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1 - Stars: Introduction introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 1 The Milky Way • Isaspiralgalaxy,about50kpcacrossandabout1kpcthick • 1parsecis3.1×1016m,or3.26lightyears(ly). • DistancebetweentheEarthandtheSuniscalledtheAstronomicalUnit,1AU= !&*78&"#( 1.5×1013cm. • Diskhasadiameterofabout50kpc, -.*)(/(011(2)( isabout300pcthick,mostlyfilled withinterstellardustandgas. 3%4( 5(62)( • IspartofLocalGroup,aclusterof some20galaxieswhichinclude theLargeMagellanicCloud,our nearestgalaxy,50kpcaway,away,and !"#$%"&'()"%*+,'*( theAndromedagalaxy,650kpcaway. • TheLocalGroupispartofthelargerVirgosupercluster. • ThevisibleUniversecontainssome1011galaxies. introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 2 The Milky Way • ThemassofourSunis1.99×1030kg=1solar mass,M¤ • ThemassoftheMilkyWayislargerthan2×1011 M¤ • 10%ofthemassisinterstellargas • 0.1%isdust(typicallypar)cleswithdiameter 0.01-0.1μm) TheLargeMagellanicCloud. • interstellargasdensityvariesfromabout109 (indarkclouds)to105atomsm-3(onthe average~1atomcm-3). • MainlyHandHe.Largeandrathercomplex moleculescontainingH,C(uptoC70 molecules),NandO(includingaminoacids) havealsobeendiscovered. DeepimageoftheVirgoCluster. introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 3 1.2 - Dark Matter ArotaEoncurveisagraphofhowfast somethingisrota)ngasafunc)onof distancefromthecenter. Hereistherota)oncurveofoursolar system.ThefartherfromSun,theslower planetsarerota)ng. Arota)oncurveisusedtomeasurethe massinside. ButastronomershavebeenfoundmanygalaxieswithflatrotaEoncurves, includingtheMilkyWay. introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 4 Flat rotation curves Therota)oncurvesshowthatmassina galaxyisnotconcentratedinthecenter, butisdistributedthroughoutthegalaxy Butmostofthismasscannotbeseen;it givesoffnolight. Observa)onsshowthatupto90%ofthe massoftheuniverseisdark(invisible) maNer! Thedarkmaaerisprobablydistributed throughoutthegalaxyhalo. introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 5 Gravitational Lensing Lightpassingbyamassiveobjectwillbend, asforexample,starlightneartheSun. Theimageofalightsourceisdistortedinto aringoranarc.Theamountofbendingis propor)onaltothemassoftheobject. Gravita)onallensingobserva)onsrevealthe amountofmassinagalaxy. Observa)onofexcep)onallylargegravita)onal lensingisafurtherproofthatgalaxiescontaina largeamountofdarkmaNer. introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 6 Gravitational Lensing Gravita)onallensinghasbeen observedbytheHubbleSpace Telescope,asseeninthispicture. Lensingarcsareclearlyvisible. Theyareindica)veofthepresence ofdarkmaaer. Thepictureisfromthegalaxy clusterAbell2029,composedof thousandsofgalaxiesenvelopedin acloudofhotgas. introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 7 1.3 - Black Holes Escapevelocity: ConsiderthekineEcenergyKandgravitaEonalpotenEalenergyUofabodyclosetoa starofmassM.Conserva)onofenergyimplies K +U i = K +U f (1.1) Thebodyescapesthegravita)onalpullofthestarifitcanreachinfinity(Uf=0).ThenKƒ= 0becausefinalvelocityiszeroandfromNewton’sgravita)onallaw 1 2 mM mve − G =0 (1.2) 2 R whereRistheini)aldistancebetweenmandM.Fromthiswegettheescapevelocity 2MG ve = (1.3) R Gistheuniversalgravita)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 ( ) ( introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce ) 8 1.4 - Typical Stars: Young stars Dwarfs Smallstars,<20M¤ andluminosityL<20,000L¤.Oursunisadwarfstar. Yellowdwarfs Small,mainsequencestars.TheSunisayellowdwarf. Reddwarf Small,cool,veryfaint,mainsequencestar.Surfacetemperature<4,000K.Reddwarfsare themostcommontypeofstar.ProximaCentauriisareddwarf. ProximaCentauri: ~4.24lyaway,intheconstella>onof