“LocalUniverse”(within~20Mpc)DistanceIndicators
ifweknowtheabsolutemagnitudeofanobject(M)andcanmeasureitsapparentmagnitude(m),wecanderivethedistancefrom
(whererememberthedistancemustbeexpressedinparsecs!)
Propagationoferrorsshowhowtheuncertaintyindistancerelatestotheuncertaintyindistancemodulus:
LocalUniverseStandard(orStandardizable)Candles:
• PulsatingVariables:Cepheids orRRLyrae stars(alreadytalkedabout)• TipoftheRedGiantBranch(TRGB)• SurfaceBrightnessFluctuations(SBF)• PlanetaryNebulaeLuminosityFunction(PNLF)• GlobularClusterLuminosityFunction(GCLF)
m�M = 5 log d� 5
�d
d⇡ 0.5⇥ �(m�M)
TipoftheRedGiantBranch
ConsidertheevolutionofstarsliketheSun.
Aftertheyexhausthydrogeninthecore,theyevolveoffthemainsequence.
Theheliumcorecontractsandheatsup;hydrogenburninghappensinashellaroundthecoreatafuriouspace.Thestarbecomesluminousandswellsup,becomingaredgiant.
Whenthecorecontractsandheatsenoughtobeginfusingheliumintocarbonandoxygen,thatenergyreleaseexpandsthecore,reducingthenuclearreactionratesandcausingthestartoevolveofftheRGBandontothehorizontalbranch.
TheRGB“Tip”isthebrightestluminosityaRGBstarcanattaininitsevolution.Ifagalaxyiscloseenoughforustoseeindividualstars,wecanuseTRGBtogetadistance.
M15:Metalpoor
47Tuc:Metalrich
RedGiantBranchMetallicity Effects
fromMadore+18
>
fromBeaton+18
CalibratingtheTip
WeneedtoknowtheabsolutemagnitudeoftheTRGB.Butthisismetallicity-dependent:metal-richRGBstarsareredder,andsotheirfluxmovesintoredderfilters.
Asafunctionofmetallicity,theRGBtipbecomesfainterinopticalfilters,brighterininfraredfilters.
WecancalibratetheRGBtipusingstellarevolutionmodels.Worksbestforoldpopulations.
fromBeaton+18
MeasuringtheTipNGC185
MeasureRGBcolorandtipmagnitude• RGBcoloràMtip =−4.06± 0.12• mtip =20.43± 0.03
m−M=20.43−−4.06=24.49thencorrectfor0.28magofextinctiontoget:
m−M=24.21± 0.03(ran)± 0.12(sys)
ord=0.7± 0.08Mpc
Currentdistancelimit~Virgo(16.5Mpc)
SurfaceBrightnessFluctuations
Thinkofaglobularclusterversusanellipticalgalaxy.Whichlooks“grainier”?
SBFmethod
Thinkoftakinganimageoftwogalaxiesatdifferentdistances.
Numberofstarsperpixel:
Fluxfromtheindividualstars:
Sothesurfacebrightnessdoesn’tchange:
Butinagivenimage,therandomscatterinpixelintensitiesgoesas
Soconsiderthepixelvariancedividedbyaveragesurfacebrightness:
wheref* canberelatedto(butisnotthesameas!)theaveragefluxperstar.Expressedinmagnitudes,thisis referredtoasthefluctuationmagnitude.
N⇤pix
⇠ d2
f⇤ ⇠ d�2
SB ⇠ N⇤ ⇥ f⇤ = constant
�I ⇠p
N⇤ ⇥ f⇤ ⇠ d�1
NearbygalaxyDistantgalaxy
�2I
SB⇠ N⇤f2
⇤N⇤f⇤
⇠ f⇤
Jensen+03
Samemetallicity effectthatwesawusingTRGBstars.
Whatkindofgalaxywouldthisworkwellfor?Whatkindwouldn’titworkwellfor?
SBFdistanceapplication:thestructureoftheVirgoCluster
(mapcourtesySpengler+18)
Virgocluster“tomography”:
Virgoellipticalgalaxiesatdifferentdistances(Mei+07)
Virgovelocityfield:
distortionoftheHubbleFlow(Mei+07)
PlanetaryNebulaLuminosityFunction
Stellarevolutionrecap:
Attheendoftheirlives,aftertheyrunoutofHeintheircore,solartypestarsejectouterlayers.
ThehotC/Ocore(youngwhitedwarf)ionizestheseexpandingshells,causingthemtofluoresce.
Weseetheminopticalemissionlines(mostnotably[OIII]5007A).
Beautifulinourgalaxy,butsmall(parsecscale).Inothergalaxiestheyaresimplyunresolvedemissionlinesources.
Pne inM101(Feldmeier+09)
[OIII]:emissionline5300:continuum(regularstarlight)
PlanetaryNebulaLuminosityFunction
PNLF:NumberofPNe asafunctionofemissionlineluminosity.
ThePNLFshowsasharpcutoffatbrightmagnitudes,relatedtothemaximumsizeoftheionizingWD.
M*=−4.53± 0.06(Ciardullo+12)
N(m) ⇠ e0.307M (1� e3(M⇤�M))
GlobularClusterLuminosityFunction
GC(M80)intheMilkyWay
GCsintheVirgoCluster(littledots)
GlobularClusterLuminosityFunction
GCLFtypicallymodeledasaGaussian.Ifthemagnitudeofthepeak(note:notthesameasthepeakmagnitude!)isconstantacrossgalaxies,thiscanbeusedasadistanceindicator.
Woodley+10
WhileGCscanbebright,youneedtoseethefaintonestoestimatethepeak!
Observationalincompletenessatfaintmagnitudesisarealcomplication.
Comparisonoflocaldistanceindicators
M101,theSombreroGalaxy(McQuinn+16)
