Stellar Evolution Physics, Vol. 2: Advanced Evolution of Single Stars

618 Pages·2013·9.55 MB·English

by  Icko Iben

StellarEvolutionPhysics
Volume2:AdvancedEvolutionofSingleStars
Thisvolumeexplainsthemicroscopicphysicsoperatinginstarsinadvancedstagesoftheir
evolutionanddescribeswithmanynumericalexamplesandillustrationshowtheyrespond
to this microphysics. Models of low and intermediate mass are evolved through the core
helium-burningphase,theasymptoticgiantbranchphase(alternatingshellhydrogenand
helium burning), and through the final cooling white dwarf phase. A massive model is
carriedfromthecorehelium-burningphasethroughcoreandshellcarbon-burningphases.
Gravothermalresponsestonuclearreaction-inducedtransformationsandenergylossfrom
thesurfacearedescribedindetail.Writtenforseniorgraduatestudentsandresearcherswho
havemasteredtheprinciplesofstellarevolution,asdevelopedinthefirstvolumeofStellar
Evolution Physics, sufficient attention is paid to how numerical solutions are obtained to
enablethereadertoengageinmodelconstructiononaprofessionallevel.
TheprocessesinthisvolumebuilduponthoseinVolume1ofStellarEvolutionPhysics:
Physical Processes in Stellar Interiors (ISBN 978-1-107-01656-9), which describes the
microscopicphysicsoperatinginstarsanddemonstrateshowstarsrespondfromformation,
through hydrogen-burning phases, up to the onset of helium burning. Stellar Evolution
Physicsisalsoavailableasa2-volumeset(ISBN978-1-107-60253-3).Takentogether,the
twovolumeswillprepareagraduatestudentforprofessional-levelresearchinthiskeyarea
ofastrophysics.
IckoIben,Jr.isEmeritusDistinguishedProfessorofAstronomyandPhysicsattheUniversity
ofIllinoisatUrbana-Champaign,wherehealsogainedhisMSandPhDdegreesinPhysics
and where a Distinguished Lectureship in his name was established in 1998. He initi-
atedhisteachingcareeratWilliamsCollege(1958–61),engagedinastrophysicsresearch
as a Senior Research Fellow at Cal Tech (1961–4), and continued his teaching career
at MIT (1964–72) and Illinois (1972–99). He has held visiting Professorships at over
a dozen institutions, including Harvard University, the University of California at Santa
Cruz,theUniversityofBologna,Italy,andNiigataUniversity,Japan.Hewaselectedtothe
USNationalAcademyofSciencesin1985,andhisawardsincludetheRussellLectureship
oftheAmericanAstronomicalSociety(1989),theGeorgeDarwinLectureship(1984)and
theEddingtonMedal(1990)oftheRoyalAstronomicalSociety,andtheEminentScientist
AwardoftheJapanSocietyforthePromotionofScience(2003–4).

Stellar Evolution Physics
Volume 2: Advanced Evolution of Single Stars
(cid:2)
ICKOIBEN,JR.
UniversityofIllinoisatUrbana-Champaign
CAMBRIDGEUNIVERSITYPRESS
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(cid:2)c I.Iben,Jr.2013
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Firstpublished2013
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LibraryofCongressCataloginginPublicationdata
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Stellarevolutionphysics/IckoIben,Jr.
p. cm.
Includesbibliographicalreferencesandindex.
ISBN978-1-107-01657-6(Hardback)