Centaurus. introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 9 Old, Large Stars Redgiant Radiusabout100)mesbiggerthanitwasoriginally,andhadbecomecooler(surface temperature<6,500K).Theyarefrequentlyorangeincolor.Betelgeuseisaredgiant. Bluegiant Huge,veryhot,bluestar.Itisapost-mainsequencestarthatburnshelium. Supergiant Largestknowntypeofstar–canbeaslargeasouren)resolarsystem.Betelgeuseand Rigelaresupergiants.Rare.Supergiantsdieassupernovaandbecomeblackholes. Betelgeuse: 20M¤ 520lyaway 1Billionkmdiameter 7,500brighterthantheSun SurfaceTemperature:6000K introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 10 Faint Stars Whitedwarf Small,verydense,hot,mademostlyofcarbon.Remainsaperaredgiantstarlosesits outerlayers.Theirnuclearcoresaredepleted(i.e.,nomorenuclearreac)ons). RWD~REarthbutMDW>>MEarth Siriusisawhitedwarf. Typicalwhitedwarf Browndwarf Massistoosmall--nonuclearfusioninitscore--notveryluminous.Masssmallerthan~ 80MJ(MJ=Jupitermass). Neutronstar Verysmall,super-dense,composedmostlyof)ghtly-packedneutrons--hasathin atmosphereofhydrogen--radius~5-16km–density~1015gm/cm3. Pulsar Rapidlyspinningneutronstarthatemitsenergyinpulses. introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 11 Binary Stars Twostarsrota)ngaroundtheircenterofmass.Abouthalfofallstarsareinbinary systems. Polaris(thepolestaroftheNorthernHemisphereofEarth)ispartofabinarystarsystem. Eclipsingbinary Twoclosestarsappearingtobeasinglestarvaryinginbrightness.Thevaria)onin brightnessisduetothestarsperiodicallyobscuringorenhancingoneanother. X-raybinarystar Oneofthestarsisacollapsedobject suchasawhitedwarf,neutronstar,or blackhole.Maaerisstrippedfromthe normalstar,fallingintothecollapsed star,andproducingX-rays. Eclipsingbinarystarsystem.(Anima)oncredit: EuropeanSouthernObservatory.) introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 12 Variable Stars Starswithvariableluminosity Cepheidvariablestars Regularlypulsateinsizeandchangeinbrightness.Asthestarincreasesinsize,itsbrightness decreases;then,thereverseoccurs. PolarisandDeltaCepheiareCepheids. Miravariablestars Brightnessandsizecycleoveraverylong)meperiod,intheorderofmanymonths.Mirasare pulsa)ngredgiants. Yerkesspectralclassifica8on TypicallightcurveforaCepheidvariablestar. introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce TYPE Ia Ib II III IV V VI VII Star Veryluminoussupergiants Lessluminoussupergiants Luminousgiants Giants Subgiants Mainsequencestars(dwarfstars) Subdwarf WhiteDwarf 13 1.5 - Luminosity and brightness Flux:thetotallightenergyemiaedbyonesquare meterofanobjecteverysecond 1m F (J/m 2 /s = W/m 2 ) (1.4) 1m Luminosity:thetotallightenergyemiaedbythewhole surfaceareaofanobjecteverysecond L = ( Area × F ) (J/s) (1.5) e.g.100Wlightbulbhasasurfaceareaofabout0.01m2 Flux=Luminosity/Area=100/0.01=10,000W/m2 RadiaEon–allbodiesradiateEMwavesatallwavelengths withadistribu)onofenergyoverthewavelengthsthat dependsontemperatureT BlackbodyradiaEon:photonsareinequilibriumwiththe systemàStefan-Boltzmannlaw: F = σT introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 4 (1.6) 14 Temperature ∞ L = ∫ Lλ dλ Totalluminosity:integraloverallwavelengths 0 (1.7) EffecEvetemperature(Te): Thetemperatureofablackbodyofthesameradiusasthestarthatwouldradiatethe sameamountofenergy.Thus,fromStefan-Boltzmannlaw σ = (5.67× 10-8 W m-2 K-4) 2 4 e L = 4πR σT (1.8) Wien’slaw:wavelengthatwhichblackbodyradiatesmostofits energyisgivenbyλmax=3,000,000/Taslongλmaxismeasuredin nanometers(nm)(1nm=10-9m=0.000000001m) GivenλmaxwecancalculateTfromT=3,000,000/λmax e.g.