THE LARGE-SCALE DISTRIBUTION OF GALAXIES Antonaldo Diaferio Max-Planck-Institut f¨ ur Astrophysik, Karl-Schwarzschild-Str. 1 D-85740, Garching bei M¨ unchen, Germany Present address: Universit` a degli Studi di Torino, Dipartimento di Fisica Generale “Amedeo Avogadro”, Via Pietro Giuria 1, I-10125 Torino, Italy ABSTRACT Visible matter in the Universe concentrates in well sepa- rated islands – the galaxies. Galaxies are not distributed uniformly in space, but they rather show a complex net- work of sheets, filaments and regions almost devoided of galaxies. The formation of galaxies depends on physical processes which occur on very different scales: from the scale of stars to that of clusters of galaxies. By combining models of the large scale structure formation in the Uni- verse and models of the main processes driving the for- mation of galaxies, we are able to investigate, at the same time, the large scale distribution of galaxies and their inter- nal properties. The properties of a large region of the Uni- verse modelled this way are remarkably similar to those of the observable Universe. This approach has substantially improved our current understanding of the galaxy forma- tion processes and provides a powerful tool to constrain cosmogonic theories. 1. GALAXIES IN THE REAL UNIVERSE Stars in the Universe concentrate in galaxies like our own Milky Way. The Milky Way contains stars, namely a hundred billion stars. There exist, however, dwarf galaxies with just a billion stars or giant galaxies with a thousand billion stars. Galaxies roughly have a size kiloparsec, namely m or 65,000 light-years. 1 This size is huge: if the distance Earth-Sun were 1 cm, the Milky Way would be a disk of radius as large as the diameter of the Earth! The average distance between galaxies is 1 megaparsec (Mpc), 50 times the size of a galaxy. Are galaxies dis- tributed uniformly? How do we find the position of a galaxy? For an observer on the Earth, three coordinates specify the position of an object in space: two angular co- ordinates giving the object position on the sky, and a third coordinate giving its distance away from the observer. We can use the Doppler effect to estimate the distance to a galaxy. An observer measuring the light emitted by a moving source measures a longer or shorter photon wave- length when, respectively, the source recedes from the ob- server or approaches the observer. This Doppler effect is identical to the effect heard in an approaching or receding train. 1 Recall that 1 parsec (pc) m light-years. The shift in the light-spectrum of a galaxy measures its velocity with respect to the Earth. Very few nearby galaxies are approaching the Milky Way and show a blue- shifted spectrum (shorter photon wavelengths). Most galax- ies show a light-spectrum shifted to longer photon wave- lengths – a redshift. When we assume that this velocity is due to cosmic expansion, Hubble’s law yields a distance to the galaxy: the distance simply is the Hubble constant times the galaxy line-of-sight velocity. In past years, galaxy redshift surveys have played a crucial role in mapping out the structure of the Universe: galaxies are not distributed uniformly, but concentrate on filamentary and sheet-like structures surrounding nearly empty regions of size 20–50 Mpc. Figure 1 shows the galaxy distribution in the local Uni- verse according to the Harvard-Smithsonian Center for Astrophysics Redshift Survey [2]. There is a striking struc- ture which extends over the whole survey volume at the distance km s Mpc: the Great Wall [3]. Apparently the galaxy distribution is not uniform on these scales. 2. STRUCTURE FORMATION The currently most viable model for the formation of the large scale structure assumes that at a very early epoch in the Universe, the matter was distributed uniformly. On scales m and smaller, however, perfect unifor- mity is impossible in the classical sense, because the laws of quantum mechanics hold. In fact, because of Heisen- berg’s uncertainty principle, 2 quantum-mechanical fluctu- ations originated tiny inhomogeneities in the distribution of matter. The Universe expanded at an exponential rate during the inflationary era. Thus, the fluctuations on sub- atomic scales inflated to cosmic scales. After the inflationary era, the Universe started expand- ing more quitely: the early inhomogeneities were ampli- fied by gravity and gave rise to the galaxy distribution we observe today. This scenario assumes that the ordinary matter we see in stars and galaxies represents only a small fraction of the total mass contained in the Universe: 90 per cent of the matter or more is actually some form of mat- 2 According to Heisenberg’s uncertainty principle, it is impossible to measure, at the same time, both the position and velocity of a particle with infinite precision.