1. Stars–Evolution. 2. Stellardynamics. I. Title.
QB806.I242012
(cid:3)
523.88–dc23
2012019504
ISBN978-1-107-01657-6Hardback
Alsoavailableaspartofatwo-volumeset,StellarEvolutionPhysicsISBN978-1-107-60253-3
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Contents
Preface pageix
PartIV Transportprocesses,weakinteractionprocesses,
andhelium-burningreactions 891
12 Particlediffusionandgravitationalsettling 893
12.1 Moments of the Boltzmann transport equation for a species under
conditionsofcompleteequilibrium 895
12.2 Amonoelementalgasincompleteequilibriumatconstanttemperature
inaconstantgravitationalfield 901
12.3 Diffusion velocities and moments in a multicomponent gas
inagravitationalfield 906
12.4 Thestrengthoftheelectrostaticfieldwhenequilibriumwithrespect
todiffusionprevails 909
12.5 Driving forces for diffusion in an initially homogeneous medium
consistingoftwoionspeciesinagravitationalfield 911
12.6 Onthedeterminationofresistancecoefficientsfordiffusion 915
12.7 Inclusion of electron-flow properties and ion–electron interactions
anddeterminationofdiffusionvelocities 918
12.8 Generalizationtoamulticomponentgas 922
12.9 Gravitationaldiffusionvelocitiesforheliumandironatthebase
oftheconvectiveenvelopeofsolarmodels 925
12.10 Morediffusionvelocitiesbelowthebaseoftheconvectiveenvelope
ofasolarmodel 930
12.11 Equations for abundance changes due to diffusion and solution
algorithms 933
Bibliographyandreferences 940
13 Heatconductionbyelectrons 941
13.1 Thebasicphysicsofthermaldiffusion 942
13.2 Themacroscopicelectrostaticfieldinanionizedmedium
inagravitationalfield 951
13.3 UseoftheBoltzmanntransportequationtofindtheasymmetry
intheelectron-distributionfunction 956
13.3.1 Thecrosssectionintegral 960
v
vi Contents
13.4 Gradientsinthermodynamicvariablesandtheelectricfield 962
13.5 Thermalconductivityintheclassicalapproximation 968
13.5.1 Generalconsiderations 968
13.5.2 Whenelectronsarenotdegenerate 970
13.5.3 Whenelectronsaredegeneratebutnotrelativistic 971
13.6 Aquantitativeestimateoftheconductiveopacity 973
13.6.1 Fits to still more sophisticated estimates of the conductive
opacity 975
Bibliographyandreferences 978
14 Betadecayandelectroncaptureinstarsathighdensities 979
14.1 Theformalism 980
14.2 Electroncaptureathighdensities 984
14.3 Electrondecayathighdensities 989
14.4 Positron decay and general considerations concerning electron
captureonapositronemitter 993
14.5 Electroncaptureonapositronemitterwhenelectronsarenotdegenerate 995
14.6 Electroncaptureonapositronemitterwhenelectronsaredegenerate 999
14.7 Urcaneutrinoenergy-lossrates 1001
14.8 Additionalneutrinoenergy-lossratesforbeta-decayreactions
involvingpositron-stableisotopes 1004
14.9 Neutrinoenergy-lossratesforelectroncaptureonapositronemitter 1008
14.10 Higherorderbetatransitionsandexperimentalproperties
ofbeta-decayreactions 1009
Bibliographyandreferences 1010
15 Current–currentweakinteractionsandtheproductionofneutrino–antineutrinopairs 1011
15.1 Thecharged-currentinteractionHamiltonianandthenecessity
fortwocouplingconstantsinnuclearbetadecay 1013
15.2 Thecharged-currentinteractionandmuondecay 1020
15.3 Annihilation of electron–positron pairs into neutrino–antineutrino
pairs and the associated energy-loss rate when electrons are not
degenerate 1024
15.4 The Dirac equation, plane-wave solutions, helicity eigenfunctions,
andgammamatrices 1033
15.5 Derivationofthecrosssectionforelectron–positronpairannihilation
intheV-Atheory 1042
15.6 A brief overview of the history and the nature of weak-interaction
inducedneutrino–antineutrinoproductionprocesses 1050
15.7 Onthecharacterofclassicalplasmaoscillations 1052
15.8 Quantizedplasmaoscillationsandtheneutrino–antineutrino
energy-lossrateduetoplasmondecay 1061
Bibliographyandreferences 1068
vii Contents
16 Helium-burningnuclearreactionsandenergy-generationrates 1070
16.1 Somebasicphysicsofresonantreactions 1072
