R e c o m m e n d e d te x tb o o k s

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P h y s ic s o f S ta rs

Prof.Dr.UlrichHeber,Prof.Dr.HorstDrechsel heber@sternwarte.uni-erlangen.de drechsel@sternwarte.uni-erlangen.de Wintersemester2013/14 1–1

1 . In tr o d u c ti o n

1–2 Introduction1

R e c o m m e n d e d te x tb o o k s

B.W.Carroll&D.A.Ostlie:“AnIntroductiontoModernAstrophysics” D.Prialnik:“AnIntroductiontotheTheoryofStellarStructureandEvolution” Hansen&Kawaler:”StellarInteriors” Ryan&Norton:”StellarEvolutionandNucleosynthesis” R.Kippenhahn&A.Weigert:“StellarStructureandEvolution” (comprehensivework,butaimingatresearchersinthisfield) Clayton:”PrinciplesofstellarEvolutionandNucleosythesis” (comprehensiveworkwithemphasisonnuclearphysics) JohnLattanzio’sstellarevolutiontutorial:

h t t p : / / w e b . m a t h s . m o n a s h . e d u . a u / ~ j o h n l / S t e l l a r E v o l n V 1 /

1–3 Introduction2

O u tl in e

•Fundamentalpropertiesofstars •Stellarstructureequations: –Continuityequation –conservationofmass,momentumandenergy –energytransport •Propertiesofstellarmaterial –Equationofstate –opacities –energygeneration •Computationofstellarmodels •Themainsequence •Thestructureofthesun,solarneutrinos

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1–4 Introduction3

O u tl in e

•postmain-sequenceevolution –low-massstars(initialmass≤8M⊙) –massivestars(initialmass

>

8M⊙) •Supernovae&γ-raybursts •Endstagesofstellarevolution •Evolutionofbinarystars •StellarPulsations •Variablestars 1–5 Introduction4

S te lla r p h y s ic s = a p p lie d p h y s ic s

Physicsneededtomodelthestructureandevolutionofstars,e.g.: •plasmaphysics •gas-radiationinteraction:atomicphysics •thermonuclearenergyproduction:nuclearphysics •neutrinoproduction:particlephysics •equationofstate:thermodynamics •convectiveenergytransport:hydrodynamics •radiativeenergytransport:physicsofradiation •...

1–6 Introduction5

F u n d a m e n ta l s te lla r p ro p e rt ie s

•distance •mass

M

•radius

R

•luminosity

L

=energyoutputpertime •(effective)temperature

T

eff •chemicalabundances 1–7 Introduction6

M a g n it u d e s

Hipparchus (??–∼127BC)

Firstclassificationofstars: •Starsof“magnitude1”:brightest(visible)stars •Starsof“magnitude6”:faintest(visible)stars http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Hipparchus.html

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1–8 Introduction7

M a g n it u d e s

Pogson(1865):Eyesensitivityislogarithmic,suchthat Abrightnessdifferenceof5magnitudescorrespondstoaratioof100in detectedflux So,ifmagnitudesoftwostarsare

m

1and

m

2,then f1 f2=100(m2−m1)/5 Thismeans:

lo g

10

( f

1

/f

2

) = m

2−

m

1 5

lo g

10100

=

2 5

( m

2−

m

1

)

or

m

2−

m

1

=

2

.

5

lo g

10

( f

1

/f

2

) =

−2

.

5

lo g

10

( f

2

/f

1

)

Note:LargerMagnitude=FAINTERStars 1–9 Introduction8

L u m in o s it y a n d d is ta n c e

Inversesquarelawlinksflux

f

atdistance

d

toflux

F

measuredatanother distance

D

:

F f = L /

4

π D

2

L /

4

π d

2

= d D

2 Convention:todescribeluminosityofastar,usetheabsolutemagnitude

M

, definedasmagnitudemeasuredatdistance

D =

10pc. Therefore,

m

−

M =

2

.

5

lo g( F /f ) =

2

.

5

lo g( d/

10pc

)

2

=

5

lo g d

−5

m

−

M

iscalledthedistancemodulus,

d

ismeasuredinpc.

