F o rm a ti o n o f s ta rs

(1)

4–1

4 . T h e m a in s e q u e n c e

4–2 Themainsequence1

F o rm a ti o n o f s ta rs

Collapseofaninterstellarcloud Considerthecollapseofaninterstellarcloud •gravitationalenergyisdissipatedintothermal energy •butthecloudisopticallythintothermalradia- tionintheearlyphaseofthecollapse •⇒temperatureandpressureincreasenotvery much⇒approximatelyfreefall •inlaterphasesthecentralregionbecomesop- ticallythick •⇒temperatureinthecentreincreasestovery highvalues

F o rm a ti o n o f s ta rs

•Eventually,thetemperatureinthe coreishighenoughtostarthydrogen- burning •thegravitationalcollapseisstopped •thestarsettlesonthemainsequence Nuclearfusionproducesenergy.Thusit increasesthetemperatureinthecentre ofthestar? 4–4 Themainsequence3

D e u te ri u m b u rn in g

•asmallfraction(3·10−5 )ofthestellar matterconsistsofdeuterium2D(ord) •Deuteriumnucleicanreactwithnor- malprotons

p

+

d

→3 He •thisreactionoperatesatlowertem- peraturesthannormalhydrogen burning.(

p

+

p

→

d

requireshigher energiesandthustemperatures) •thereisashortdeuterium-burning phaseduringpre-mainsequenceevo- lutionbeforetheregularhydrogen- burningstarts

(2)

D e u te ri u m b u rn in g

•fusion(inthiscasedeuteriumburn- ing)replenishestheenergylosses duetosurfaceradiation •delaysthefurthergravitationalcol- lapse •delaysfurtherheatingofthecore 4–6 Themainsequence5

C o m p u ta ti o n o f s te lla r m o d e ls F o u r e q u a ti o n s o f s te lla r s tr u c tu re

dm dr=4

π r

2

ρ

(

r

)(1)massconservation dP dr=−Gm(r)ρ(r) r2(2)hydrostaticequilibrium dL dr=4

π r

2

ǫ

(

r

)(3)energygeneration dT dr=−3 4acκ(r)ρ(r) T3(r)L(r) 4πr2(a)radiative (4)energytransport dT dr=γad−1 γadT PdP dr(b)convective Schwarzschildcriterionforconvectiveinstability: dT dr > γad−1 γad

T P

dP dr

C o m p u ta ti o n o f s te lla r m o d e ls

Numericalmodels Samplegridformainsequencemodel

•themodelstarisdividedintoanumber oflayers •constant

T ,ρ ,. .. .

,chemicalabun- dancesassumedineachlayer •thedifferentialequationsbecomedif- ferenceequations dT dR→∆T ∆R,etc. •Lagrangecoordinatesystem,i.e.the gridisdefinedinmasscoordinatesnot ingeometricalcoordinates Advantage1:noartificialmixingwhenlayersexpand/contract 50to100layerssufficientformainsequencemodels,1000andmorenecessary foradvancedstages 4–8 Themainsequence7

C o m p u ta ti o n o f s te lla r m o d e ls

Numericalmodels mainsequenceredgiant Advantage2:appropriatedistributionoflayers–manygridpoints“wherethe actionis”andnotuselessresolutioninuninterestingpartsofthestar

(3)

C o m p u ta ti o n o f s te lla r m o d e ls

(I)massconservation∂r ∂Mr=1 4πr2ρ (II)hydrostaticequation∂P ∂Mr=−GMr 4πr4−1 4πr2∂2r ∂t2 (III)energyconservation∂Lr ∂Mr=ǫ−ǫν−cP∂T ∂t+δ ρ∂P ∂t (IV)energytransport∂T ∂Mr=−GMrT 4πr4P∇ (V)chem.composition ∂Xi ∂t=mi ρ 

X jrji−

X krik

 i=1,...,I Systemof

I

+4Equationsfor

I

+4variables:

r, P ,T ,L

r

,X

1

,. .. ,X

I. 4–10 Themainsequence9

T h e z e ro -a g e m a in s e q u e n c e

•homogeneousstar(model)withabundanceofinterstellargas ≈solarforrecentlyformedstars •ZAMS:Zero-AgeMainSequence •compositionoftheSun(bymass):

X

H=0

.

685,

Y

=0

.

294,

Z

=0

.