Visible matterin the Universeconcentratesin well sepa-ratedislands– the galaxies.Galaxiesarenot distributeduniformly in space,but they rathershow a complex net-work of sheets,filamentsandregionsalmostdevoidedofgalaxies.The formationof galaxiesdependson physicalprocesseswhich occuron very differentscales:from thescaleof starsto thatof clustersof galaxies.By combiningmodelsof the large scalestructureformationin the Uni-verseandmodelsof the main processesdriving the for-mationof galaxies,we areableto investigate,at thesametime,thelargescaledistributionof galaxiesandtheirinter-nalproperties.Thepropertiesof a largeregionof theUni-versemodelledthiswayareremarkablysimilarto thoseoftheobservableUniverse.This approachhassubstantiallyimprovedour currentunderstandingof thegalaxyforma-tion processesandprovidesa powerful tool to constraincosmogonictheories.
1. GALAXIES IN THE REAL UNIVERSE
Starsin theUniverseconcentratein galaxieslike our ownMilk y Way. TheMilk y Waycontains������� stars,namelyahundredbillion stars.Thereexist,however, dwarfgalaxieswith just a billion starsor giantgalaxieswith a thousandbillion stars.Galaxiesroughlyhave a size ��� kiloparsec,namely ����� m or 65,000light-years.1 This sizeis huge:if thedistanceEarth-Sunwere1 cm,theMilk y Waywouldbeadiskof radiusaslargeasthediameterof theEarth!
Theaveragedistancebetweengalaxiesis 1megaparsec(Mpc), 50 times the size of a galaxy. Are galaxiesdis-tributed uniformly? How do we find the position of agalaxy? For an observer on the Earth, threecoordinatesspecifythepositionof anobjectin space:two angularco-ordinatesgiving theobjectpositionon thesky, anda thirdcoordinategiving its distanceaway from theobserver.
We canusetheDopplereffect to estimatethedistanceto a galaxy. An observermeasuringthelight emittedby amoving sourcemeasuresa longeror shorterphotonwave-lengthwhen,respectively, thesourcerecedesfrom theob-server or approachestheobserver. This Dopplereffect isidenticalto theeffectheardin anapproachingor recedingtrain.
1Recallthat1 parsec(pc) ���� ������������� m ���� ��� light-years.
The shift in the light-spectrumof a galaxymeasuresits velocity with respectto the Earth. Very few nearbygalaxiesareapproachingtheMilk y Wayandshow ablue-shiftedspectrum(shorterphotonwavelengths).Mostgalax-iesshow a light-spectrumshiftedto longerphotonwave-lengths– a redshift. Whenwe assumethatthis velocity isdueto cosmicexpansion,Hubble’s law yields a distanceto thegalaxy: thedistancesimply is theHubbleconstanttimesthegalaxyline-of-sightvelocity.
In pastyears,galaxy redshift surveys have playedacrucial role in mappingout thestructureof theUniverse:galaxiesarenot distributeduniformly, but concentrateonfilamentaryand sheet-like structuressurroundingnearlyemptyregionsof size20–50Mpc.
Figure1showsthegalaxydistributionin thelocalUni-verseaccordingto the Harvard-SmithsonianCenter forAstrophysicsRedshiftSurvey [2]. Thereisastrikingstruc-ture which extendsover the whole survey volumeat thedistance��� �"!��#�� km s$ � �%���#� Mpc: the GreatWall[3]. Apparentlythegalaxydistribution is not uniform onthesescales.
2. STRUCTURE FORMATION
Thecurrentlymostviablemodelfor the formationof thelarge scalestructureassumesthat at a very early epochin theUniverse,thematterwasdistributeduniformly. Onscales�&���'$ � � m andsmaller, however, perfectunifor-mity is impossiblein theclassicalsense,becausethelawsof quantummechanicshold. In fact, becauseof Heisen-berg’suncertaintyprinciple,2 quantum-mechanicalfluctu-ationsoriginatedtiny inhomogeneitiesin the distributionof matter. The Universeexpandedat an exponentialrateduringtheinflationaryera.Thus,thefluctuationson sub-atomicscalesinflatedto cosmicscales.
