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12.1Ellipticalgalaxies [slide 1] We now turn our attention to the other end of the Hubble sequence, the elliptical galaxies. [slide2]InHubble'sdefinition,ellipticalswereold,boringsystemscontainingjustoldstarswith no star formation. No dust. No gas. The first theories of their formation were that they form throughasinglemonolithiccollapseofgiantproto-galaxywhereallthestarsaremade.Turns out, all of these are incorrect. The modern view is that ellipticals are actually fairly complex systems.Theydocontainlotsofgas,exceptmostofitisX-raygas.Sometimestheyhavestar formation. Sometimes they have dust lines, and they probably form through hierarchical mergingofsmallerpieces,although,dissipativecollapsewasprobablyalsoinvolved. They're also not simple systems; they have subsystems, just like spiral galaxies do. Some ellipticalsseemtoshowweakdisks.Somehavespecialdecoupledcoresinthemiddle.Mostof them have super massive black holes in the centers. One important distinction between ellipticalsandspiralsisthat,whereasspiralshavecontainedmostoftheirkineticenergyinthe orderedrotationalmotion,intheellipticalgalaxiesmostofthekineticenergyisintheformof randommotions.Sowecallthempressure-supportedstars,movinglikemoleculesingas. [slide 3] And here is a blatant example of dust in elliptical galaxies. This is an elliptical galaxy NGC 1316, which is in the center of the nearby Fornax Cluster. The reason why it has all this dustisthatitgobbledupaspiralgalaxywhichhadplentyofdustinitsdisk,andsothat'sstill beingdigestedsomehow. [slide4]Wedoseethesignatureofmergersinellipticals,andaparticularlyinterestingoneis so-called shells. If you turn the contrast up in some of the elliptical galaxies, you'll see these shell-likestructuresoftheradii,andnowwethinkweknowwheretheycomefrom.Ifyouhave largelytwo-dimensionalstellarcomponents,suchasthisgalaxy,andthenyoumergeitintoan ellipticalgalaxy,thestarswillstillstayonsortoftwo-dimensionalsurfaceuntilsometimelater. And so, what we see are diluted, stretched, curved pieces of former galactic disks that have beennowwrappedaroundtheellipticalgalaxy,astheyarebeingmergedin.Thishasbeingseen innumericalsimulationsand,certainly,observations. [slide5]Thewaywequantifystructureofellipticalgalaxiesisthroughsurfacephotometry.We measurebrightnessasafunctionoftheradiusandtheazimuth.And,whilethisislight,wecan thentrytoconvertthatintomassthroughkinematicalmeasurements. Thewaywequantifystructureofellipticalgalaxiesisfirstbymeasuringtheirradialbrightness profiles,so-calledsurfacebrightnessprofiles.Andthereareanumberofformulaeproposedto account for the shape of these brightness profiles. The most popular of them is so-called de Vaucouleurs profile, it was invented by Gerard de Vaucouleurs, and it's a purely empirical formula. It says that the log of the surface brightness, which is luminosity per unit area, is proportionaltoradiustothe–1/4power,anditwassometimescalledr–1/4law. There is a parameter, because it's an exponential involved, and that is called the effective radius.Ifyoutweaktheconstantmultiplyingthatpower-law,thatradiuscanbemadesothatit containsexactlyonehalfofallprojectedlight.So,it'ssometimescalledaneffectiveradiusora half-lightradius.And,typically,forellipticalgalaxies,itsvalueistheorderoffewkiloparsecs,not toodifferentfrom,say,typicalscalinglengthsofspiralgalaxydisks. [slide6]So,herearesomeplotsofsurfacebrightnessforathousandellipticalgalaxies.What's showhereisalogarithmofthesurfacebrightnessonthey-axis,measuredinmagnitudesper squarearcsecond,versusradiustothe1/4power.And,thedeVaucouleursprofilelookslikea straightlineinthosecoordinates.Indeed,forsomegalaxiesitseemstofitremarkablywell,inat leastsomepartoftheradialrange.Butintheothersitdoesnot,andsothesedeviationsare alsoofsomeinterest. [slide7]Otherprofileshavebeensuggested.Theonethat'scurrentlymostpopularisso-called Sersic profile, which is a generalization of the de Vaucouleurs profile, that log of a surface brightness goes as the radius to the -1/n, where n is some number. And in case of the de Vaucouleursprofile,nisequalto4,soit'sproportionaltotheradiustothe-1/4.Incaseofadisk galaxy,nis1,sothenyouhavejusttraditionalolddecliningexponential.Thisformulaturnsout toactuallytoworkremarkablywellforellipticalgalaxies,aswellasdarkhalos,whichisavery interestingthing.Itsphysicaloriginisnotreallywellunderstood.Itisalsopurelyanempirical formula. Hubble himself proposed a different profile. This is essentially a power-law with surface brightnessgoingas1overtheradiussquared,exceptinthemiddlewhereit'ssoftened,sothere isaparametercalledcoreradius.Withinthatcoreradius,profileismoreorlessflat,andthenit turns around and goes into the power-law. Now, one problem with Hubble's profile, or as originallyenvisioned,isthatitdiverges.Ifyouintegratethesurfacebrightnessprofileinradius, you'll reach infinite total luminosity at infinite radius, and that clearly can't work. So, Hubble profilehastotruncateatsomepoint. [slide 8] So, it's actually quite remarkable that the ellipticals can be fit by the same family of profiles that have, say, just two parameters. In case of the de Vaucouleurs, it's the effective radiusthatscalestheradialcoordinateandeffectivesurfacebrightnessthatscalesthevertical coordinate. In case of Sersic profile, there is that shape parameter, little n, for which de Vaucouleursisfixed.And,ifitwerealwaysfixed,thenellipticalswouldbeahomologousfamily ofobjects–onecanbescaledintoanother.Turnsout,that'sprettyclose,butit'snotexactly true.And,thedeviationsfromthatareactuallyquiteimportant.Onedeviationthatwealready talkedaboutbeforeisthediffuseenvelopesofcDgalaxiesandclusters,butyoumayrecallthat thosearereallystarsthatbelongtotheclusteritself,justco-spatialwiththegalaxyitself. [slide 9] Nevertheless, if you obtain surface brightness profiles of many, many ellipticals, and thenifyoufitSersiclawtoallofthemandplotthevalueoftheSersicparameter–whichinthis plotontheleftisconfusinglylabeledasMbytheauthorsofthepaper–youfindoutthatthe shapeparameter,Sersicparameter,dependsonthesizeofthegalaxyandbythesametokenon the luminosity of the galaxy, and goes in the sense that galaxies with larger radii or larger luminosities have shallower profiles. A more direct way to see this is to simply bin together profiles of many ellipticals, average them up, and plot profile response to certain bin of luminosity.That'sshowninthelowerright,donebyJimSchombert.Andagain,youcanseethat