021 •Vogt-Russelltheorem:Foragivenmassandchemicalcompositionexists onlyonesolutionofthestellarstructureequations –Relevance:Thestructureofamainsequencestardoesnotdependonthe initialconditionsofstarformation –provenforsimplifiedmodels –notproveninthestrictmathematicalsenseformoregeneralmodels

T h e z e ro -a g e m a in s e q u e n c e

mainsequencemodel

•startfromanextendedgascloudand followthecontraction(inacrudeway) untilH-burningignites,or •startwithasimple(e.g.polytropic model),relaxitinthecomputersimu- lationsuntilastaticmodelisreached, or •scalingofexistingmodeltonewstellar mass(homologyrelations) •moresophisticatedtreatmentofstar formationprocessesispossible(part4: pre-mainsequenceevolution) •however,theVogt-Russelltheoremtellsusthatthisisunnecessary •theformationhistoryisforgotten,whenthestarreachesthemainsequence 4–12 Themainsequence11

T h e z e ro -a g e m a in s e q u e n c e

ZeroAgeMainSequence Themainsequence(ZAMS)inthetheoretical Hertzsprung-Russelldiagram

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T h e H R d ia g ra m

ObservedHertzsprung-Russell diagramofthesolarneighbour- hood ResultsfromtheastrometricsatelliteHip- parcos 4–14 Themainsequence13

M a s s -r a d iu s re la ti o n

symbols:datafrombinaries

R

∼

M

a lowermainsequence

a

=0

.

8 uppermainsequence

a

=0

.

57 “break”causedbytransitionfromconvectivetoradiativeenvelopes

M a s s -l u m in o s it y re la ti o n L

∼

M

b lowermain

b

=3

.

2 sequence

M

=1

.. .

10:

b

=3

.

88 Changecausedbyswitch ofthedominantH-burning modefrompptoCNOpro- cess ⇒

R

∼

L

^a b

L

∼

R

2

T

4 eff∼

L

²

a b

T

4 eff⇒

L

1−2a b∼

T

4 eff⇒

L

∼

T

c eff with

c

=4 1−2a b 4–16 Themainsequence15

M a in S e q u e n c e L if e ti m e L

∼

M

3.2...3.88 .Howeverthe amountof“fuel”increases only∼

M

..⇒lifetimeof starsstronglydecreasingfor highermasses.

(5)

M a in S e q u e n c e L if e ti m e

Uppermainsequence:

T

MS=

M M

3.88=

M

−2.88 Lowermainsequence:

T

MS=

M M

3.2=

M

−2.2 4–18 Themainsequence17

In te rn a l s tr u c tu re o f th e s u n

In te ri o r s tr u c tu re o f m a in s e q u e n c e s ta rs M <

0

.

25

M

⊙:fully convective 0

.

25

M

⊙

< M <

1

.

2

M

⊙: envelopeconvective, coreradiative (Hionisationzone) 1

.

2

M

⊙

< M <

90

M

⊙: enveloperadiative, coreconvective (strong

T

depen- denceofCNOpro- cess) Energygenerationconcentratedinsidetheinnermost15%(bymass) 4–20 Themainsequence19

In te ri o r s tr u c tu re o f m a in s e q u e n c e s ta rs

Centraltemperatures anddensities(

ρ

c

,T

c)of mainsequencestars Uppermainsequence •lowcentraldensities •highcentraltemperatures •energygenerationbyCNOcycle •significantradiationpressure Lowermainsequence •highcentraldensities •“low”centraltemperatures •energygenerationbyppprocess •forlowestmassessignificant electrondegeneracy

(6)

M a in -s e q u e n c e e v o lu ti o n

He(the“ash”ofH-burning)accumulatesinthestellarcore⇒nolonger homogeneouschemicalstructure H-abundanceinthesolarinteriorasafunctionoftime 4–22 Themainsequence21

M a in -s e q u e n c e e v o lu ti o n

Evolutionofa7M⊙ star

A:ZAMS B:lowesttemperatureduringitsmainse- quenceevolution

X

≈0

.

05age:2

.

38· 107 years C:centralhydrogenexhausted,endofcentral hydrogenburning,endofmainsequence phase(TAMS:terminalagemainsequence) age:2

.

49·107 years The“hook”(B→C)isproducedduringtheevo- lutionofstarsoftheuppermainsequencewith aconvectivecore.

M a in -s e q u e n c e e v o lu ti o n

The“hook”isproducedduringtheevolutionofstarsoftheuppermainsequence withaconvectivecore. Uppermainsequence: (

M >

1

.

2

M

⊙)Convectivecore →HookattheendofMSlife- time Lowermainsequence: (

M <

1

.

2

M

⊙):Nocon- vectivecore→Nohook,more gradualevolution 4–24 Themainsequence23

O b s e rv e d H R d ia g ra m s o f o p e n c lu s te rs

Comparisonoftheobservedturn-offwiththeoreticalmainsequencelifetimes allowsdeterminationofclusterages

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4–25 TheSun1

T h e s u n

Basedonobservationsof •SolarMass:1

M

⊙=1

.

