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Or Absolute Magnitude TheNatureofStars SurveyofAstronomyA110 TheNatureofStars SurveyofAstronomyA110 • TheNatureofStars • Star – Ballofgasheldtogetherbygravity. – Energygeneratedincentralregions. – Outerlayersemitenergytransportedtothemfrominner region. – Starsemitaspectrumsimilar tothatofblackbodies. • TypicalParameters – Masses:0.2to100SolarMasses – Luminosities:0.001to106 SolarLuminosities – Radii:0.01to1000SolarRadii – SurfaceTemperature:3000to100,000K TheNatureofStars SurveyofAstronomyA110 TheNatureofStars SurveyofAstronomyA110 TheNatureofStars SurveyofAstronomyA110 TheNatureofStars SurveyofAstronomyA110 • StellarDistances: • TrigonometricParallax • – Themostfundamentalmethod astronomersusetomeasurethedistancesofnearbystarsistrigonometric parallax. – Parallax--- theeffectthatnearbyobjectsappeartomovewithrespecttoverydistantobjectswhenviewed fromadifferentlocation. – Trigonometricparallaxreferstohalftheanglethroughwhichastarappearstobedisplaced(inrelationto extremelydistantstars)astheEarthmovesfromonesideoftheSuntotheother. • Thedistance(d)toastarinparsecsis: – d=1/(p /1”)pc • wheretheparallax(p)isinarcseconds. • Oneparsec=2x105 astronomicalunits • =9.5x1012 km – =3.26lightyears • TrigonometricParallaxcanonlybeusedtomeasuredistancesfor theneareststars. – Measureaccurateparallaxesforstarsoutto100parsecs(330lightyears) – Thisisonly1%ofthedistancetothecenterofthegalaxy. • Hipparcos:HighPrecisionParallaxcollectingSatellite TheNatureofStars SurveyofAstronomyA110 TheNatureofStars SurveyofAstronomyA110 TheNatureofStars SurveyofAstronomyA110 • StellarMotions • Stellarmotions[duetoe.g. – theorbitalmotionofonestararoundanother(i.e.binaries); – theorbitalmotionofthestarabouttheGalacticcenter] • canbeobservedintwoways: • 1.Stellarmotionstowardorawayfromusareradial(alongoursightline) motions --- causedby thestarsradialvelocity.RadialvelocitiescauseDopplerEffectsintheobservedspectraofstars. ∆λ / λ o =vr /c • 2.StellarMotionsperpendiculartoourlineofsightaretransversemotions --- causedbythestars transversevelocities.Transversevelocitiesaredeterminedfrom imagesorpicturesofstars. Whenpicturesofstarstakenoveralongperiodoftimeareexamined,thenearbystarsarefound tomove.Thisiscalledpropermotion(µ).Measuredinarcsecperyear. • Inordertocalculatethetransversevelocity(vt)ofastar,thestar'spropermotionanddistance mustbeknown. µ – vt =4.74( /1“/yr)(d/1pc)km/s • Theradialvelocityandtransversevelocityofastarcanbeusedtodetermineastar'sspace velocityororbitintheGalaxy. TheNatureofStars SurveyofAstronomyA110 • LuminosityandBrightness • Luminosity(L) – Measureofthetotal amountofenergyemittedbyastarpersecond. – Thisisthestar'sactualorintrinsicbrightness. – MeasuredinWatts. – Theluminosity(L)ofastardependsonitssurfacetemperature(T)and itsdiameter(D). – NB.TheluminosityofalightbulbisidenticaltoitsWattage. • ApparentBrightness – WhenwemeasuretheamountofenergyarrivingattheEarth(perunit time)wearemeasuringtheapparentbrightness oftheemittingsource. – Theapparentbrightnessisdistinctfromthestar’sluminosityorintrinsic brightnesssinceastarappearsfainteraswemoveitfartheraway. – Theapparentorperceivedbrightnessofastardependson: • (1)thestar'sactualorintrinsicbrightness(luminosity) • (2)thestar'sdistance. – IfweknowthedistancetothestaritsINTRINSICLUMINOSITY canbe calculatedfromitsapparentbrightnessusingtheinversesquarelaw. TheNatureofStars SurveyofAstronomyA110 • InverseSquareLaw • Theapparentbrightnessofastar(oranypointsourceofelectromagneticradiation)is proportionaltothestar’sintrinsicluminosity,andinverselyproportionaltothedistancetothe objectsquared. • Mathematically 2 • b=L/(4π d ) • whereb istheAPPARENTbrightness,andLtheINTRINSICluminosity.bhasunitsW/m2 or Joules/m2/s. • (Wegenerallydescribetheapparentbrightnessasanobservedenergyflux). • Examples – IfweweretwiceasfarfromtheSun,theSunwouldappear1/22 =1/4asbright. – Ifwewere10timesclosertotheSun,theSunwouldappear102=100timesbrighter. • MagnitudeSystem • Usedtomeasurebothastarsintrinsicandapparentbrightness. • Themagnitudescaleisnotlinear--- itislogarithmic. • Lowermagnitudesmeansbrighter! • Ifthemagnitudeofastardecreases by1unit,thatcorrespondstothestarbeingabout2.5times brighter. • Ifthemagnitudeofastar decreases by5units,thatcorrespondstothestarbeing100times brighter. TheNatureofStars SurveyofAstronomyA110 TheNatureofStars SurveyofAstronomyA110 • Apparentmagnitude(m) • Usedtospecifytheapparentorperceivedbrightnessofastar. Theapparent magnitudedependsbothonthestar'sintrinsicbrightness(absolutemagnitude)and thestar'sdistance. • Examples: α – Vega( Lyrae)hasmv =0 – Sun:mv =-26.8 – Moon:mv =-12.6 – Venusatmaximumbrightness:mv =-4.4 – Sirius(thebrighteststar):mv =-1.4 – Thefainteststarswecanseewiththeunaidedeye:mv =6. • Theapparentmagnitude(m)andbrightness(b)of2starsarerelatedbytheformula: – m2-m1=2.5log(b1/b2) • Photometry • Techniqueastronomersusetomeasuretheapparentbrightness(or apparent magnitude)ofanobject.Usuallydonewithafilterthatonlyallowslightfromavery specificbandofwavelengthstobemeasured.Bymakingseveralmeasurementsin differentcolorfiltersastar'scolorandhencetemperaturecan bemeasured. λ λ λ • MostcommonfiltersareU( c=3600),B( c=4300),andV( c=5500). • Byconventionan(average)A0starhasU=B=V=0 TheNatureofStars SurveyofAstronomyA110 TheNatureofStars SurveyofAstronomyA110 TheNatureofStars SurveyofAstronomyA110 • Absolutemagnitude(M) • Usedtospecifytheintrinsicbrightness(luminosity)ofastar. Theabsolutemagnitude ofastarisdefinedtobethesameastheapparentmagnitudeof thestarat10parsec. – Example: • Sun:4.8 • Sirius:1.4 • Theabsoluteandapparentmagnitudesarerelatedby • m- M=5log(d/10pc) • BolometricMagnitude(Mbol) – SpecialnamefortheAbsoluteMagnitudeasmeasuredoverallwavelengths.Itistotalenergy emittedatallwavelengths. • Mbol =4.72- 2.5log(L/Lsun) • AbsoluteVisualMagnitude(Mv ) – IntrinsicLuminositythroughtheVfilter.Theabsolutevisualmagnitudeandbolometric magnitudearerelatedby: – Mbol = Mv +BC • BCisthebolometriccorrection(typicallylessthanzero)andaccountsforthatfact thatstarsofdifferenttemperaturesemitdifferentamountsofenergyintheIRand UVrelativetothevisibleband.TheBCisafunctionofthestarstemperature. TheNatureofStars SurveyofAstronomyA110 TheNatureofStars SurveyofAstronomyA110 • StellarSpectra • AstarisnotaperfectBlackBodyhoweverastarscontinuousspectrumis generallyshapedlikethatemittedbyaBlackBody.Arealstellarspectrum containsabsorption(and/oremission)lines.Thesefeaturesallowusto