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1 - Stars: Introduction
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• Isaspiralgalaxy,about50kpcacrossandabout1kpcthick• 1parsecis3.1×1016m,or3.26lightyears(ly).• DistancebetweentheEarthandtheSuniscalledtheAstronomicalUnit,1AU=
1.5×1013cm.
• Diskhasadiameterofabout50kpc,isabout300pcthick,mostlyfilledwithinterstellardustandgas.• IspartofLocalGroup,aclusterofsome20galaxieswhichincludetheLargeMagellanicCloud,ournearestgalaxy,50kpcaway,away,andtheAndromedagalaxy,650kpcaway.• TheLocalGroupispartofthelargerVirgosupercluster.
• ThevisibleUniversecontainssome1011galaxies.
The Milky Way
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The Milky Way
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• ThemassofourSunis1.99×1030kg=1solarmass,M¤
• ThemassoftheMilkyWayislargerthan2×1011M¤
• 10%ofthemassisinterstellargas
• 0.1%isdust(typicallypar)cleswithdiameter0.01-0.1μm)
• interstellargasdensityvariesfromabout109(indarkclouds)to105atomsm-3(ontheaverage~1atomcm-3).
• MainlyHandHe.LargeandrathercomplexmoleculescontainingH,C(uptoC70molecules),NandO(includingaminoacids)havealsobeendiscovered.
DeepimageoftheVirgoCluster.
TheLargeMagellanicCloud.
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1.2 - Dark Matter
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ArotaEoncurveisagraphofhowfastsomethingisrota)ngasafunc)onofdistancefromthecenter.
Hereistherota)oncurveofoursolarsystem.ThefartherfromSun,theslowerplanetsarerota)ng.
Arota)oncurveisusedtomeasurethemassinside.
ButastronomershavebeenfoundmanygalaxieswithflatrotaEoncurves,includingtheMilkyWay.
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Therota)oncurvesshowthatmassinagalaxyisnotconcentratedinthecenter,butisdistributedthroughoutthegalaxyButmostofthismasscannotbeseen;itgivesoffnolight.
Observa)onsshowthatupto90%ofthemassoftheuniverseisdark(invisible)maNer!Thedarkmaaerisprobablydistributedthroughoutthegalaxyhalo.
Flat rotation curves
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Lightpassingbyamassiveobjectwillbend,asforexample,starlightneartheSun.
Theimageofalightsourceisdistortedintoaringoranarc.Theamountofbendingispropor)onaltothemassoftheobject.
Gravitational Lensing
Gravita)onallensingobserva)onsrevealtheamountofmassinagalaxy.Observa)onofexcep)onallylargegravita)onallensingisafurtherproofthatgalaxiescontainalargeamountofdarkmaNer.
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Gravita)onallensinghasbeenobservedbytheHubbleSpaceTelescope,asseeninthispicture.Lensingarcsareclearlyvisible.Theyareindica)veofthepresenceofdarkmaaer.ThepictureisfromthegalaxyclusterAbell2029,composedofthousandsofgalaxiesenvelopedinacloudofhotgas.
Gravitational Lensing
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1.3 - Black Holes
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Escapevelocity:ConsiderthekineEcenergyKandgravitaEonalpotenEalenergyUofabodyclosetoastarofmassM.Conserva)onofenergyimpliesThebodyescapesthegravita)onalpullofthestarifitcanreachinfinity(Uf=0).ThenKƒ=0becausefinalvelocityiszeroandfromNewton’sgravita)onallawwhereRistheini)aldistancebetweenmandM.FromthiswegettheescapevelocityGistheuniversalgravita)onalconstant(G=6.67×10−11m3kg−1s−2)Examples:(a)Earth’smass(5.94×1024kg),R=6,400kmàve=11km/s
(b)objectwithM¤andR=3kmàve>3×108km/s(largerthanspeed oflight)àblack-hole
K +U( )i = K +U( ) f
12mve
2 −G mMR
= 0
ve =2MGR
(1.1)
(1.2)
(1.3)
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DwarfsSmallstars,<20M¤ andluminosityL<20,000L¤.Oursunisadwarfstar.YellowdwarfsSmall,mainsequencestars.TheSunisayellowdwarf.ReddwarfSmall,cool,veryfaint,mainsequencestar.Surfacetemperature<4,000K.Reddwarfsarethemostcommontypeofstar.ProximaCentauriisareddwarf.
ProximaCentauri:~4.24lyaway,intheconstella>onofCentaurus.
