Download 1 - Stars: Introduction

1 - Stars: Introduction
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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.
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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.
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1.2 - Dark Matter
ArotaEoncurveisagraphofhowfast
somethingisrota)ngasafunc)onof
distancefromthecenter.
Hereistherota)oncurveofoursolar
system.ThefartherfromSun,theslower
planetsarerota)ng.
Arota)oncurveisusedtomeasurethe
massinside.
ButastronomershavebeenfoundmanygalaxieswithflatrotaEoncurves,
includingtheMilkyWay.
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Flat rotation curves
Therota)oncurvesshowthatmassina
galaxyisnotconcentratedinthecenter,
butisdistributedthroughoutthegalaxy
Butmostofthismasscannotbeseen;it
givesoffnolight.
Observa)onsshowthatupto90%ofthe
massoftheuniverseisdark(invisible)
maNer!
Thedarkmaaerisprobablydistributed
throughoutthegalaxyhalo.
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Gravitational Lensing
Lightpassingbyamassiveobjectwillbend,
asforexample,starlightneartheSun.
Theimageofalightsourceisdistortedinto
aringoranarc.Theamountofbendingis
propor)onaltothemassoftheobject.
Gravita)onallensingobserva)onsrevealthe
amountofmassinagalaxy.
Observa)onofexcep)onallylargegravita)onal
lensingisafurtherproofthatgalaxiescontaina
largeamountofdarkmaNer.
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Gravitational Lensing
Gravita)onallensinghasbeen
observedbytheHubbleSpace
Telescope,asseeninthispicture.
Lensingarcsareclearlyvisible.
Theyareindica)veofthepresence
ofdarkmaaer.
Thepictureisfromthegalaxy
clusterAbell2029,composedof
thousandsofgalaxiesenvelopedin
acloudofhotgas.
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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
(
) (
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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.
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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
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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.
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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.)
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Variable Stars
Starswithvariableluminosity
Cepheidvariablestars
Regularlypulsateinsizeandchangeinbrightness.Asthestarincreasesinsize,itsbrightness
decreases;then,thereverseoccurs.
PolarisandDeltaCepheiareCepheids.
Miravariablestars
Brightnessandsizecycleoveraverylong)meperiod,intheorderofmanymonths.Mirasare
pulsa)ngredgiants.
Yerkesspectralclassifica8on
TypicallightcurveforaCepheidvariablestar.
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TYPE
Ia Ib II III IV V VI VII Star
Veryluminoussupergiants
Lessluminoussupergiants
Luminousgiants
Giants
Subgiants
Mainsequencestars(dwarfstars)
Subdwarf
WhiteDwarf
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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
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(1.6)
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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
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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
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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
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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.
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Apparent magnitude m
(how bright stars appear)
Credit:ESA(EuropeanSpaceAgency)
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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.
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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
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(1.13)
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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.
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