stellar astrophysics

170 Pages·2017·8.44 MB·English

by  Edward Brown

E DWA R D B ROW N
S T E L L A R
A S T R O P H Y S I C S
OPEN ASTROPHYSICS BOOKSHELF
Aboutthecover: TheimageshowsthestarfieldinthedirectionofthesecondcloseststartoEarth,Proxima
Centauri.
Credit&Copyright: DavidMalin,UKSchmidtTelescope,DSS,AAO
©2015,2021EdwardBrown
gitversion6f0150ea...
cbna
Exceptwhereexplicitlynoted,thisworkislicensedundertheCreativeCommonsAttribution-NonCommercial-
ShareAlike4.0International(CCBY-NC-SA4.0)license.
iii
Preface
Thesenoteswerewrittenwhileteachingagraduate-levelastronomy
courseonstarsatMichiganStateUniversity. Theonlybackground
preparationforthiscourseisundergraduatephysicsandacourseon
radiativeprocesses,andsoportionsofthesenotescouldbeuseful
forupper-levelundergraduates. Thetextlayoutusesthetufte-book
(https://tufte-latex.github.io/tufte-latex/)LATEXclass: the
mainfeatureisalargerightmargininwhichthestudentscantake
notes;thismarginalsoholdssmallfiguresandsidenotes. Exercises
areembeddedthroughoutthetext. Theserangefrom“readingex-
ercises”tolonger,morechallengingproblems. Inaddition,thereare
severalnumericalexercisesthatusetheMESAstellarevolutioncode,
availablefromhttp://mesa.sourceforge.net/. Thesenumericalex-
ercisesareprefacedwiththelogo ,usedbykindpermission
oftheMESAcouncil. Becausetheexercisesarespreadthroughout
thetext,thereisa“ListofExercises”inthefrontmattertohelpwith
lookingforspecificproblems.
Thecoursenoteswereoriginallymeantasasupplementtothe
1
maintext,Hansenetal. ;insomeeditionsofthecourseIalsodrew 1CarlJ.Hansen,StevenD.Kawaler,
fromClayton2 andKippenhahnandWeigert3. Thesenotestherefore andVirginiaTrimble. StellarInteriors.
Springer-Verlag,2dedition,2004
tendtoexpandupontopicsnotalreadycoveredthere. Inthesec-
2DonaldD.Clayton. PrinciplesofStellar
ondhalfofthecourse,thestudentstypicallygavepresentationson EvolutionandNucleosynthesis. University
currenttopicsinstellarevolution,andIsupplementedthosewith ofChicagoPress,1983
4 3R.KippenhahnandA.Weigert. Stellar
readingsfromtheMESAinstrumentpapers . Asaresult,however,
StructureandEvolution. Springer-Verlag,
mynotesontopicsofstellarevolutionhavelaggedbehindtherestof 1994
thetextandarenotyetreadyforposting. 4BillPaxton,LarsBildsten,Aaron
Dotter,FalkHerwig,PierreLesaffre,
SomeofthematerialwasinspiredbythreecoursesatUC-Berkeley
andFrankTimmes. Modulesfor
inthemid-90’s: “StarswithLars”,taughtbyProfessorL.Bildsten; experimentsinstellarastrophysics
StatisticalPhysics,taughtbyProfessorE.Commins,andFluidMe- (MESA). ApJS,192:3,January2011;
andBillPaxton,MatteoCantiello,
chanics,taughtbyProfessorJ.Graham. Iamalsoindebtedtothe
PhilArras,LarsBildsten,EdwardF.
studentswhotooktheMSUstellarphysicscoursefortheirquestions, Brown,AaronDotter,Christopher
Mankovich,M.H.Montgomery,Dennis
feedback,andencouragement. AdditionalthanksgotoMSUgradu-
Stello,F.X.Timmes,andRichard
atestudentsDanaKoeppeandWeiJiaOngforreadinglatestagesof Townsend. Modulesforexperiments
thedraftsandtestingthenumericalexercises. instellarastrophysics(MESA):Planets,
oscillations,rotation,andmassivestars.
ApJS,208:4,2013
Please be advised that these notes are under active de-
velopment; torefertoaspecificversion,usetheeight-character
stamplabeled“gitversion”onthecopyrightpage.

Contents
1
1 The Sun on a Blackboard
19
2 Equations of Stellar Structure
29
3 Convection
41
4 Polytropes
49
5 Equation of State
65
6 Radiation Transport
79
7 Transport in a Plasma
85
8 Stellar Atmospheres
99
9 Contraction to the Main Sequence
103
10 Nuclear Physics
123
11 Main Sequence
vi
129
12 Low-Mass Post-Main Sequence
135
13 Stellar Pulsations
143
14 The Initial Mass Function
147
15 Binaries
153
A Technical Notes
159
Bibliography
Figures
1.1 GraphicaloutputfromaMESArunofa1M(cid:12) PMSstar. 11
3.1 Onsetofconvectioninatea-milkmixture. 29
3.2 Illustrationofcriteriaforconvectiveinstability. 30
3.3 AnEulerianperturbation: wecomparefluidquantitiesatcorrespond-
inglocations. 32
3.4 ALagrangianperturbation: wecomparefluidquantitiesforcorre-
spondingfluidelements. 32
3.5 Asimplemechanismforgeneratingturbulence. 36
3.6 Snapshotofconvectivevariablesthroughoutthestar. 39
4.1 SolutionsoftheLane-Emdenequationforselectedvaluesofthein-
dex n. 43
6.1 SchematicofapencilofradiationpropagatingintoanangledΩ. 66
7.1 Geometryforscatteringproblem. 80
7.2 Schematicofaparticleincidentonacylindercontaining n×(cid:96)×
A particles. 81
7.3 Anelementoffluidwithashear ∂v /∂z. 82
y
8.1 Spectraldistributionfromagreyatmosphere. 88
10.1 CompetitionbetweenBoltzmannfactorandpenetrationofCoulomb
barrierinsettingthethermally-averagedreactionrate. 110
13.1 AnEulerianperturbation: wecomparequantitiesatcorresponding
locations. 135
13.2 ALagrangianperturbation: wecomparequantitiesforcorrespond-
ingfluidelements. 135
15.1 SchematicofRochelobes 147
A.1 Adisturbancesteepeningasitpropagates. 156
A.2 Schematicofapistondrivingashock. 157

Tables
2.1 Selectedgram-molecularweights. 23
4.1 PropertiesoftheLane-Emdensolutions. 44
5.1 Selectedionizationpotentialsandhalf-ionizationtemperatures 56
8.1 Requirementforconvectioninthestellaratmosphere 89
8.2 Interactionsinstellaratmospheres 93
10.1 CoefficientsfortheWeizäckermassformula. 104
10.2 Parametersfornon-resonantreactions 111
10.3 Neutronorbitals 112
11.1 Characteristicsofmain-sequencestars 126