themoreluminousellipticalsseemtohaveshallowerprofiles. [slide10]Ontheotherend,nearthecentersofgalaxies,thereareinterestingthingshappening. In Hubble's days, seeing an angular resolution simply was not good enough to actually tell what'shappeningintheinnerarcsecondorso.NowadayswithHubblespacetelescope,wecan probetheinnerportionsoftheellipticalgalaxies,andinterestingthingsarehappeningthere. Insomecases,therearecores,flatdensitydistributions,sortoflikeHubbleenvisioned.Inother cases,therearedensitycusps,densitygoesasapower-lawallthewayin,asfaraswecantell. Andthosemayberelatedtothepresenceofsupermassiveblackholes.And,carryingonwith whathappensatlargerradii,youseethatmoreluminousellipticalstendtobethosethathave flatcores,andsmallellipticalstendstobethosewithcusps. [slide11]So,hereisjustacollectionofsurfacebrightnessprofilesfromHubble,andtheyhave beendivided,empirically,intothosethatshowacore,whichareshownassolidlineshere,and those that look like power-law cusps - not pure power-laws, maybe slightly curved, but neverthelessthecusps–andthoseareshownasdashlines. [slide12]So,theshapeofthesurfacebrightnessprofilechangesatsmallerradii.Andso,people whostudythishavecomeupwithabrokenpower-law,orNukerprofile,thathasonepowerlawasymptoticallyatsmallerradiiandadifferentpower-lawasymptoticallyatlargeradii,and thereissometransitionradiusbetweenthemwhereonebendsintotheother. [slide 13] And here are the examples what those profiles look like. On the left, you see what happensaswechangetheinnerslope,whereas,theouteronesremainmoreorlessfixed.On theright,it'stheopposite-wekeeptheinnerslope,butchangetheouterslope.Galaxiesseem tofitalloverthisparticularfamilyofprofiles. [slide 14] So next, we will talk about two-dimensional and three-dimensional shapes of ellipticals. 12.2:EllipticalGalaxies:Shapes [slide1]Letusnowturntotheshapesofellipticalgalaxies.They'recalledellipticalsforareally goodreason. [slide2].Theirprojectedsurfacebrightnessprofileslookprettyclosetoellipses.And,hereare twointensitymaps,linesofequalsurfacebrightness.Intheimageontheleft,thelittleknots areactuallystarsintheforeground,becausetheirbrightnessgetsmeasuredtoo.And,youcan obviously see that elliptical galaxies really do look like ellipses, although, ellipticity may be changingasafunctionofradius.Generally,theytendtobealittlerounderinthemiddle. [slide3]Originally,peoplethoughtthatellipticityisduetorotationalflattening.Ellipticalgalaxy spins,centrifugalforcestretchesitintwodirections,orthogonaltothespinaxis,butthatturned outnottobethecase.And,moremodernstudiesindicatedthat,infact,ellipticals,firstofall, don'trotateverymuch.And,second,theirshapeisnotduetorotation,itisduetothevelocity anisotropy. As you would recall, the stars in elliptical galaxies move randomly, sort of like moleculesingas.That'swhytheycallthempressure-supported.But,it'spossibleinadynamical system like that, that velocity dispersion is different along x, y, and z-axis. A galaxy may be a littlehotterinoneaxisthantheother,andsothatmeansthestarswillgofurtheroutalongthat axis,soit'llbelonger. Andnow,wethinkthattheshapesofellipticalgalaxiesaredueentirelytothisanisotropy.Their temperature, if you will, is different in different directions. We can use statistics of observed shapestotrytodecompose,deprojectwhat'sgoingon.What'sshownhereinthehistogramis the distribution of through ellipticities, through dimensional ellipticities, if indeed ellipticals were simple flattened or elongated prolate ellipsoids. But in reality, they can have three axes and,therefore,twoaxisratios,andthatplaysalittlemorecomplicatedly. [side4]So,thesimplestcaseisifthey'rereallyspherical.Therearen'tmanygalaxieslikethat. Another possibility is that two axes are equal, and the third one is longer – it is a prolate ellipsoid, like the Amercan football. If the third axis is shorter than the other two, we have oblateellipsoid.Moregenerally,wehavethreeaxesofdifferentlengths,oratriaxialellipsoid. So,onaverage,theactualratiosareshownhere.Infact,ellipticalsarefairlyclosetobeoblate ellipsoids, flattened along one direction, but not perfectly so. In addition to the dynamical evidenceforanisotropicvelocities,whichI'llshowyouinthenextmodule,wecanactuallytell thisfrompicturesthemselves.And,thisislittletrickytoenvision,butitworkslikethis. [slide5]Ifyoulookatthesetofnestedtriaxialellipsoidsfromsomeobliqueangle,youwill,in fact,seethattheirapparentprojectedmajoraxisseemstomove,rotateonthesky.And,thatis calledtheisophotaltwists. [slide 6] You can again see here. You can look from same triaxial ellipsoid from different directions,andtheregionsofhigherdensitywillprojectincertainmajoraxisdirection.Atlower densities,youwillseeitfromslightlydifferentangle–anellipsewilllooklikeifit'sturning–and sothat'sexactlywhat'sobserved. [slide 7] Even in our immediate neighbor Andromeda Galaxy, Andromeda has two dwarf ellipticalcompanions,andifyoustretchthepictureathighcontrast,youcanseethatforoneof them, NGC 205, the outer isophotes are twisted and actually a little boxy, which is another interesting question. What's shown on the lower left is set of isophotes for some elliptical galaxy,andmajorandminoraxesaredrawn.Youcanseeasyougotoeverlargerradii,theaxes seemedtorotate. [slide8]So,thisisstillellipticalshapes.But,actually,ellipticalsarenotpurelyellipticalinshape. Prettyclose,butnotalwaysexactly.And,thefirstdeviationthatyoucanquantifyisifthereisan extra harmonic, if you will, around a given isophote. You can think of an elliptical galaxy isophote as, say, a single period wave as you go in the azimuth. But, suppose that there is a twiceashighfrequencycomponent,thenyouwillseetwowavesasyougoaround.And,there aretwopossibilitieshere.Oneisthattheycanbeco-alignedwithmajoraxisandminoraxis,in whichcasethey'rejustgoingtobumpouttheisophotesalongtheaxis,andthethingwouldlook likeit'sgotalittlelemon-likeshape.Thesearecalleddiskygalaxies,becausethat'sexactlywhat yougetifyouaretoprojecttogetheraverythindiskatopofanellipticalisophote. Theotherpossibilityisthatthey'reoutofphase.And,sothenyougetkindofbumpsbetween themajorandminoraxes.Thosearecalledboxyellipticals,andwebelievethattheirshapeis duemoretoanisotropyandlesstorotation.Ofcourse,disksarealwayssupportedbyrotation, evenifthelargerellipticalcomponentissupportedbyanisotropy. [slide9]Andso,hereareacoupleexamples.Oneofadiskyelliptical,andnowwethinkthat,in fact, most elliptical galaxies – those originally classified as elliptical – show these kind of isophotes,lemon-shaped.Actuallyyouhavedisks,andthey'remaybeclosertoaszeroesthan