λmax=1000nmgivesT=3,000,000/1000=3,000K introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 15 Brightness Inversesquarelaw: Increasethesizeofaspherefromradiusr Toradius2ràAreaincreasesfrom4πr2to 4π(2r)2=16πr2,i.e.,byafactorof22=4.Therefore flux(lightenergypersecondperunitarea)decreases byafactorof22=4. F Fobserver = 2 r (1.9) 10milliondollarsquesEon:Assumetwostars thatlooktohavesamebrightness. - Aretheyatthesamedistancefromour solarsystem? - Ordotheyhavedifferentbrightness,with themorebrightstarfartherfromoursolar systemthanthelessbrightstar? 1 AU = Astronomical Unit = distance Sun-Earth introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 16 Apparent magnitude mv (how bright stars appear) • OriginswithHipparchus(120BC)andPtolemy(150AD) Magnitudeisalogarithmicmeasureof luminositywiththebrightest starshavingthelowestmagnitude. Starsareclassifiedbygivinganumber1-6 • Brighteststarsareclass1 • Dimmeststarsvisibletonakedeyeareclass6 • Class1istwiceasbrightasclass2,class2istwiceasbrightasclass3,andsoon. • Therefore,class1is26=64)mesasbrightasclass6 Modifiedinthe19thCentury • Modernscaleisdefinedsothat6thmagnitudestarsareexactly100)mesbrighterthan1st magnitudestars • àstarsthatdifferinmagnitudeby1differbyafactorof2.512(e.g.a3rdmagnitudestar is2.512)mesbrighterthana2ndmagnitudestar):(2.512)5=100 introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 17 Modern definions: Apparent & absolute magnitudes Thehistoricalclassifica)onofstarsintobrightnessclassesiscalledvisual,orapparent magnitude,mv,orsimplym.Itreferstotheamountofradia)onwhichfallsonunitareaofa detectorontheEarth'ssurface. Theabsolutemagnitude,M,isameasureoftherealstar’sluminosity(orbrightness).Itisalso definedsothatadifferenceof5magnitudescorrespondstoafactorofexactly100)mesin intensity.Inthisscale,theSunhasM=+5. Theapparentmagnitudeisdefinedsothatifthestarisat10parsecs(or32.6ly)distance fromus,thenitsapparentmagnitudeisequaltoitsabsolutemagnitude.Themagnitudesm1 andm2fortwostarswithcorrespondingapparentluminosi)esF1andF2arerelatedby F1 m – m = 2.5 log 2 1 (1.10) F2 àreasonableagreementwiththehistoricales)matesbecausethehumaneyemostclosely respondstothelogarithmoftheluminositythantotheluminosityitself. Examples:(a)m=-1.5forSirius(brighteststar),(b)m=-26.8fortheSun,and(c)m=25for thefaintestobjectvisiblefromEarthtelescopes. introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 18 Apparent magnitude m (how bright stars appear) Credit:ESA(EuropeanSpaceAgency) introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 19 Absolute magnitude M (How bright stars would appear if they were all the same distance away) • 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. m – M = 5 log(d / 10) where d is in pc. (1.11) m–M 0 1 2 3 4 5 6 7 8 9 10 15 20 d(pc) 10 16 25 40 63 100 160 250 400 630 1000 10,000 100,000 m-Misknownasthedistancemodulusandcanbeusedtodeterminethedistancetoanobject. introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 20 1.5 - Distance to stars: Bolometric magnitude Mbol Magnitudesaremeasuredinsomewavelengthband.Tocomparewiththeoryitismore usefultodeterminebolometricmagnitude–definedasabsolutemagnitudethatwouldbe measuredbyabolometer*sensi)vetoallwavelengths.Thedifferenceinbolometric magnitudeisrelatedtotheluminosityra)oaccordingto: *Abolometermeasuresthepowerofincidentelectromagne)cradia)onviathehea)ngofa material. M star bol –M Sun bol L = −2.5 log LSun (1.12) Parallax Candeterminedistanceifwemeasureparallax-apparent stellarmo)ontoorbitofeartharoundSun. 1 au p Forsmallangles p=1au/d d=1/p(parsecs) Ifpismeasuredinarcsecs d introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce (1.13) 21 Limits of parallax method Measured energy flux depends on distance to star (inverse square law) Hence if d is known then L determined F = L / 4πd 2 (1.14) • 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~0.05arcsecàverydifficulttomeasureRofstars directly. introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 22