16.2 Thetriple-alphareactionsintheclassicalapproximation 1078
16.3 Triple-alphareactionsatlowtemperatures 1086
16.4 Theformationof16Obyalphacaptureon12Candtheconversion
of14Ninto22Ne 1091
16.5 Neutronproductionby(α,n)reactionson13Cand22Ne 1094
16.6 Onthecontributionofthe7Li(p,γ)8Bereactiontotheproduction
ofcarboninmetal-freestars 1099
Bibliographyandreferences 1099
PartV Evolutionduringhelium-burningphases 1101
17 Evolutionofalowmassmodelburningheliumandhydrogen 1103
17.1 Heliumshellflashesduringevolutionfromtheredgiantbranch
tothehorizontalbranch 1104
17.2 Horizontalbranchandearlyasymptoticgiantbranchevolution 1149
17.3 Thefirstheliumshellflashontheasymptoticgiantbranch 1175
17.4 Systematicsofthermalpulsesalongtheasymptoticgiantbranch 1191
17.5 The roles ofnuclear burning, convective mixing, and gravothermal
activityindeterminingabundancechangesanddredge-upduring
theTPAGBphase 1206
17.6 Neutronproductionandneutroncaptureinhelium-burningregions 1214
Bibliographyandreferences 1218
18 Evolutionofanintermediatemassmodelburningheliumandhydrogen 1220
18.1 Evolutionduringthecorehelium-burningphase 1223
18.2 Transitionto,evolutionalong,andtransitionfromtheearly
asymptoticgiantbranch 1235
18.3 The thermally pulsing asymptotic giant branch phase and the third
dredge-upphenomenon 1260
Bibliographyandreferences 1290
19 NeutronproductionandneutroncaptureinaTPAGBmodelstarofintermediatemass 1291
19.1 Historyofs-processnucleosynthesisandoutline 1291
19.2 Neutron-productionandneutron-capturereactionrates 1293
19.3 Formationofa13Cabundancepeakandneutronproduction
andneutroncaptureinthepeak 1302
19.4 Neutronproductionandcaptureduringtheinterpulsephaseinmatter
processedbyhydrogenburning 1313
19.5 Neutron-capturenucleosynthesisintheconvectiveshellduring
thefifteenthheliumshellflash 1322
viii Contents
19.6 Neutron-capturenucleosynthesisinTPAGBstarsandheavys-process
elementproductionintheUniverse 1336
Bibliographyandreferences 1338
20 EvolutionofamassivepopulationImodelduringhelium-andcarbon-burningstages 1339
20.1 Evolution of surface and central characteristics of a 25 M(cid:4) model
duringquiescentnuclearburningstagesandcomparisonofcharacter-
isticsofmodelsofmass1 M(cid:4),5 M(cid:4),and25 M(cid:4) 1340
20.2 Evolutionofinternalcharacteristicsandproductionoflights-process
elementsina25 M(cid:4) modelduringcoreheliumburning 1346
20.3 Coreandshellcarbon-burningphases 1359
20.4 Commentsonneon-,oxygen-,andsilicon-burningphases 1380
20.5 Moreontherelationshipbetweendirectandinversetranformations 1385
20.6 Concludingremarksonmassivestarevolution 1389
Bibliographyandreferences 1389
PartVI Terminalevolutionoflowandintermediatemassstars 1391
21 WindmasslossontheTPAGBandevolutionasaPNcentralstarandasawhitedwarf 1393
21.1 Introduction 1393
21.2 Superwindejectionoftheenvelopeandplanetarynebulaevolution 1395
21.3 Departureofa1 M(cid:4)modelfromtheTPAGB,evolutionasthecentral
starofaplanetarynebula,andthetransitionfromnuclear
togravothermalenergyastheprimarysourceofsurfaceluminosity 1397
21.4 Coulombforces,propertiesofmatterinthesolidphase,andacriterion
formelting 1410
21.4.1 TheWigner–Seitzsphere 1411
21.4.2 Debyetheoryandterrestialmetals 1412
21.4.3 Acharacteristicfrequencyofoscillationinthestellarcontext 1415
21.4.4 Oscillationamplitudeandthemeltingpoint 1418
21.4.5 ApplicationoftheThomas–Fermimodeloftheatom 1420
21.4.6 Thezero-pointenergyandtheHelmholtzfreeenergy 1426
21.5 Algorithmsforestimatingtheenergydensityandpressureofliquids
andsolidsinstars 1429
21.6 Whitedwarfevolution 1433
21.7 Diffusionandtheformationofapurehydrogensurfaceabundance 1456
21.8 Therelationshipbetweenthefinalwhitedwarfsurfaceabundanceand
whereinthethermalpulsecycletheprecursorfirstleavestheAGB 1460
21.9 Theoreticalandobservedwhitedwarfnumber–luminosity
distributionsandtheageofthegalacticdisk 1464
Bibliographyandreferences 1470
Index 1472