ellipticalsproper,butthereisacontinuumofproperties,therearenosharpdistinctions. Theotheroneshownisalsoaboxygalaxy.Somegalaxieshaveboth,atdifferentradii.Asyougo out in radius, what looks in inner part as a boxy elliptical, may start looking like a disky one, becausethereisadiskyouseeatlargeradius,ortheotherwayaround.And,sothisisnota fundamentaldistinctionlikepurespiralsversuspureellipticals,it'smoreinanatureofgradual changeofthemix. [slide10]Therearesometrendsthatsupportthatthereisphysicallymeaningfulthinggoingon, whichhastodowithvelocityanisotropy.Theboxygalaxiesaremoreanisotropic.Theyalsotend tobemoreluminousonesandalsohavehigherextraluminosities.Thosecanbeunderstoodin termsofmerging.Randommergingofpiecesintoanellipticalgalaxywillbothanisotropizeits velocitydispersion,anditwillcontributetothemass-makingthembigger–andcanalsoheat the gas. And so there is a trend – sometimes people overstate that – that boxy galaxies are productsofmergers,whereasthediskyonesarelargerproductsofdissipativecollapse.Neither isthecaseinreality.Thereisamixtureofthoseformingmechanisms,andit'sjustaquestionof thedegree. [slide11]Nexttimewe'lltalkaboutinternalkinematicsofellipticals. 12.3EllipticalGalaxies:Kinematics [slide1]Letusnowturntotheinternalmotionsinsideellipticalgalaxies.Thisturnsouttobe reallythekeytotheirnatureandunderstanding. [slide2]So,thestarsinellipticalgalaxieshavelargelyrandommotions.Andso,therefore,their kineticenergycanbecharacterizedbyavelocitydispersion.Youcanthinkofthedistributionas being pretty close to Gaussian. Because they're supported by random motions rather than rotation,they'recalledpressure-supportedsystems. The way we usually measure this is through Doppler broadening of their absorption lines. As, I'msureyouknow,spectraofgalaxies,composedofstars,havemanydifferentabsorptionlines due to different elements. And, each of these lines is pretty sharp when it originates, but becausetherearemany,manydifferentstarsmovingatrandomvelocities,thetotalobserved linewillbeaweightedsumofthose,anditsshapewillreflecttheoverallDopplerbroadeningby thevelocitydistribution.So,bydeconvolvinganunsmearedline,say,fromtemplates,spectral stars that are like those that make ellipticals, convolved with, say, Gaussian distribution of Doppler shifts, we can infer what is the underlying velocity dispersion of the elliptical galaxy. Notethatwhereaswemeasurerotationbyasimpleshiftofaline,theredorblue.Here,theline isnotshifted,it'sjustbroadened. [slide3]Andherearesomevelocityprofilesofellipticalgalaxies.Thevelocitydispersionontop, rotationalspeedonthebottom.Insomecases,thereisactuallyarotationalcomponent;those tendtobediskyellipticals.Inothercases,thereisnonetoverallrotation,butthereisalotof velocitydispersion.Generallyspeaking,velocitydispersionstendtobehighernearthecenterof the galaxy, but, by and large, they remain nearly flat by analogy with flat rotation curves of spiralgalaxies. [slide 4] A nice new way to measure this is so-called integral field spectroscopy. Here a spectrographiscomposedofmanydifferententranceapertures–usuallyit'sdonewithoptical fibers–andthenspectrumistakenofeachoneofthose.So,you'regettingaspectroscopically resolved picture of the sky. And from that, you can reconstruct what Doppler shifts and broadeningsareanywhereacrossthefaceofthegalaxy.Youcanalsoaddupallthelightand thenyouhavesurfacebrightnessdistribution. So,herearesomeexamplesfromaninstrumentcalledSauronofseveralellipticalgalaxies,as indicatedhere.Thetoprowshowstheirsurfacebrightnessdistribution,justaddingupthelight. Themiddlerowshowstherotationalvelocitycomponent,andit'scodedinintuitivefashion:red ones going away from us, blue ones approaching us. And, you can see that there is definitely some rotation present in some cases. Actually, in all cases in this particular set, which is not chosenrandomly.And,thebottomshowsthedistributionofvelocitydispersion.There,youcan seethereisgenerallyatendencytobealittlehigherinthemiddle,butotherwise,itdoesnot seemtohavemuchofashapedistribution. [slide 5] So, when velocity dispersions and rotational speeds were measured for ellipticals, to everybody'ssurprisebackthen,itwasfoundoutthatshapesarenotallduetotherotational velocity.And,youcancomputefromsimpledynamicalmodelsthatforagivenellipsoidthat's supported largely by rotation and has a commensurate amount of random motions, viewed from different angles, what should be the ratio between maximum rotational speed and velocity dispersion. And, you can divide the two. So for purely rotationally supported oblate ellipsoids,that'salineinthediagramthatshowstheratioofvelocity–therotationalspeedto velocitydispersion–asafunctionofellipticity.Asitturnsout,theellipticalsdogouptothat line,butmostofthemarebelow,meaningthattheyhavetoolittlerotationalspeedfortheir ellipticity and their radial velocity component. And so, that also means that they cannot be supported entirely by rotation. And so, a great majority of elliptical galaxies are supported by velocityanisotropy. [slide 6] And you can take that the ratio of maximum rotational speed to velocity dispersion, align for perfect oblate, rotationally supported ellipsoid, and normalize by that line, so that rotationallysupportedoblateellipsoidwillhavethenormalizedvalueofexactlyone.Lowerthan one means more anisotropy. So, now we can plot this normalized quantity, the relative importanceofvelocityanisotropy,asafunctionof,say,galaxyluminosity,anditwasfoundthat more luminous galaxies are more anisotropic. This can be understood as a consequence of randommerging.Youmayrememberthatdiskshavetoinvolvedissipativeformation.Youhave to dissipate energy, not the angular momentum, to get a disk, then make stars. Whereas, randommergingdoesnotpreserverotation–itscramblesupanyrotation–andjustcreatesa pressure-supportedsystem.Soifyou,indeed,youbuildupellipticalsthroughrandommerging, thenyouwouldexpectthemoreluminousonestobemoreanisotropic,andthat'sexactlywhat wesee. [slide7]Aswemeasurespectra,wecantellaboutchemicalcompositionofstars,notjusttheir velocities. And so, we can measure strengths of absorption lines of elements, such as iron or magnesium which are fairly common, and use that as an indicator of the chemical evolution historyofthegalaxy.So,itwasfoundthatellipticalgalaxiesaremoremetal-richnearthemiddle than on the outskirts. There was a more recycling of interstellar material through subsequent episodesofstarformationsinthecentralportions.Now,youcannotdothisthroughmerging.In fact, merging will scramble any such