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

618 Pages·2013·9.55 MB·English
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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 Cambridge,NewYork,Melbourne,Madrid,CapeTown, Singapore,SãoPaulo,Delhi,MexicoCity CambridgeUniversityPress TheEdinburghBuilding,CambridgeCB28RU,UK PublishedintheUnitedStatesofAmericabyCambridgeUniversityPress,NewYork www.cambridge.org Informationonthistitle:www.cambridge.org/9781107016576 (cid:2)c I.Iben,Jr.2013 Thispublicationisincopyright.Subjecttostatutoryexception andtotheprovisionsofrelevantcollectivelicensingagreements, noreproductionofanypartmaytakeplacewithout thewrittenpermissionofCambridgeUniversityPress. Firstpublished2013 PrintedandboundintheUnitedKingdombytheMPGBooksGroup AcatalogrecordforthispublicationisavailablefromtheBritishLibrary LibraryofCongressCataloginginPublicationdata Iben,Icko,1931– 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 CambridgeUniversityPresshasnoresponsibilityforthepersistenceor accuracyofURLsforexternalorthird-partyinternetwebsitesreferredto inthispublication,anddoesnotguaranteethatanycontentonsuch websitesis,orwillremain,accurateorappropriate. 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

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This volume explains the microscopic physics operating in stars in advanced stages of their evolution and describes with many numerical examples and illustrations how they respond to this microphysics. Models of low and intermediate mass are evolved through the core helium-burning phase, the asympto
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