Download 12.1 Elliptical galaxies

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.