arrangement. So, there has to be a dissipative selfenrichment component to the formation of ellipticals that then reflects itself through this dependenceofstellarpopulationasthefunctionofredshift. [slide8]Now,spectraarehardtoobtainbecausetheyrequirelongobservationtimes.Amuch easier thing to measure are colors, which are ratios of fluxes in two different filters. Now, it turnsoutthatmoremetal-richstellarpopulationshavemoreabsorptionlinesinthebluepartof thespectrum,removingsomebluelight.So,themoremetal-richpopulationswillhavearedder color. And, you can measure colors fairly easily, use them as a proxy for the metallicity of galaxies.And,itturnsoutthatmoreluminousonesareredder;they'remoremetal-rich.And, you may recall that there's a picture whereby supernova ejecta, which is where metals come fromintothenewgenerationofstars,canescapefromlow-massgalaxies,butarestillboundto thehigher-masshostgalaxies,whereitcanberecycledintonewstars.So,itmakessensethat subsequent episodes of star formation in deeper potential wells – in more luminous, more massivegalaxies–wouldresult,afteralittlewhile,inamoremetal-richstellarpopulation.So, weseethatbothwithinindividualgalaxies,moremetal-richstuffnearthemiddle,andbetween differentgalaxies,themoreluminousormoremassiveonesretainmoreoftheirmetals. Likewise, you can use velocity dispersion instead of luminosity, and find out that those which have higher velocity dispersions – which are really kinetic energy per unit mass, therefore reflecting in a virial equilibrium the depth of a potential well – also have higher metallicities. Deeperpotentialwells,morerecyclingofthemetals. [slide9]Wealreadytalkedaboutgasinellipticalgalaxies.Whereasspiralgalaxieshaveplentyof interstellarmedium,coldones-hydrogenmostly,inellipticalgalaxiesthereishardlyanycold gas-onlyifit'sbeenrecentlyaccreted.But,thereisplentyofgasalltold,andthatgascomes largely as a product of stellar evolution, but some of it is accreted from the outside, and it's heated to millions of degrees, which is a virial equilibrium temperature for the corresponding potentialwellsinellipticalgalaxies. [slide10]Nowthatwecanmeasurekinematicsofellipticals,reflectingtheirpotentialwells,we can fit dynamical models, and find what their masses are. So, here is from a large survey of elliptical galaxies by a group called SPIDER: La Barbera, de Carvalho and collaborators. Plot of stellarmasses,directlyfromintegrationofvisiblelight,versusdynamicalmasses,whicharenow inferred from kinematics – velocities of stars reflecting total mass, not just the visible component. And they're proportional, right? But, there is a trend: the more massive galaxies tendtohavealargercomponentofdarkmatter,or,Ishouldsay,moremassesinformofthe darkcomponent. So,themostgalaxiesareinthisband,whereoneenvelopeisthatthereisnodarkmatter,there is just stars. The other envelope is that the dynamical mass is about 6 times the amount of visiblemassinstars.Interestinglyenough,thatcorrespondstotheratioofΩmattertotheΩbaryons inuniverseatlarge.Ifyoucanthinkofstellarmassesproxyforluminosity,thenthatmeansthat mass-to-lightratioswillbehigherforthemoremassivegalaxies.And,that'sindeedwhat'sseen throughanumberofotherpiecesofevidence. [slide11]So,fittingdynamicalmodelsindetailtogalaxies,wecanfigureoutexactlywhattheir masses are, and you can plot mass-to-light ratio versus luminosity, or versus mass, and here theyare.Themoremassiveormoreluminousgalaxieshavehighermass-to-lightratios,whicha priorineednotspecifytheamountofdarkmatter–itcouldbethereisinvisiblebaryons.But, therearegoodreasonstobelievethatinfactmostofthisisduetotherelativeabundanceor relativeamountsofdarkluminousmatterwithintheregionswherewemeasurethis. Now, notice that qualifier. Remember that we already talked about how in galaxies, baryonic componentismorecondensatethandarkmatter.Darkmatterhalosarefluffieranddominate more at large radii. This is certainly true in elliptical galaxies as well. So, if you're measuring velocity dispersions and what not in the luminous parts of the galaxies, you're liable to be findingmostlyluminousbaryonicmass.Iftheratioofdistributionofdarkandluminousmatter changes as a function of mass, so that halo distributions are more extended, but the light distributions tend to be more condensed for smaller galaxies, as is indeed the case – if you rememberhowsurfacebrightnessprofilesdependonluminosity–well,thenyouwouldexpect toseejustthis.Soit'snot100%clearatthispointhowmuchofthiseffectisduetoadifferent distributionofluminousanddarkmatterversusdifferentamountsofluminousanddarkmatter. It'sprobablyacombinationofboth. [slide 12] A gravitational lensing provides a completely different way of measuring masses, independentofalltheschematics.And,sothiswasdone,forasampleofgalaxies,usinggalaxies themselvesaslenses,and,what'splottedhere,confusinglyinthesamediagram,isthemass-tolight ratios for the total mass, that's sort of the tilted component, and for the luminous mass alone, which is a kind of flat component. And, we find out that for the luminous mass alone, mass-to-light ratio doesn't change as the function of mass. Meaning, ellipticals of all different masses have the same stellar populations and consistent with what we expect from stellar evolution laws. But, there is always more total mass, so higher total mass-to-light ratio, and moresoathighermassend,whichisexactlywhatyou'veseenfrompreviousdiagrams,butthis timemeasuredinacompletelydifferentwaythusgivingussomeconfidencethatthisis,infact, correct. [slide13]YetanotherindependentwayofassessingthisisthroughtheirX-rayprofiles,justlike we used X-ray measurements to constrain masses inside clusters of galaxies, you can do the same thing inside elliptical galaxies. And there again you find out, using X-ray gases dust particles, that the ratio of total, or non-luminous mass to the luminous ones, increases as a functionofradius. [slide 14] And next time we'll talk about supermassive black holes in galactic centers, and somethingthat'scompletelyunrelated–dwarfgalaxies. Module 12.4: Massive Black Holes in Galactic Nuclei and Dwarf Galaxies [slide1]Let'snowturntotwodifferentextremeendsofearlytypegalaxyproperties.Oneisthe supermassiveblackholesandtheirnuclei,andtheotheroneisthedwarffamilyofgalaxies. [slide 2] As it turns out, supermassive black holes, measured in millions and billions of solar massesorevenmore,areubiquitous.Theyarepresentinessentiallyeverygalaxyofsubstantial size near us. In most cases, they don't do very much. But, sometimes, they