1 - stars: introductionfaculty.tamuc.edu/cbertulani/ast/lectures/lec1.pdf · introduc)on to...

introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 1

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


The Milky Way


•  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.


1.2 - Dark Matter


ArotaEoncurveisagraphofhowfastsomethingisrota)ngasafunc)onofdistancefromthecenter.

Hereistherota)oncurveofoursolarsystem.ThefartherfromSun,theslowerplanetsarerota)ng.

Arota)oncurveisusedtomeasurethemassinside.

ButastronomershavebeenfoundmanygalaxieswithflatrotaEoncurves,includingtheMilkyWay.

introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 5introduc)ontoAstrophysics,C.Bertulani,TexasA&M-Commerce 5

Therota)oncurvesshowthatmassinagalaxyisnotconcentratedinthecenter,butisdistributedthroughoutthegalaxyButmostofthismasscannotbeseen;itgivesoffnolight.

Observa)onsshowthatupto90%ofthemassoftheuniverseisdark(invisible)maNer!Thedarkmaaerisprobablydistributedthroughoutthegalaxyhalo.

Flat rotation curves


Lightpassingbyamassiveobjectwillbend,asforexample,starlightneartheSun.

Theimageofalightsourceisdistortedintoaringoranarc.Theamountofbendingispropor)onaltothemassoftheobject.

Gravitational Lensing

Gravita)onallensingobserva)onsrevealtheamountofmassinagalaxy.Observa)onofexcep)onallylargegravita)onallensingisafurtherproofthatgalaxiescontainalargeamountofdarkmaNer.


Gravita)onallensinghasbeenobservedbytheHubbleSpaceTelescope,asseeninthispicture.Lensingarcsareclearlyvisible.Theyareindica)veofthepresenceofdarkmaaer.ThepictureisfromthegalaxyclusterAbell2029,composedofthousandsofgalaxiesenvelopedinacloudofhotgas.

Gravitational Lensing


1.3 - Black Holes


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)


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


Old, Large Stars


RedgiantRadiusabout100)mesbiggerthanitwasoriginally,andhadbecomecooler(surfacetemperature<6,500K).Theyarefrequentlyorangeincolor.Betelgeuseisaredgiant.BluegiantHuge,veryhot,bluestar.Itisapost-mainsequencestarthatburnshelium.SupergiantLargestknowntypeofstar–canbeaslargeasouren)resolarsystem.BetelgeuseandRigelaresupergiants.Rare.Supergiantsdieassupernovaandbecomeblackholes.

Betelgeuse:20M¤520lyaway1Billionkmdiameter7,500brighterthantheSunSurfaceTemperature:6000K


Faint Stars


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


Binary Stars


Twostarsrota)ngaroundtheircenterofmass.Abouthalfofallstarsareinbinarysystems.Polaris(thepolestaroftheNorthernHemisphereofEarth)ispartofabinarystarsystem.EclipsingbinaryTwoclosestarsappearingtobeasinglestarvaryinginbrightness.Thevaria)oninbrightnessisduetothestarsperiodicallyobscuringorenhancingoneanother.X-raybinarystarOneofthestarsisacollapsedobjectsuchasawhitedwarf,neutronstar,orblackhole.Maaerisstrippedfromthenormalstar,fallingintothecollapsedstar,andproducingX-rays.

Eclipsingbinarystarsystem.(Anima)oncredit:EuropeanSouthernObservatory.)


Variable Stars


StarswithvariableluminosityCepheidvariablestarsRegularlypulsateinsizeandchangeinbrightness.Asthestarincreasesinsize,itsbrightnessdecreases;then,thereverseoccurs.PolarisandDeltaCepheiareCepheids.MiravariablestarsBrightnessandsizecycleoveraverylong)meperiod,intheorderofmanymonths.Mirasarepulsa)ngredgiants.

TYPE StarIa VeryluminoussupergiantsIb LessluminoussupergiantsII LuminousgiantsIII GiantsIV SubgiantsV Mainsequencestars(dwarfstars)VI SubdwarfVII WhiteDwarf

Yerkesspectralclassifica8onTypicallightcurveforaCepheidvariablestar.


e.g.100Wlightbulbhasasurfaceareaofabout0.01m2

Flux=Luminosity/Area=100/0.01=10,000W/m2


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)


Temperature


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)


Brightness


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)


Magnitudeisalogarithmicmeasureofluminositywiththebrighteststarshavingthelowestmagnitude.

Modern definions: Apparent & absolute magnitudes


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)


Credit:ESA(EuropeanSpaceAgency)

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.

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


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)


Limits of parallax method


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)

1 - stars: introductionfaculty.tamuc.edu/cbertulani/ast/lectures/lec1.pdf · introduc)on to...

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