997×1030 kg=1

.

997×1033 g •SolarLuminosity:1

L

⊙=3

.

846×1026 W=3

.

846×1033 ergs−1 •age:

t

=4

.

5×109yrs •Solarchemicalcomposition(=elementalabundances)atthesurface:73.81% H,24.85%He,1.34%metals(bymass) itispossibletousetheequationsofstellarstructuretodetermineamodelforthe structureoftheSun,i.e.,Mr,Lr,ρ(r),T(r),abundances(r)startingwitha homogeneousmodelandallowfor4.5Gyrsofevolution. 4–26 TheSun2

T h e s u n

centralconditionsinthesun: •

T

c=1

.

57×107 K •

P

c=2

.

34×1016 Nm−2 •

ρ

c=1

.

53×105 kgm−3 •Hydrogenfraction:

X

=0

.

34(bymass) •Heliumfraction:

Y

=0

.

64(bymass)

Coreradiative zone 14 Mio Kcoronal loops energetic particles

Thermonucl. Reactions

photosphere, neutrinos prominence

1 Mio Kcoronal hole magnetic flux tubes

chromospheric flares bright spots and short lived magnetic regions

6000 K spot X−rays/gamma−rays

radio outbursts

radio emission

convective zone

turbulent convection

visible, UV, and IR outbursts (c) Scientific American 4–28 TheSun4

S ta n d a rd S o la r M o d e l

Standardsolarmodel: Temperature&pressureprofileDensity&interiormassprofile (Carroll&Ostlie)

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4–29 TheSun5

S ta n d a rd S o la r M o d e l

0.00.20.40.60.81.0 r/rO

0.0

0.2

0.4

0.6

0.8

1.0 Mass Fraction

H 4He StandardsolarmodelofBahcall&Serenelli(2005,ApJ626,530) 4–30 TheSun6

S ta n d a rd S o la r M o d e l

0.00.20.40.60.81.0 r/rO

10−5

10−4

10−3

10−2

10−1

100

Mass Fraction

H 4He 3He12C 14N

16O StandardsolarmodelofBahcall&Serenelli(2005,ApJ626,530)

4–31 TheSun7

S o la r E v o lu ti o n : L u m in o s it y

Bahcall,Pinsonneault&Basu(2001,ApJ555,990) 4–32 TheSun8

S o la r E v o lu ti o n : R a d iu s

Bahcall,Pinsonneault&Basu(2001,ApJ555,990)

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4–33 TheSun9

S o la r E v o lu ti o n : E n e rg y G e n e ra ti o n

Bahcall,Pinsonneault&Basu(2001,ApJ555,990) 4–34 TheSun10

S o la r E v o lu ti o n : C e n te r

Bahcall,Pinsonneault&Basu(2001,ApJ555,990;XcisthecentralHfraction)

4–35 TheSun11

S o la r N e u tr in o s

afterBahcall

Thesolarmodelpredicts asolarneutrinospectrum thatcanbecompared withEarthbased measurements.Thisis themostdirecttestof theoryofstellarstructure known. Problem:Neutrinosare difficulttodetectsincetheir interactioncrosssectionis verysmall =⇒largedetectorsare needed. 4–36 TheSun12

S o la r N e u tr in o s

Thefirstneutrinoexperimentinthe Homestakemine(J.Davisetal.,1968ff.). Basedonreaction

ν

e+37 Cl−→37 Ar+e− UseChlorineinlarge tetrachloroethylenetank(615T),detect Arwithradiochemicalmethods.37Ar decayswithahalflifeof37days. Sensitiveforelectronneutrinosat energiesabove814keV Expectedrate:8.5±1.9SNU Detectedrate:2.6±0.2SNU 1SNU:10−37capturestargetatom−1s−1. BrookhavenNationalLaboratory

(10)

4–37 TheSun13

S o la r N e u tr in o s

Clevelandetal.(1998,ApJ596,505; atotalof76637Aratomscreatedby solarneutrinosweredetected. Nobelprize2002toRaymondDavis SolarNeutrinoProblem:Solarneutrinofluxis∼1/3ofpredictedneutrinoflux. Caveat:Theexperimentdoesnotallowtomeasurep-pneutrions(cut-offat420keV,butonly neutrinosfromBeandBreactions. Ratesofthestandardsolarmodelmaybewrong? 4–38 TheSun14

S o la r N e u tr in o s

GALLEX(basedinGranSassoUndergroundLaboratory) uses30TofGallium(galliumtrichloride-hydrochloricacid) todetectneutrinosvia νe+71Ga−→71Ge+e− 71Gedecays(halflife:11.7days),radiochemicaldetection methods(conversionto71GeH4similartotheCldetector Thresholdenergy233keV→allowstodetectp-p neutrinos p-pNeutrinosdetectedforthefirsttime.