accrete material fromoutsideandthatcausesburstofgreatluminosityandactivity.Thosearetheactivegalactic nuclei,whichwewilldiscussinmoredetaillaterinclass. Thesupermassiveblackholeparadigmforactivegalacticnuclei,quasarsandsuch,isnowvery well-established. And, it's interesting to figure out where did those supermassive black holes comefrom.Ifthey'renotdoinganythingveryspecial,beingX-raysourcesorradioorsomething, onethingthatwecandoisprobetheirmassesusingstarsastestparticles.Wecandothisby measuringkinematicsofstarsintheverycentersofearly-typegalaxies.Whenthiswasdonefor theMilkyWay,wefoundoutthatthereisa3or4millionsolarmassblackholethere,whichis notveryactive–justsputtersoccasionally.But,itcouldhavebeenaluminousactivenucleusin thepast. And, as it turns out, masses of these large black holes in cores of ellipticals or, in fact, all galaxies, correlate remarkably well with a whole number of other properties of galaxies, and that is telling us something about formative and evolutionary mechanisms. We now, in fact, thinkaboutco-evolutionofgalaxiesandtheirsupermassiveblackholes. [slide3]So,hereisoneofthefirstcases,thesmall,ellipticalsatelliteofAndromedaM32,and what's'shownontherightisprofileofitsvelocitydispersion.Youcanseethereisasharpspike rightinthemiddle,whichiswhatyouwouldexpectifyouweretoembedalargepointmass, likeablackhole,inanotherwisenormalgalacticcore. [slide4]Thiswasmeasuredformany,manymoregalaxies,andseveralinterestingtrendswere found.Thefirstonewasthatthemassoftheblackholeisproportionaltothetotalstellarmass of the host galaxy, amounting to something like 0.1%. That alone suggests that there is some sortofcommonformativemechanism.Amoreinterestingcorrelationisbetweenmassofthe black hole and the velocity dispersion of its host galaxy measured at large radii, where the dynamicofinfluenceofblackholeiscompletelynegligible.So,somehowpropertiesofgalaxies onscalesofkiloparsecsarerelatedtotheblackholesintheircores,whichareofmicroparsecs. Thereissomethingthatcouplesthemthrough9ordersofmagnitudeinsize. [slide5]Anotherapproachtothisisbyconsideringallofthequasarlighteveremitted.Wehave nowareasonablygoodunderstandingoftheevolutionofactivegalaxypopulationasafunction oftime.And,wecanassumecertainefficiencyofaccretions,say,thatmaybe10%ofallmatter thatfallsintoblackholesisconvertedintoluminousoutput,wecandiscussthatlater,andthen simplyadduphowmuchmassshouldhavebeenaccumulatedthroughthehistoryofuniverse. And,ifwedothis,wefindoutthat,onaverage,youexpectthattypicalluminousgalaxytoday would have about 10 million solar mass black hole in its core. And, Milky Way has a 3 or 4 millionsolarmassone,soit'sperfectlysensible.Andromedaoneismaybealittlemoremassive. So, this can be compared directly to the measurements from kinematics in census of supermassive black holes in galaxies. And, we find out the two agree very well, and they correspond to the local average black hole density of about 500,000 solar masses per cubic megaparsec,whichisaboutthreeordersofmagnitudelessthanmassdensityofstars. [slide6]AnevenmoreinterestingrelationwasfoundbyLauraFerrareseandcollaborators.And she estimated masses of dark halos of galaxies from their kinematics. And, it turns out that thosearecorrelatedwithsupermassiveblackholesaswell.Superblywell.But,interestingly,ina non-linear fashion, whereas the masses of black holes were proportional directly to the luminous stellar mass, or at least for the bulge component, here we find out that they're proportionaltoasteeperpowerofhalomass.Meaning,thatmoremassivehalos,moremassive galaxiestherefore,aremoreefficientinmakingblackholes.Youcouldunderstandthatbythe moremassiveonesbeingmoreefficientinobstructingmergingfuel.And,maybethat'swhat's going on. But, what's remarkable abouttheserelationsisthattheyhavesucha smallscatter. We think that merging is a fairly random stochastic process, efficiency will vary, and yet somehow, after Hubble time or so, there is remarkably sharp correlations. So, we can qualitatively understand where they come from, but the quantitative understanding, why they'resosharp,isstillamystery. [slide7]Andheretheyare,allonsameplot.Topleftisproportionbetweenblackholemass andtheluminousstellarmass.Thenthereisproportionbetweenblackholemassandvelocity dispersion, which looks a little bit like Tally-Fisher or Faber-Jackson relation. Again, circular velocity,andagainstthehalomass,proportionaltothehalomasstoroughly1.6power. [slide 8] And now for something entirely different – dwarf galaxies. In Hubble's days, and for sometimeafter,peoplethoughtthereisonekindofthingcalleddwarfellipticals,andthey're justsmallellipticals.Nowweknowthisisnotthecase.They'reaverydifferentfamilyofobjects, and,infact,theymaybetwodifferentfamiliesofobjects,inadditiontosimpledivisionofbeing gas-poororgas-richinmakingstars.Thereasonwhywethinkthey'reverydifferentisthatthey followverydifferentcorrelationsbetweentheirfundamentalproperties,whichI'llshowyouina moment. And, if those correlations are a product of formative evolutionary processes for galaxies, then that suggests that they're two different paths and, therefore, two different families. As it turns out, dwarf galaxies, dwarf spheroidals in particular, are totally dark matter dominated. They have higher mass-to-light ratios than any other galaxies, and we think we understand why this is. Again, remembering the scenario where supernova explosions can expellgasfromgalaxies,theycandosoinshallowpotentialwellsthusremovingbaryons.But, supernovashockswouldnoteffectdarkmatteratall.Andso,darkmatterwillstay.So,lowerluminositygalaxieswillbemoreefficientinlosingtheirluminousmasswhileretainingthedark matter, and, therefore you expect them to be more dark matter dominated, which is exactly what'sobserved. [slide 9] So, here is a set of correlations. produced by John Kormendy, that shows some properties of elliptical galaxies, dwarf spheroidals, and globular clusters, which really don't belong in this diagram at all, but they're there just for symmetry's sake as all stellar systems. And, they show central surface brightness versus radius in the top left. The central surface brightness versus luminosity top right. The velocity dispersion versus radius in the lower left. And velocity dispersion versus luminosity on the lower right. The two families with thicker symbols are elliptical galaxies, and dwarf ellipticals and dwarf spheroidals. The little dots are globularclusters.And,youcanseethatobviouslytheyseparateverycleanlyinthisparameter