“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)