AllowedTransitions . . . . . . . . . . . . . . . . . . . . . . . 47
3.16 HydrogeninNebulae . . . . . . . . . . . . . . . . . . . . . . 48
4. ComplexAtoms 51
4.1 GeneralConsiderations . . . . . . . . . . . . . . . . . . . . . 51
4.2 CentralFieldModel . . . . . . . . . . . . . . . . . . . . . . . 52
4.3 IndistinguishableParticles . . . . . . . . . . . . . . . . . . . 54
4.4 ElectronConfigurations . . . . . . . . . . . . . . . . . . . . . 55
4.5 ThePeriodicTable . . . . . . . . . . . . . . . . . . . . . . . . 57
4.6 Ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.7 AngularMomentuminComplexAtoms . . . . . . . . . . . 59
4.7.1 L–SorRussell–Saunderscoupling . . . . . . . . . . . 60
4.7.2 j–jcoupling . . . . . . . . . . . . . . . . . . . . . . . . 61
4.7.3 Whytwocouplingschemes? . . . . . . . . . . . . . . 62
4.8 SpectroscopicNotation . . . . . . . . . . . . . . . . . . . . . 62
4.9 ParityoftheWavefunction . . . . . . . . . . . . . . . . . . . 64
4.10 TermsandLevelsinComplexAtoms . . . . . . . . . . . . . 64
5. HeliumSpectra 69
5.1 HeIandHeIISpectra . . . . . . . . . . . . . . . . . . . . . . 69
5.2 SelectionRulesforComplexAtoms . . . . . . . . . . . . . . 71
5.3 ObservingForbiddenLines . . . . . . . . . . . . . . . . . . . 74
5.4 GrotrianDiagrams . . . . . . . . . . . . . . . . . . . . . . . . 75
5.5 PotentialFeltbyElectronsinComplexAtoms . . . . . . . . 77
5.6 EmissionsofHelium-LikeIons . . . . . . . . . . . . . . . . . 78
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Contents ix
6. AlkaliAtoms 81
6.1 Sodium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
6.2 Spin-OrbitInteractions . . . . . . . . . . . . . . . . . . . . . 84
6.3 FineStructureTransitions . . . . . . . . . . . . . . . . . . . . 88
6.4 AstronomicalSodiumSpectra . . . . . . . . . . . . . . . . . 89
6.5 OtherAlkaliMetal-LikeSpectra . . . . . . . . . . . . . . . . 93
7. SpectraofNebulae 99
7.1 Nebulium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
7.2 TheBowenMechanism . . . . . . . . . . . . . . . . . . . . . 104
7.3 TwoValenceElectrons . . . . . . . . . . . . . . . . . . . . . . 108
7.4 AutoionisationandRecombination . . . . . . . . . . . . . . 110
8. X-RaySpectra 116
8.1 TheSolarCorona. . . . . . . . . . . . . . . . . . . . . . . . . 119
8.2 IsotopeEffects . . . . . . . . . . . . . . . . . . . . . . . . . . 120
9. MolecularStructure 124
9.1 TheBorn–OppenheimerApproximation . . . . . . . . . . . 125
9.2 ElectronicStructureofDiatomics . . . . . . . . . . . . . . . 126
9.2.1 Labellingofelectronicstates . . . . . . . . . . . . . . 128
9.2.2 Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . 130
9.2.3 Statelabels . . . . . . . . . . . . . . . . . . . . . . . . 132
9.3 Schro¨dingerEquation . . . . . . . . . . . . . . . . . . . . . . 132
9.4 Fractionation . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
9.5 Vibration–RotationEnergyLevels . . . . . . . . . . . . . . . 138
9.6 TemperatureEffects . . . . . . . . . . . . . . . . . . . . . . . 141
9.6.1 Rotationalstatepopulations . . . . . . . . . . . . . . 141
9.6.2 Vibrationalstatepopulations . . . . . . . . . . . . . . 143
9.6.3 Electronicstatepopulations . . . . . . . . . . . . . . 144
10. MolecularSpectra 146
10.1 SelectionRules:PureRotationalTransitions . . . . . . . . . 146
10.1.1 Isotopeeffects . . . . . . . . . . . . . . . . . . . . . . 151
10.1.2 Rotationalspectraofothermolecules . . . . . . . . . 151
10.1.3 Rotationalspectraofmolecularhydrogen . . . . . . 154
10.2 VibrationalTransitions . . . . . . . . . . . . . . . . . . . . . 155
10.2.1 Structureofthespectrum . . . . . . . . . . . . . . . . 156