space. [slide10]So,let'slookatthisinlittlemoredetail.Thisisjustplotofmeansurfacebrightness, with an effective radius, versus luminosity. And, whereas for normal ellipticals, which is the upperrightsetwiththeredlinegoingthroughthem,thereisatrendthatthemoreluminous oneshavelowersurfacebrightness,becausetheyhavemorediffusesurfacebrightnessprofiles. Theexactoppositetrendhappensforthedwarfgalaxies.Notonlyisthetrendopposite,butthe interceptisdifferentaswell.So,intheregionwheretheyoverlap,thedifferenceorratherthe ratiobetweensurfacebrightnessatthegivenluminosityimpliestheratioofthree-dimensional luminositydensitiesbyaboutthefactorof1,000ormore,whichislikebetweenuraniumand air. [slide11]So,thesearenotdwarfellipticals,they'readifferentkindofthing.It'sjustlikecalling cotton puffs dwarf cannon balls. And, here is a really telling diagram of mass-to-light ratio versus luminosity. I did not plot globular clusters and ellipticals, non-ellipticals as individual points,justindicatedwherearetheyinthisdiagram.And,Iplotteddwarfspheroidalsassolid dots,anddwarfellipticals,likethosearoundAndromeda,astheopensymbols.And,youcansee thatthereisthisbranchofdwarfspheroidalsthatjustshootsup,reachingmass-to-lightratios oftheorderof100atverylowmassend.Thishasbeenconfirmedbymany,manysubsequent observations,nowweknowmoreofthesegalaxies. [slide 12] This will lead into the next discussion, about how we can use scaling relations in correlationsforgalaxyfamiliestolearnsomethingabouttheirinternalphysicsinformation. Module12.5:GalaxyScalingRelations–PartI [slide2]Finally,letusturntotheexaminationofcorrelationsbetweengalaxianpropertiesor scalingrelations,which,inmyopinion,isprobablythemostimportantandmostinterestingpart ofthiswholething.Thisiswhatisreallytellingusofsomethingaboutformationofgalaxies,and whytheyarethewaytheyare. [slide2]Wecallthemscalinglaws,becausethey'repower-lawsthatgalaxiescanbescaledas thepowerofsomething,likeluminosity'sproportionaltosomepowerofvelocitydispersion,for example.And,theimportanceofthesecorrelationsisthattheyaretellingussomethingabout how galaxies form, what is the physics behind it. In some cases, either correlations between distance-dependent and distance-independent quantities, they are used as distance indicator relations,likeTully-Fisherorfundamentalplane.And,thisisaquantitativewayofdistinguishing physicallydistinctfamiliesofgalaxies,asopposedtosomethinglikethesuperficialappearance andimagestakenofaparticularwavelength.Thesearephysicalpropertiesandtheydiffer,you sawthisinthelastmodule,likefordwarfellipticals,whicharenotellipticals,andrealellipticals. [slide 3] So, a classic example of this type of relation is the Tully-Fisher relation between the circular speed of galactic disks and the total luminosity of a galaxy. And, it goes roughly as luminositygoesasthe1/4powerofthecircularspeed–powerdiffersalittlebit,anddepending on the wavelength, and so on – but that's roughly what it is. And, we can measure circular speed either optically through, say, spectra along the major axis of the galaxy, or through neutralhydrogen.Or,evenifyoujusttakethewholegalaxyintoonespectrum,thebroadening ofHI21-cmlinetellsyouwhatistheamplitudeofthecircularspeed.Notethatinordertoget the intercept of this relation correct, you have to know the distances. But, to get slope, you don'tneedtodothis;youneedtojustknowtherelativedistances.And,interestingthingabout Tully-Fisherrelationisthatit'saverygoodone.Itsintrinsicscatterismaybe10%,maybeeven lessinsomecases. [slide4]Thisiswhatitlookslikeinfivedifferentfilters:blue,visualred,andverynearinfrared, andnearinfrared.And,youcannoticeaninterestingtrend:thefurtherredyougo,thebetter correlation you see – the scatter is smaller. We can understand this because blue light is susceptiblebothtoextrasfromregionsofyoungstarformation,whichareunusuallybright,and decreasesduetothegalacticextension.Bluelightismoresensitivetothegalacticdust,whereas in infrared, you bypass much of these two problems. So, you can think of the infrared TullyFisherrelationasbeingthemoreindicativeofintrinsicone.Theslopealsochanges,andthat'sa slightlydifferentstory. [slide5]Andthereasonwhythisissointerestingisthatcircularspeedisabasicallyaproperty ofthedarkhalo.And,luminosityisaproductoftheintegratedstellarevolutioninthegalaxyor Hubbletime.So,somehow,darkhalomassseemstoregulatestarformationhistoryofagalaxy. Thatinitselfisinteresting,butevenmoreinterestingisthesmallscatter,becausewecanthink ofanynumberofreasonswhythescattercanincrease–bychangingratiosofdarkmatterto luminousone,bytweakingupstarformationdifferentlyindifferentenvironments,bydifferent kindsofmerging,andsoon.Yetsomehow,intheend,weendupwithwhat'salmostaperfect correlation. [slide6]Thishasbeenprobedinmanydifferentways.Youmayrecallthatthereisthiswhole familyoflowsurfacebrightnessdisks,whichdohavenormalamountsofdarkmatter,andgas, butjustnotverymanystars.And,so,eventheyfollowTully-Fisherrelation,whichissaying,this isnotsomuchrelationbetweenstarlightandpropertyofdarkhalo,butbetweentotalbaryonic massandthedarkhalo.Now,thatbeginstomakealittlemoresense. [slide 7] An equivalent relation for elliptical galaxies is called Faber-Jackson relation. Because, therotationalspeedsarenotimportantinellipticals,byandlarge,velocitydispersionis-that's where kinetic energy is. Similar thing applies, that luminosity is proportional to roughly the fourthpowerofthevelocitydispersionhere,playingtheroleofthecircularspeedforthedisks. It's a pretty good correlation, but it has large scatter, which cannot be explained by the measurementpairsalone.Therewassomethingthatwascausingthescatteredcircle'ssecond parameter,andnowweknowwhatthatis. [slide8]Theotheringredientforellipticalgalaxiesisso-calledKormendyRelation,whichrelates the effective radii of galaxies with their mean surface brightness. And, it goes in the sense of meansurfacebrightnessbeingsmallerforthelarger,therefore,alsomoreluminousellipticals. This is reflected also in the fact that the more luminous, the larger ones tend to have more diffusedsurfacebrightnessprofiles.Thistooisaprettygoodcorrelation,roughlygoesaslopeof -0.8,butit'snotaperfectone.Ittoohasascatterthat'slargerthanwhatmeasurementerror suggest.Again,implyingthereisasecondparameterinvolved. [slide9]But,let'sjustplaywithKormendyrelationforamomenttoillustratehowyoucanuse these correlations to glean something about galaxy formation. A simple Virial Theorem argumentisthatmassbeproportionaltotheradiusandvelocityofdispersionsquared.Now,if