deducethecompositionandpressureofthestarsatmosphere. • Spectraofdifferentstarsshowsdifferentabsorptionlines.Wecanclassify thestarsbylumpingthemintogroupssothatthestarsineachgroupshow thesameabsorptionlines. • Thestellarclassificationscheme,fromhottesttocoolest, isasfollows: – OBAFGKM. • Somepeoplememorizethisbysaying:`Oh,BeA • FineGirl/Guy,KissMe.' • Theclassificationisatemperatureclassificationbecausestars ofthesame surfacetemperatureshowapproximatelythesamesetofabsorptionlines. TheNatureofStars SurveyofAstronomyA110 TheNatureofStars SurveyofAstronomyA110 • Eachspectralclassisfurtherdividedinto10subclasses.eg. – B0(hottest),B1,B2,....B9(coolest) – A0followsB9 • Theshapesoftheabsorptionlinesareinfluencedbythesizeof thestar.Therefore starshavebeenfurtherclassifiedbasedontheirlineshape.Romansymbolsareused toindicatewhetherthestarisadwarf(V),giant(ΙΙΙ),orsupergiant (I) • Sun:G2Vstar(i.e.G2dwarf,T=5800K) • e.g. • Becauseasupergiant isbrighterthanadwarf(withthesametemperature)theI,III, andVareknownastheluminosityclass. • Thespectraofastarchangeswithtemperaturesincethepopulationoftheenergy levelschangewithtemperature.Asastarbecomeshotter,collisionscanexcitethe “lazy”electronsintohigherenergyorbits. – e.g.IntheSun,mostofthehydrogenisinthegroundstate.TheBalmer series(level2-n) appearonlyweaklyinabsorption,sincethereaveryfewatomswithelectronsinthen=2 orbit. – Ontheotherhand,hydrogencanbeseenstronglyinabsorptionintheatmospheresofA stars(10,000degreesKelvin). – MoleculescanbeseenintheatmospheresofMstars(3,500degreesKelvin). TheNatureofStars SurveyofAstronomyA110 TheNatureofStars SurveyofAstronomyA110 TheNatureofStars SurveyofAstronomyA110 • SummaryofFundamentalStellarProperties • Wehavediscussed3fundamentalstellarpropertieswhichcanbe determinedfromobservations: – 1.SpectralType. Thisisameasureofastar'ssurfacetemperature.Itcanbe determinedfromastar'scolorandspectrallines.Thespectrallinesalsoprovide someinformationonthesize/luminosityoftheemittingstars. – 2.Luminosity (orAbsoluteMagnitude).Thisisameasureofastar'sactualor intrinsicbrightness.Itcanbedeterminedfromastar'sapparentbrightness(or apparentmagnitude)anditsdistancefromtheEarthbyapplyingtheinverse squarelaw. – 3.StellarDiameter.Astar'sdiameter(D)cansometimesbeobservedoritcan bedeterminedonceastar'ssurfacetemperature(T)andluminosity(L)are known. • Recall: – TheStefan-Boltzmann Law(E=σT4)helpsuscalculatetheluminosityofastarof agivensurfacetemperatureandradius(L=E4πR2). – Henceifthesurfacetemperatureisknownfromspectralobservations,theradius ofastarcanbeinferredfromitsluminosity. TheNatureofStars SurveyofAstronomyA110 TheNatureofStars SurveyofAstronomyA110 TheNatureofStars SurveyofAstronomyA110 TheNatureofStars SurveyofAstronomyA110 TheNatureofStars SurveyofAstronomyA110 TheNatureofStars SurveyofAstronomyA110 • TheHertzsprung-RussellDiagram • TheHertzsprung-RussellDiagram(orHRdiagram)is formedbymakingaplotorgraphof: – 1.AbsoluteMagnitudevs.SpectralType,or – 2.AbsoluteMagnitudevs.coloror – 3.Luminosityvs.SurfaceTemperature • HRdiagramsarethemostfundamentaltoolthat astronomershaveforstudyingthepropertiesand evolutionofstars. • NotetheH-RdiagramisaLog-Logplot. TheNatureofStars SurveyofAstronomyA110 TheNatureofStars SurveyofAstronomyA110
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