1–10 Introduction9

D is ta n c e s

•Distancesofstarsarecrucialtoderiveab- solutevaluesofstellarparameterslikeab- solutemagnitude

M

V

= V

−5

lo g( d/

10

p c)

orluminosity

L

. •parallaxmeasurementistheonlydirect method •todaywecanreachanaccuracyof 1milliarcsec,i.e.distancesuptoafew hundredparseccanbemeasuredwithrea- sonableaccuracy(Hipparcosandground based) •Thisincludessomeimportantopenclusters likeHyadesandPleiades 1–11 Introduction10

D is ta n c e s

Bestparallaxmeasurementstodate:ESA’sHipparcossatellite •systematicerrorofposition:∼0.1mas •effectivedistancelimit:1kpc •standarderrorofpropermotion:∼1mas/yr •broadbandphotometry •colours:B−V,V−J •magnitudelimit:12mag •completeto7.3–9.0mag(seelater) Resultsavailableat

h t t p : / / a s t r o . e s t e c . e s a . n l / H i p p a r c o s /

: Hipparcoscatalogue:120000objectswithmilliarcsecondprecision. Tychocatalogue:106 starswith20–30masprecision,two-bandphotometry

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1–12 ThermalRadiation1

B la c k b o d y R a d ia ti o n B la c k b o d y ra d ia ti o n

Definition: •ablackbodyisinthermalequilibriumwithitssurroundings •itisaperfectabsorberandemitterofradiation •ablackbodyemitsacontinuousspectrumwhoseshape(asafunctionof wavelength)isdefinedbyitstemperaturealone Realisationinnature: •blackbodyverywellapproximatedifphotonsarefrequentlyabsorbedand re-emitted(shortfreepaths) •fulfilledinthestellarinterior •notfulfilledinstellaratmospheres •blackbodystillausefulfirstapproximation 1–13 ThermalRadiation2

B la c k b o d y R a d ia ti o n

describedbythePlanckfunction

B

λ

( T ) =

2

h c

2

λ

51

ex p

hc λkT −1 (powerperunitarea/wavelengthinterval/solid angle) Integrationoverallwavelengthsandsolidan- glesgivestheStefan-Boltzmannlaw

F = σ T

4 Surfacefluxperunitarea.

σ =

5

.

67×10−8W m−2K−4istheStefan-Boltzmann constant.

1–14 ThermalRadiation3

B la c k b o d y R a d ia ti o n

Totalpowerradiatedbya(stellar)surfaceisflux×surfacearea:

L =

4

π R

2

F

ForablackbodyradiatorwecanusetheStefan-Boltzmannlawtoderivea relationbetweenluminosity,radiusandsurfacetemperature

L =

4

π R

2

σ T

4 Definetheeffectivetemperature

T

effofastarasthetemperatureofa blackbodyradiatingthesameenergy/time.

L =

4

π R

2

σ T

4 eff 1–15 ThermalRadiation4

B la c k b o d y R a d ia ti o n

Thewavelengthatwhichtheenergyoutput fromablackbodypeaksisgivenbyWien’s law

λ

max×

T =

2

.

898×10−3

m K

objecttemperature

λ

maxband Sun5800K≈500nmvisible earthlings310K≈10,000nminfrared

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1–16 SpectralClassification1

S p e c tr a l C la s s ifi c a ti o n

He HD 13256SAO 81292HD 94082Yale 1755HD 260655HD 158659HD 12993 HD 30584 HD116608 HD 9547 HD 10032 BD 61 0367 HD 28099 HD 70178 HD 23524 SAO 76803

Fe TiOMgHTiO

NaHeHα TiO

Hβ AnnieCannon(around1890):Starshavedifferentspectra.NOAO 1–17 SpectralClassification2

S p e c tr a l C la s s ifi c a ti o n

Summaryspectralclassesasatemperaturesequence.