1.4 - Typical Stars: Young stars
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Old, Large Stars
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RedgiantRadiusabout100)mesbiggerthanitwasoriginally,andhadbecomecooler(surfacetemperature<6,500K).Theyarefrequentlyorangeincolor.Betelgeuseisaredgiant.BluegiantHuge,veryhot,bluestar.Itisapost-mainsequencestarthatburnshelium.SupergiantLargestknowntypeofstar–canbeaslargeasouren)resolarsystem.BetelgeuseandRigelaresupergiants.Rare.Supergiantsdieassupernovaandbecomeblackholes.
Betelgeuse:20M¤520lyaway1Billionkmdiameter7,500brighterthantheSunSurfaceTemperature:6000K
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Faint Stars
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WhitedwarfSmall,verydense,hot,mademostlyofcarbon.Remainsaperaredgiantstarlosesitsouterlayers.Theirnuclearcoresaredepleted(i.e.,nomorenuclearreac)ons).RWD~REarthbutMDW>>MEarthSiriusisawhitedwarf.BrowndwarfMassistoosmall--nonuclearfusioninitscore--notveryluminous.Masssmallerthan~80MJ(MJ=Jupitermass).NeutronstarVerysmall,super-dense,composedmostlyof)ghtly-packedneutrons--hasathinatmosphereofhydrogen--radius~5-16km–density~1015gm/cm3.PulsarRapidlyspinningneutronstarthatemitsenergyinpulses.
Typicalwhitedwarf
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Binary Stars
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Twostarsrota)ngaroundtheircenterofmass.Abouthalfofallstarsareinbinarysystems.Polaris(thepolestaroftheNorthernHemisphereofEarth)ispartofabinarystarsystem.EclipsingbinaryTwoclosestarsappearingtobeasinglestarvaryinginbrightness.Thevaria)oninbrightnessisduetothestarsperiodicallyobscuringorenhancingoneanother.X-raybinarystarOneofthestarsisacollapsedobjectsuchasawhitedwarf,neutronstar,orblackhole.Maaerisstrippedfromthenormalstar,fallingintothecollapsedstar,andproducingX-rays.
Eclipsingbinarystarsystem.(Anima)oncredit:EuropeanSouthernObservatory.)
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Variable Stars
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StarswithvariableluminosityCepheidvariablestarsRegularlypulsateinsizeandchangeinbrightness.Asthestarincreasesinsize,itsbrightnessdecreases;then,thereverseoccurs.PolarisandDeltaCepheiareCepheids.MiravariablestarsBrightnessandsizecycleoveraverylong)meperiod,intheorderofmanymonths.Mirasarepulsa)ngredgiants.
TYPE StarIa VeryluminoussupergiantsIb LessluminoussupergiantsII LuminousgiantsIII GiantsIV SubgiantsV Mainsequencestars(dwarfstars)VI SubdwarfVII WhiteDwarf
Yerkesspectralclassifica8onTypicallightcurveforaCepheidvariablestar.
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e.g.100Wlightbulbhasasurfaceareaofabout0.01m2
Flux=Luminosity/Area=100/0.01=10,000W/m2
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Flux:thetotallightenergyemiaedbyonesquaremeterofanobjecteverysecond 1m
1mF (J/m2 /s = W/m2 )
Luminosity:thetotallightenergyemiaedbythewholesurfaceareaofanobjecteverysecond
L = Area × F( ) (J/s)
RadiaEon–allbodiesradiateEMwavesatallwavelengthswithadistribu)onofenergyoverthewavelengthsthatdependsontemperatureT
BlackbodyradiaEon:photonsareinequilibriumwiththesystemàStefan-Boltzmannlaw:
F = σT4
(1.4)
1.5 - Luminosity and brightness
(1.5)
(1.6)
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Temperature
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Totalluminosity:integraloverallwavelengths ∫∞
=0
λλdLLEffecEvetemperature(Te):Thetemperatureofablackbodyofthesameradiusasthestarthatwouldradiatethesameamountofenergy.Thus,fromStefan-Boltzmannlaw
σ = (5.67× 10-8 W m-2 K-4)
424 eσTπR L =Wien’slaw:wavelengthatwhichblackbodyradiatesmostofitsenergyisgivenbyλmax=3,000,000/Taslongλmaxismeasuredinnanometers(nm)(1nm=10-9m=0.000000001m)
e.g.λmax=1000nmgivesT=3,000,000/1000=3,000K
GivenλmaxwecancalculateTfromT=3,000,000/λmax
(1.7)
(1.8)
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Brightness
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Inversesquarelaw:
IncreasethesizeofaspherefromradiusrToradius2ràAreaincreasesfrom4πr2to4π(2r)2=16πr2,i.e.,byafactorof22=4.Thereforeflux(lightenergypersecondperunitarea)decreasesbyafactorof22=4.