After theinflationaryera,theUniversestartedexpand-ing morequitely: the early inhomogeneitieswereampli-fied by gravity andgaveriseto thegalaxydistribution weobserve today. This scenarioassumesthat the ordinarymatterweseein starsandgalaxiesrepresentsonly asmallfractionof thetotalmasscontainedin theUniverse:90percentof thematteror moreis actuallysomeform of mat-
2Accordingto Heisenberg’s uncertaintyprinciple,it is impossibletomeasure,at the sametime, both the positionandvelocity of a particlewith infinite precision.
Figure 1: Galaxy distribution in the nearbyUniverseaccordingto the Harvard-SmithsonianCenterfor AstrophysicsRedshiftSurvey. For clarity, thethree-dimensionalvolume,which is 900million light-yearsdeep,hasbeensplittedintothreeslicescenteredon theMilk y Way: theupperslice is on top of the left lower slicewhich, on turn, is on top of theright lowerslice.Eachdot is agalaxy. Thereis a structureat redshift (*)+�,���-!��#�� km s$ � extendingfrom left to right ineachslice: becausetheslicesareactuallyon top of eachother, this structureis a singlesheetcoveringanareaof at least. �0/���1#� Mpc andonly 10 Mpc thick. It hasbeennamed“the GreatWall” by GellerandHuchra[3].
Figure2: A simulatedregion of theUniverseat thepresenttime. Theregion shown coversanarea �323�0/4�52�� Mpc andis 16 Mpc thick. Thegrey scaleshows thedarkmatterdensitydistribution: darkregionsareseveralhundredtimesdenserthan light regions. Colour dots indicatethe locationof galaxies. The colour sequencered to blue (or white to black)indicatesanincreasingstarformationrate,from non-starforminggalaxiesto galaxieswith largestarformationrates.Theinhomogeneousdistributionof galaxiesis comparableto theobserveddistributionshown in Figure1.
ter which interactsgravitationally but not with photons:becauseit doesnot emit or absorbphotons,this matterisnameddark matter.
Thegrowth of structurein thedarkmattercomponentof the Universehasbeenstudiedwith computersimula-tions for the last twentyyears.In thesesimulations,a fi-nite volumeof theuniverseis representedby a systemofa largenumber6 of massiveparticleswhich interactwitheachothergravitationally. Thecosmologicalmodelspec-ifies theinitial conditions.Thecomputerthenfollows thegrowth of structurein thevolumeby integratingtheequa-tionsof motionfor the 6 -particlesystem.State-of-the-artsimulationscontain 67� . � million particles,but, at theMax-PlanckInstitut in Garching,two simulationswith abillion particleshavebeenrecentlyrun.3
Darkmatter-only simulations,however, haveaseriousshortcoming: making quantitative comparisonsbetweenthe simulateddistribution of the unobservable dark mat-ter andthe distribution of the observable galaxiesis nottrivial. Sofar, ad hoc assumptionshave beenmadeabouthow thedistributionof galaxiestracksthatof theunderly-ing dark matter. The simplestpossibility is that galaxiesprovide a statisticallyfair sampleof thedarkmatter. Un-fortunately, the formationefficiency of galaxiesdependson theenvironmentin which they aresituated:in fact,weobserve, for example,that in high densityregionsof theUniverse,most galaxiescontainvery little cold gasandhave no ongoingstar formation,whereasin low densityregions,galaxiesform starsvigorously.
3. HOW CAN WE COMPARE THE MODEL WITHTHE REAL UNIVERSE?
In order to understandthe relationshipbetweengalaxiesanddarkmatteron largescales,we have adopteda com-pletelynew approach[1,4,5,6]: first, we simulatethefor-mationof thelargescalestructurefollowingonly thegrav-itationaldynamicsof thedarkmatter;second,we includeasetof phenomenologicalprescriptionsfor whereandhowgalaxiesform andevolve in thesedarkmatter-only simu-lations.
We prescribethatgalaxiesform whenthegasreacheshighenoughdensitiesto cool,sink to thecentreof its sur-roundingdark matterhalo and form stars. Afterwards,evolvedmassivestars(supernovae)explodeandinjecten-ergy in the intergalacticmedium;moreover, galaxiesor-biting within acommondarkmatterhaloeventuallymergeandgiveriseto theobservedvarietyof galaxies.