weassumethatmass-to-lightratiosareroughlyconstant,whichisnotsuchabadassumption after all, then you can use luminosity as a proxy for the mass. And, therefore, you can use projected mass density instead of surface brightness. So, if you form ellipticals through dissipationlessmerging-justpuregravity,nocooling,nothinglikethat–thenkineticenergyper unitmassremainsconstant.Kineticenergyperunitmassisdirectlyproportionaltothevelocity dispersionsquared.And,now,goingbacktotherelationbetweenvelocitydispersion,mass,and theradius,weinferthatradiusshouldbeproportionaltothesurfacebrightness,projectedmass distributionifyouwill,tothe-1power,whichistoosteeprelativetoobservations. Now,assumeinsteadthatellipticalsformentirelythroughdissipativecollapse,thereisnoextra stuffbeingaddedin,galaxyjustshrinks.And,becausethemassisconservedinthistime,the radiusgoesdown,surfacebrightnesshastogoupbyasquare,andsoradiuswillbeinversely proportional to square root of surface brightness, which is now too shallow for Kormendy relation.So,it'sin-between.And,thatsuggeststhatbothdissipativecollapseanddissipationless mergingplayaroleinformationofellipticalgalaxies,andthat'salmostcertainlytrue. [slide10]Now,theresolutionofthesecondparameterproblemwasdiscoveryoftheso-called fundamentalplane,afamilyofcorrelationsforellipticalgalaxiesthatunifyanynumberoftheir properties into two-dimensional scaling relations, often expressed between radius, velocity dispersion,andsurfacebrightness,butyoucanuseluminosityinplaceofradiusaswell.Andso, herearethefourdifferentprojections.TheKormendyrelation,theupperleft.Andyouseethe littlearrowbarsymbolinthecorner,andthattellsyouwhattheerrorsare,soquicklythereis extra scatter involved. The Faber-Jackson relation on the top right. The plot of velocity dispersion, which is like kinetic temperature of stars versus surface brightness, which is like projected density, in the lower left, which is the same coordinates as the cooling diagram for galaxies. And, there we see absolutely no correlation whatsoever. Naively, you might expect that galaxies with higher kinetic temperatures would also need to have higher densities, but that'ssimplynotthecase. Thissetofplotsimmediatelytellsyouthatthereareatleasttwoindependentcoordinateshere, which is why there is no correlation in the bottom left. But, since there is some correlation, chancesarethatthisisaflatteneddistributioninmultidimensionalspace.And,indeed,ifyou combine quantities in such a way to look at this new two-dimensional correlation edge-on, it looksessentiallyperfectwithinmeasurementerrors,thatisthefundamentalplane.Itisaplane, because there are two independent variables, and it's fundamental, because it connects fundamentalpropertiesofellipticals. [slide 11] Well, can we understand where these correlations come from? Yeah, up to some point. So, we can always start with the Virial Theorem, that always has to apply, and we can thensubstitutemassforluminosityusingmass-to-lightratios.Now,hereisthecrucialpart.Ifall galaxieswerehomologous,hadjustsamekindofstructure,onlyscaledversionsofeachother, then we can relate the important three-dimensional values of, say, mean radius and mean kinetic energy, putting the mass of the observed ones to some constant of proportionality K. And, we can account for density structure again with some proportionality constant, because wejustassumetheyallhavesameshape. Thenwecansimply,fromtheVirialTheorem,comeupwiththeexpressionthatradiusshould scale as measure of velocity to the second power, that could be velocity dispersion, surface brightness to the -1 power, and mass-to-light ratio to the -1 power. Likewise, we can deduce that luminosity will scale of fourth power of velocity, or velocity dispersion, just like in TullyFisherorFaber-Jackson,-1powerofsurfacebrightness,and-2powerofmass-to-lightratio.So, youcanseethat,inTully-Fisherrelation,thatsuggestthatsurfacebrightnessandmass-to-light ratiosomehowtogetherplaytheroleofthesecondparameter.ForFaber-Jackonrelation,the same. For Kormendy relations, its velocity dispersion and mass-to-light ratio play the role of secondparameter. [slide 12] So, this is what Virial Theorem plus homology imply. Any deviations of observed correlations from these are telling you something about their assumptions. One of them or anotheriswrong.Wewilltalkmoreaboutthisinthenextmodule. 12.5:GalaxyScalingRelations–PartII [slide1]Now,let'scontinueourinquiryintoscalingrelationsforgalaxies. [slide 2] I've already introduced the fundamental plane of elliptical galaxies. It is a set of bivariatecorrelationsbetweenmanyoftheirdifferentproperties,alwaysunifiedinawaythat anyoneofthemcanbeexpressedasalogarithmiccombinationoftwoothers.Andso,usually it'sexpressedasscalingarelationbetweenradius,surfacebrightness,andvelocitydispersion, becausethat'saveryusefulwayoftakingit,butitcouldbeanyother.And,what'sshownhere is the plot of what it looks like, almost face-on, or you don't see much correlation at all, an essentiallyedge-on,wheretheonlythicknessisduetomeasurementerrors. [slide3]Imentionedthatyoucanusedifferentquantities,andindeed,youcan.So,forexample, youcansubstituteluminosityforradius,andsothisyoucanthinkofastheimprovedversionof Tully-Fisherrelation,butit'sreallyafundamentalplaneprojectedslightlydifferently.And,you canalsousegalaxymetallicity,expressedasstrainsofindices,likemagnesiumoriron,where, which implies a couple of interesting things – that history of star formation and ellipticals, therefore their chemical enrichment, is tightly coupled to their structure of dynamical parameters. And, that in itself is a very important fact. It really tells us how dynamical and stellarevolutionhistoryofgalaxiesmustbeconnectedinaverytightfashion,whichis,Iwould say,stillnotperfectlywell-understood. [slide4]Youwillrecallfromourhand-wavingderivationofthescalingrelationsthatifyoutake aVirialTheorem,whichconnectsthreevariables,say,radius,mass,andcharacteristicvelocity scale,orradius,density,andcharacteristicvelocityscale,thereforeitimpliesthereisaplanein the parameter space of these three quantities, which we can call virial plane. And, then we make some assumptions about homology, that all galaxies are scaled versions of each other, and about mass-to-light ratios that say you can substitute mass directly for luminosity, that shouldleadintotheobservablethinglikefundamentalplane.Now,anydifferencesintheslope oftheobservedversusvirialplanearetellingussomethingaboutourassumptions. [slide5]And,infact,youcanshowthatifyoucanexpressmass-to-lightratioassomepowerof