4–39 TheSun15

S o la r N e u tr in o s

GALLEXcountrateconsistentifallneutrinosarefromp-preaction,thusno neutrinosfromBeandB.ButChlorineexperimenthasseensome. Solarneutrinoproblempersists! 4–40 TheSun16

S o la r N e u tr in o s

(Super-)Kamiokandeexperiment:DetectionofneutrinosviaCherenkov radiationbyphotomultiplier Detector:LargetankofhighlypurifiedwaterinKamiokamine(Japan)

ν

interactswith

e

− →superluminalmotion. Thresholdenergy:≈5MeV→detectsonly8

B

neutrinos.

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4–41 TheSun17

S o la r N e u tr in o s

Wikipedia CherenkovradiationElectronmovesfasterthanthespeedoflightinwater.

n

is therefractionindexofwater,

c

isthevacuumspeedoflight. 4–42 TheSun18

S o la r N e u tr in o s

Superkomiokandecollaboration Detectionofasolarneutrino Arrivaltimeanddirectioncanbereconstructed!

4–43 TheSun19

S o la r N e u tr in o s

http://www-sk.icrr.u-tokyo.ac.jp/sk/lowe/soltimevar.html Neutrinoscomefromthesun 4–44 TheSun20

S o la r N e u tr in o s

http://www-sk.icrr.u-tokyo.ac.jp/sk/physics/image/image_solarnu/solpic_1500d_2_1.ps Thesunontheneutrinosky

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4–45 TheSun21

T h e s o la r n e u tr in o p ro b le m s (p re -2 0 0 1 )

•Deficitofneutrinosinallthreeex- periments •Super-KamiokandevsChlorine: –Super-Kamiokandemeasures 8

B

−

ν

–Chlorinemeasuresboth8

B

−

ν

&7

B e

−

ν

–But:Detectionrate:Super- Kamiokande>Chlorine 4–46 TheSun22

N e u tr in o o s c ill a ti o n s

Standardsolarmodel(SSM)vsstandardmodelofelementaryparticlephysics •changestoSSM:decreasecentraltemperature –lowmetallicityincentre:

Z

=1 10

Z

⊙ –fastrotationofthecore –verystrongmagneticfield(109 Gauss) –weaklyinteractingmassiceparticles(darkmatter) –... •Threeflavoursofneutrinos:

ν

e,

ν

µ,

ν

τ •beyondtheStandardmodelofelementaryparticlephysics: –Neutrinomassmaybenon-zero→neutrinooscillations:

ν

e⇋

ν

µ⇋

ν

τ –Mikheyev-Smirnov-Wolfenstein(MSW)-Effekt(1986):Oscillationsamplified whentravellingthroughmatter –oscillationlength?

4–47 TheSun23

S o la r N e u tr in o s

SudburyNeutrinoObservatory:uses1000Tofheavy water,i.e.,D2O,2000mbelowground. Possibleneutrinoreactions: chargedcurrent:νe+D→p+p+e−−1.442MeV neutralcurrent:ν+D→p+n+ν−2.224MeV elasticscattering:ν+e− →ν+e− −2.224MeV Theneutralcurrentreactionissensitivetoanyflavor ofneutrino. SNOdetects∼5000neutrinoeventsperyear. courtesySNO 4–48 TheSun24

S o la r N e u tr in o s

courtesySNO

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4–49 TheSun25

S o la r N e u tr in o s

Acrylicvesselsurroundedby photomultipliertubes. Viewthroughfisheyelens. courtesySNO 4–50 TheSun26

S o la r N e u tr in o s

Bahcall SNO(2001):Whentakingallneutrinoflavoursintoaccount,the measuredandpredictedneutrinofluxesagree=⇒Neutrinoschange theirflavor.

4–51 TheSun27

S o la r N e u tr in o s

)−1 s−2 cm6 10× (eφ00.511.522.533.5

) ₋₁ s ₋₂ ⁶ cm ₆ ⁵ 10 × ( ^{τ µ}⁴φ ³ ² ¹ ⁰

68% C.L.CCSNOφ 68% C.L.NCSNOφ 68% C.L.ESSNOφ 68% C.L.ESSKφ

68% C.L.SSMBS05φ 68%, 95%, 99% C.L.τµNCφ Aharminetal.,2005(dashedline:predictionofstandardsolarmodel) SNO(2001):2/3ofallνeproducedinSunchangeintoντorνµontheirwayfromSunto Earth:neutrinooscillations=⇒physicsbeyondthestandardmodelofparticlephysics!