Wemodelcubicboxes170Mpc onasidewith 17mil-lion darkmatterparticles.Figure2 shows a slice16 Mpcthick of one of our simulationboxes. This slice repre-sentsa volumeof the Universeat the presenttime. Thematter density distribution is shown in grey scale: thedarkestregionsareseveralhundredtimesdenserthanthelightest ones. Galaxiesare also shown as colour dots.The sequencered to blue (or white to black) representsthe sequenceof increasingrate at which galaxiesform
3Thesesimulations,known astheHubbleVolumeSimulations,werecarriedout by theVirgo Consortium,which usessupercomputersbasedat theComputingCentreof theMax-PlanckSocietyin Garching,andattheEdinburgh ParallelComputerCentre.
stars. Blue (or black) galaxies,which aregalaxieswithlarge star formation rates,mainly populatelow densityregions, whereasred (or white) galaxies,namelygalax-ieswherethestarformationrateis low, aremostlywithinlarge galaxyclusters.This samecorrelationbetweenthepropertiesof thegalaxypopulationandthe local numberdensityof galaxiesis observedin therealUniverse.
Figure3 shows thetime evolutionof a rich cluster. Atearly times( )98;: , namely11 billion yearsago),only asmall numberof galaxieshave formed: they have a quitelargestarformationrateand,therefore,appearquiteblue(or black). As time goeson, new blue (or black) galax-iesfrom thesurroundingfall ontothecluster, whereasthecentralgalaxiesrun out of cold gas,which is the fuel re-quiredto form stars,andbecomered(or white/grey).
A light ray takesa finite time interval to travel fromits sourceto the observer. Thereforethe further is thesourcethe earlier is the time at which we areobservingthat source. The Hubble SpaceTelescopeand ground-basedtelescopeswith 8 m diamatermirrors enableus toobserve very faint objects.Most of themareso far awaythatnow weseethelight they emittedseveralbillion yearsago.Therefore,weareableto probetheUniverseat theseearly times. The observationsperformedin the last fewyearsindicatethat thestarformationratein theUniverseincreaseswith look-backtime,in agreementwith ourmodel.
4. CONCLUSION
We have designedand implementeda techniquewhichfollows, for the first time, the formationandevolution ofgalaxiesin a large volumeof the Universe. We arethusableto provideimportantinsightsinto boththecosmolog-ical modelandthe processesgoverningthe formationofgalaxies.
We find thatthecosmologicalmodelandsomegalaxyformationprocesses,for exampletheenergy injectionbysupernovae, are tightly linked. This result is somewhatsurprising,becausesupernovaexplosionsoccuronthescaleof starsbut affect the distribution of galaxieson scalestwelve ordersof magnitudelarger. Thereasonis thehugeamountof energy releasedin afew secondsduringthestarexplosion.This power is similar to thetotal luminosityofa normalgalaxy!
Our techniquealso provides insightsinto the galaxyformationprocesses,like thegascoolingrateandthestel-lar evolution,whentheseprocessesaffect thegalaxyinter-nalpropertiesbut not thelargescaledistributionof galax-ies.
Wearenow focussingourattentionontheevolutionofgalaxiesin clustersandgroupsfor comparisonwith datafrom theHubbleSpaceTelescopeandground-basedtele-scopes.Moreexciting resultsontheformationof theUni-versewe live in will becomingsoon.
Acknowledgments. At thetimeof thisproject,I wasaMarie CurieFellow andheldgrantERBFMBICT-960695of the Training andMobility of Researchersprogrammefinancedby the EuropeanCommunity. I thankJorg Col-berg, GuinevereKauffmannandSimonWhite for permis-sionto reproduceresultsfromourjoint researchprogramme
Figure3: Timeevolutionof aclusterof galaxies.Timerunsfrom left to right andfrom topto bottom.In thecosmologicalmodelshown,at redshift )+8<: , 2, 1, and0, theUniverseis 1.6,2.5,4.6,and13billion yearsold, respectively. Thepresenttime correspondsto )=8>� . Eachpanelis a slice42 Mpc on a sideand16 Mpc thick. Thegrey scaleis thedarkmatterdensityfield: bright spotsarethehigh densityregions,darkspotsthe low densityregions. Colourdotsareasin Figure2. Note that (1) the averagestarformationratewithin galaxiesdecreasesasthe clusterevolves(therearemorered,orwhite/grey, galaxiesat low redshift),and(2) non-starforming(red,or white/grey) galaxiestendto segregatein thedensestregions.Both featuresareobservedin therealUniverse.
within theGermanIsraeliFoundation(GIF) collaboration.
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