Fobserver =Fr2
10milliondollarsquesEon:Assumetwostarsthatlooktohavesamebrightness.- Aretheyatthesamedistancefromour
solarsystem?- Ordotheyhavedifferentbrightness,with
themorebrightstarfartherfromoursolarsystemthanthelessbrightstar?
1AU =Astronomical Unit = distance Sun-Earth
(1.9)
• OriginswithHipparchus(120BC)andPtolemy(150AD)
Starsareclassifiedbygivinganumber1-6• Brighteststarsareclass1• Dimmeststarsvisibletonakedeyeareclass6• Class1istwiceasbrightasclass2,class2istwiceasbrightasclass3,andsoon.• Therefore,class1is26=64)mesasbrightasclass6Modifiedinthe19thCentury• Modernscaleisdefinedsothat6thmagnitudestarsareexactly100)mesbrighterthan1st
magnitudestars• àstarsthatdifferinmagnitudeby1differbyafactorof2.512(e.g.a3rdmagnitudestar
is2.512)mesbrighterthana2ndmagnitudestar):(2.512)5=100
Apparent magnitude mv (how bright stars appear)
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Magnitudeisalogarithmicmeasureofluminositywiththebrighteststarshavingthelowestmagnitude.
Modern definions: Apparent & absolute magnitudes
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Thehistoricalclassifica)onofstarsintobrightnessclassesiscalledvisual,orapparentmagnitude,mv,orsimplym.Itreferstotheamountofradia)onwhichfallsonunitareaofadetectorontheEarth'ssurface.Theabsolutemagnitude,M,isameasureoftherealstar’sluminosity(orbrightness).Itisalsodefinedsothatadifferenceof5magnitudescorrespondstoafactorofexactly100)mesinintensity.Inthisscale,theSunhasM=+5.Theapparentmagnitudeisdefinedsothatifthestarisat10parsecs(or32.6ly)distancefromus,thenitsapparentmagnitudeisequaltoitsabsolutemagnitude.Themagnitudesm1andm2fortwostarswithcorrespondingapparentluminosi)esF1andF2arerelatedbyàreasonableagreementwiththehistoricales)matesbecausethehumaneyemostcloselyrespondstothelogarithmoftheluminositythantotheluminosityitself.Examples:(a)m=-1.5forSirius(brighteststar),(b)m=-26.8fortheSun,and(c)m=25forthefaintestobjectvisiblefromEarthtelescopes.
m2 – m1 = 2.5 log F1F2 (1.10)
Apparent magnitude m (how bright stars appear)
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Credit:ESA(EuropeanSpaceAgency)
Absolute magnitude M (How bright stars would appear if they were all the same distance away)
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• Absolute Magnitude M defined as apparent magnitude of a star if it were placed at a distance of 10 pc (M is a theoretical quantity)
• Ranges from -8 for the most energetic star to 15 for less energetic.
where d is in pc.
m – M = 5 log(d /10) m–M
0123456789101520
d(pc)1016254063100160250400630100010,000100,000
m-Misknownasthedistancemodulusandcanbeusedtodeterminethedistancetoanobject.
(1.11)
1.5 - Distance to stars: Bolometric magnitude Mbol
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Magnitudesaremeasuredinsomewavelengthband.Tocomparewiththeoryitismoreusefultodeterminebolometricmagnitude–definedasabsolutemagnitudethatwouldbemeasuredbyabolometer*sensi)vetoallwavelengths.Thedifferenceinbolometricmagnitudeisrelatedtotheluminosityra)oaccordingto:
Mbolstar – Mbol
Sun = −2.5 log LLSun
*Abolometermeasuresthepowerofincidentelectromagne)cradia)onviathehea)ngofamaterial.
Candeterminedistanceifwemeasureparallax-apparentstellarmo)ontoorbitofeartharoundSun.
Parallax
1 au p
d
Forsmallanglesp=1au/dd=1/p(parsecs)Ifpismeasuredinarcsecs
(1.12)
(1.13)
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Limits of parallax method
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Measured energy flux depends on distance to star (inverse square law) Hence if d is known then L determined
24πd L /F =• Since nearest stars d > 1 pc à must measure p < 1 arcsec, e.g., at d = 100 pc,
p = 0.01 arcsec (notation: sec = ‘, arcsec = “)
• Telescopes on ground have resolution ~1” – Hubble telescope has resolution 0.05” à measure by parallax is difficult!
• Hipparcos satellite measured 105 bright stars with δp ~ 0.001" ⇒ confident distances for stars with d < 100 pc
• Hence ~ 100 stars with well measured parallax distances
Stellar radius: Angular diameter of Sun at distance of 10 pc: θ = 2R¤/10 pc = 5 × 10-9 radians = 10-3 arcsec
ComparewithHubbleresolu)onof~0.05arcsecàverydifficulttomeasureRofstarsdirectly.
(1.14)