O - B - A - F - G - K - M 3 0 0 0 0 K 3 0 0 0 K “e a rl y ty p e ” “l a te ty p e ”

plussubtypes:B0...B9,A0...A9,etc. SunisG2.MKGFABO Spectral Class Rel. Strength of Lines

Ionised Helium Neutral HeliumHydrogenIonised MetalsNeutral Metals

Molecules

Note:“early”and“late”hasnothingtodowithage! Mnemonics: (http://lheawww.gsfc.nasa.gov/users/allen/obafgkmrns.html) OBeAFineGirlKissMe Mid-1995:Twonewspectralclassesadded:L&T

1–18 Hertzsprung-Russelldiagram1

H e rt z s p ru n g -R u s s e ll d ia g ra m

SeveraldifferentversionsofHR diagramsinuse: Original:absolutemagnitudes plottedversusspectral types Physical:luminosityversusef- fectivetemperature(note: increasingfromrighttoleft) Photometric:absolutemag- nitudeversusphotometric “colour”

L

,

R

and

T

effarelinkedtogethervia

L =

4

π R

2

σ T

4 eff.Everypointhasaunique valueforallthreeparameters. 1–19 Hertzsprung-Russelldiagram2

H R d ia g ra m – th e o re ti c a l

EvolutionarytrackfortheSuninHR diagram Thetrackshowstheevolutionfrom theprotostarphasedowntothemain sequence(A)andthelaterevolution toaredgiant(D–E)andbeyond.

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1–20 Hertzsprung-Russelldiagram3

C o lo u rs

BR

Colour←→temperature Fluxratiosindifferentwave- lengthbands(e.g.BandR) constructaquantitativecolour index(e.g.B−R)whichre- flectsthetemperature.

T =

7500K:highfluxinB,lowerfluxinR

F

B

/F

R

>

1

T =

4500K:lowfluxinB,higherfluxinR

F

B

/F

R

<

1 1–21 Fundamentalparametersorstars1

M a s s e s

Measurementoftheorbitalmotion ofvisualbinarysystems Orbitsoftenelliptical.Twopossible reasons: 1.eccentricorbit

e

6=0 2.inclinationoftheorbitalplane againstthelineofsight

i

6=0 However,thesecasescanbedis- tinguished: 1.

i =

0

; e

6=0:primaryinfocal pointofsecondaryorbit 2.

i

6=0

; e =

0:primaryincentre ofsecondarymotion

1–22 Fundamentalparametersorstars2

M a s s e s α

:measuredapparentmajoraxis (arcsec) Ifthedistance

d

isknown:

a = d si n α si n i

Kepler’sthirdlaw:

P

2

=

4π2a3 G(M1+M2)⇒

M

1

+ M

2 Iforbitsaremeasuredabsolutely(notonlyrelativetoeachother)wecanuse

M

1

/M

2

= a

2

/a

1todeterminevaluesfortheindividualmasses

M

1and

M

2.This hasbeendoneforatotalofaboutadozensystems. 1–23 Fundamentalparametersorstars3

S p e c tr o s c o p ic b in a ri e s

Spectroscopicbinaries:Thesesystemsarerelativelyclosetogetherandthe orbitalmotioncanbemeasuredviatheDopplershiftofspectrallines. Sometimesbothcomponentsarevisible(SB2),sometimesonlyone(SB1).In eclipsingSB2systemstheinclinationanglecanbedetermined(usuallycloseto

i =

90◦)andmassesforbothcomponentscalculated.

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S p e c tr o s c o p ic b in a ri e s

θ

θ 1

23 4 786

5 radial velocity

Earth

Timev r

vForspectroscopicbinaries:canonly measureradialvelocityalonglineofsight Forcircularorbit,angleθonorbit:

θ = ω t

where

ω =

2

π /P

. Observedradialvelocity:

v

r

= v co s( ω t )

Iforbithasinclination

i

,then

v

r

( t ) = v si n i co s( ω t )

Fromobservationof

v

r

( t ) =

⇒

v si n i

. (“velocityamplitude”) 1–25 Fundamentalparametersorstars5

S p e c tr o s c o p ic b in a ri e s

Double-linedspectra,caseSB2 Assumecircularorbit(e=0)