massorluminosity,andallowforscalingthoseasroughly1/5power,thenyoucanaccountfor thedifferenceinthetiltoftheobservedplanetotheVirialTheorem.So,youcanachievethisin variousways.Therecouldbeadifferentmixofdarktoluminousmatter,aswediscussedearlier. Therecouldbedifferentamountsofdarktoluminousmatter.Ortherecanbedifferentstellar populations.But,inanycase,theyhavetobeverytightlycorrelatedwiththegalaxymassitself. And,thatisnotanobviousthingtoarrange. [slide6]Now,thatwecanmeasuremassesofellipticals,usingeitherVirialTheoremestimates orbetteryet,gravitationallensing,whichdoesnotdependonanyassumptionsofanisotopyand what not, we can now form mass equivalent fundamental plane using mass instead of luminosity,ormassdensityinsteadofluminositydensityorsurfacebrightness.And,hereitis, anditlooksveryclosetotheobservedone.Theslopenowismoreorlesswithintheerrors– exactlywhatyou'dexpectfromVirialTheorem–whichindeedsuggeststhatsomeassumptions aboutmass-to-lightratiosandhomologyareprobablywhat'swrong. [slide7]YouwillrememberthatbothTuly-Fisherandfundamentalplanehavebeenusedasthe distanceindicatorrelations,andthosearecrucialindeterminingpeculiarvelocitiesofgalaxies. So, the question then is, are those relations universal? Are they same everywhere, in all environment?Becauseiftheyreflectdifferentevolutionaryhistories,say,formationofgalaxies, evolutionofgalaxies,anddenseclustermaybedifferentthanfield,thenyoumightexpectto seedifferencesincorrelations.And,itturnsout,yes,therearesomedependencies. ThisoneisfromthestudybytheSPIDERgroup–LaBarberaetal.–thatI'veshownyouearlier. And, it shows the dependence of the intercept on the projected galaxy density, around the galaxy in question, as well as projected slope, and I can see there are small, but significant trends.Theycanmeasuretheseonlybecausetheyhadinexcessof10,000galaxies,sotheycan putlotofgalaxiesineachbin.So,theeffectsarethere.Weknowthemandwecanmeasure them,buttheyareverysubtle.Essentially,whatthesesubtleeffectssayisthatourassumptions werealmostright.Ellipticalgalaxiesdoformaverywell-regulatedfamily,whereinmass-to-light ratiochangesasafunctionofluminosity,butatanygivenmassthereissolittlescatter,thatit's trulyamazing.Itcouldbeconsistentwithzero,justmeasurementerrors. [slide 8] So, this is an outstanding puzzle that all elliptical galaxies in all enviroments everywhere, independent of the size, mass or anything else. Just two numbers determine at least a dozen of fundamental quantities, that describe the galaxies, having to do with their masses, densities, kinetic temperatures, luminosities, star formation histories, and so on. Just two numbers. And we can come up with any number of scenarios why this shouldn't be the case.Why,evenifyoustartedwithpureVirialTheoremtyperelation,you'regoingtoscramble up by different evolutionary paths. And yet, that doesn't happen, even though processes of galaxyformationarefairlystochasticintermsofrandommerging,andsoon.Somehow,inthe end, galaxies always end up following these correlations. Note also that there are quantities that do not participate in these correlations. Usually those are quantities that describe the shapeofthelightdistribution. [slide9]So,howcanthispossiblybe?Now,wecanturntonumericalsimulationsofstructured galaxy formation, and it turns out that if you do this very carefully, you can make synthetic ellipticalsincomputer.Theytoofollowfundamentalplane,justasobserved.Therewasnonew physicsputin.Thereisnothingmagical;sameoldgravity,dissipation,andsoon.Andsomehow, thiscorrelationemergesintheend.Wecanreproducethiscorrelationinacomputer,butthat doesn'tmeanweunderstandit.So,thetiltisrelativelyeasilyunderstoodbychanginghomology andmass-to-lightratioassumptions,thethicknessisnot.Whythethicknessissosmallistruly anoutstandingmystery.SamethingforTully-Fisherrelation. [slide 10] So, you can look at this in a more general way. You can think of the galaxies, as families of objects, form two-dimensional sequences in a three-dimensional space – or tendimensionalspaceifyouwant–butatleastthree,andfundamentalplanewouldbeonethem. This is my analogy with stars in H-R diagram, which is a parameter space of stellar luminosity and stellar temperature, and there, stars of different families form linear sequences in that space, whether it's main sequence, giant branch, horizontal branch, and so on. So, here we have,forgalaxies,two-dimensionalsequencesinthree-dimensionalparameterspace.So,thisis just like H-R diagram for galaxies. And, like we used H-R diagram to understand and probe stellarstructuredevolution,wecandothesameforgalaxiesinthisgalaxyparameterspace. [slide11]And,further,let'slookatdarkhalos,canwelookattheirscalingrelations?Atfirstit soundsridiculous,butinfactwecould.Thisisimportantbecauseweknowalreadythatmany galaxian properties seem to be driven by the properties of their halos, because that's where mostofthemassis.Now,innumericalsimulationswecanseewhatdarkhaloslooklike.Wecan plot their density profiles, and several have been suggested. One is this one called Navarro, Frenk, and White profile. But, Sersic profile works just as well. And, just as it describes distributionoflightinthegalaxies,soitseemstodescribedistributionofdarkmatteratleastin modelgalaxies. [slide12]Whataboutobservations?So,hereisjustasetofdarkmatterdensityprofiles,derived from simulations, and the lines going through them are the fit of the Navarro-Frenk-White profile. [slide13]Well,that'sthetheory.Whatabouttheobservations?Darkmatteriskindofhardto observe.But,wecaninfersomethingaboutthisdistributionfromobservablethingsingalaxies, like,thisishowwedorotationcurves.And,indeed,withsomecareanddelicacy,Kormendyand Freeman have done this for a whole lot of different galaxies, estimating their central halo densities,theircoreradiihalodistribution–characteristicradiihalomassdistribution,aswellas theireffectivevelocitydispersion–thekineticenergyperunitmassthattheyhavetohavein ordertobalancetheirownself-gravity.And,soafterdoingthis,theyfoundoutthatthereare scaling relations for dark halos, and here they are. The quantities like core radius, central density, and kinetic energy, they're proportional to some shallow power of galaxy luminosity, and therefore, galaxy mass. So, it is quite remarkable that we can actually measure scaling relationsforgalaxyhalos,whichmightbeactuallytherootofexistenceofthosethatweseefor visiblelight. [slide14]Andthatconcludesourstudyofgalaxianpropertiesassuch.Next,wewillstarttalking aboutgalaxyevolutionandgalaxyformation.