K

1

,K

2velocityhalfamplitudesofcomponents1&2

P

orbitalperiod 2

π a

1/2orbitalradiiofcomponents1&2

K

1/2

=

2

π a

1/2

P si n i =

⇒

a

1/2

si n i =

P 2π

K

1/2 again

si n i

remainsindetermined

S p e c tr o s c o p ic b in a ri e s

centreofmasslaw: M1 M2

=

a2 a1

=

K2 K1 Kepler’sthirdlaw:

M

1

+ M

2

=

4π2 GP2

a

3

, a = a

1

+ a

2

=

P 2π

( K

1

+

P 2π

K

2

) / si n i =

⇒

M

1

+ M

2

=

4π2 GP2P3 (2π)3(K1+K2)3 (sini)3

( ⋆ ) =

⇒

M

1

+ M

2

=

P 2πG(K1+K2)3 (sini)3

( M

1

+ M

2

)( si n i )

3

=

P 2πG

( K

1

+ K

2

)

3 =⇒twoequationsforthreeunknowns(

M

1

+ M

2

, si n i

),

si n i

canonlybedeterminedforeclipsingbinaries 1–27 Fundamentalparametersorstars7

S p e c tr o s c o p ic b in a ri e s

Single-linedspectra,caseSB1 (onlyonespectrumvisible):

K

2unknown:

K

2

= K

1M1 M2 Insertinequation(⋆):

( M

1

+ M

2

)( si n i )

3

= P

2

π G ( K

1

+ K

1

M

1

M

2

)

3

M

2

(

1

+

M1 M2

)( si n i )

3

(

1

+

M1 M2

)

3

= P K

3 1 2

π G

Massfunction

f ( M )

:

f ( M ) =

M2(sini)3 (1+M1 M2)2

=

PK3 1 2πG

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R a d ii

R a d ii E c li p s in g B in a ri e s

•diametersdAanddB:

d

A

+ d

B

= v ( t

5−

t

2

) d

A−

d

B

= v ( t

4−

t

3

) =

⇒

d

A

= v ( t

5−

t

2

+ t

4−

t

3

) /

2

d

B

= v ( t

5−

t

2−

t

4

+ t

3

) /

2 •requiresextremelyaccurate photometry independentofdistance

1–30 Starclusters1

S ta r c lu s te rs – te s tb e d s o f s te lla r e v o lu ti o n

Pleiades age:150Myr

NGC7789 age:1.5Gyr M67 age:5Gyr openclusters 1–31 Starclusters2

S te lla r c lu s te rs – te s tb e d s o f s te lla r e v o lu ti o n

globularclusters M13–age:12Gyrs

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S te lla r c lu s te rs – te s tb e d s o f s te lla r e v o lu ti o n

•Starsinastellarclusterwerebornduringonestarformationeventfromone interstellarcloud •theyallhavethesameageandinitialchemicalabundances (“metallicity”) •theyhavethesamedistance •distancescanbecalibratedwithwellunderstoodstars 1–33 Starclusters4

H R d ia g ra m o f th e g lo b u la r c lu s te r M 3

•Starsnotdistributeduniformlyin HRdiagram.Majorgroupings alongmainsequenceandredgi- antbranch •Majorgroupingsindicateslow evolutionaryphases,i.e.stable phasesofstellarevolution •Obviously,certainconfigurations ofstellarmaterialaremorestable thanothers

H R d ia g ra m o f th e g lo b u la r c lu s te r M 3

Majorevolutionaryphases MS:mainsequence,Hburningin core.StarsleavetheMSatthe turn-off(TO) RGB:redgiantbranch,Hburningin ashellaroundHecore HB:horizontalbranch(redclumpin youngerpopulations),Heburning incore AGB:asymptoticgiantbranch,Hand HeburningshellsaroundCandO core 1–35 Stellarstructureequations1

N e x t: S te lla r s tr u c tu re e q u a ti o n s

1.massconservation 2.hydrostaticequilibrium 3.energygeneration 4.energytransport