The cosmic web and the orientation of angular momenta

0.69 MB·English

by  Noam I. Libeskind

Mon.Not.R.Astron.Soc.000,000–000(0000) Printed18January2012 (MNLATEXstylefilev2.2)
The cosmic web and the orientation of angular momenta
Noam I Libeskind1, Yehuda Hoffman2, Alexander Knebe3, Matthias Steinmetz1,
Stefan Gottlo¨ber1, Ofer Metuki2, & Gustavo Yepes3
1Leibniz-Institutefu¨rAstrophysikPotsdam(AIP),AnderSternwarte16,D-14482Potsdam,Germany
2
2RacahInstituteofPhysics,HebrewUniversity,Jerusalem91904,Israel
1
3GrupodeAstrof´ısica,DepartamentodeFisicaTeorica,ModuloC-8,UniversidadAuto´nomadeMadrid,CantoblancoE-280049,Spain
0
2

n
18January2012
a
J

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ABSTRACT
1
We use a 64h−1Mpc dark matter (DM) only cosmological simulation to examine the large

] scaleorientationofhaloesandsubstructureswithrespectthecosmicweb.Awebclassification
O scheme based on the velocity shear tensor is used to assign to each halo in the simulation a
C webtype:knot,filament,sheetorvoid.Using∼106haloesthatspan∼3ordersofmagnitude
inmasstheorientationofthehalo’sspinandtheorbitalangularmomentumofsubhaloeswith
.
h respect to the eigenvectors of the shear tensor is examined. We find that the orbital angular
p momentumofsubhaloestendstoalignwiththeintermediateeigenvectorofthevelocityshear
-
o tensor for all haloes in knots, filaments and sheets. This result indicates that the kinematics
r ofsubstructureslocateddeepwithinthevirializedregionsofahaloisdeterminedbyitsinfall
t which in turn is determined by the large scale velocity shear, a surprising result given the
s
a virilaizednatureofhaloes.Thenon-randomnatureofsubhaloaccretionisthusimprintedon
[ theangularmomentummeasuredatz =0.Wealsofindthathaloes’spinaxisisalignedwith

the third eigenvector of the velocity shear tensor in filaments and sheets: the halo spin axis
1
v pointsalongfilamentsandliesintheplaneofcosmicsheets.
5
1 INTRODUCTION Clouds,UrsaMinor,CarinaandFornax)havepropermotionscon-
6
sistentwith“rotationalsupport”oftheso-called“disc-of-satellites”
3
3 Satellitegalaxiesrepresentaparticularlyfascinatingsubsetofthe (Metzetal.2008),anobservationrecentlyattributedtotheangular
. lowredshiftuniverse.Amongtheirinterestingpropertiesistheso- momentumbiasofsatellitesfallinginalongtheirhostsmainaxis
1 called “Holmberg effect” (Holmberg 1969; Zaritsky et al. 1997) (Deasonetal.2011).Althoughexaminingadifferentenvironment
0
which finds that satellites tend to be oriented close to the poles andmassrangeofhaloes,Tormen(1997)wasthefirsttosuggest
2
oftheirhostdiscgalaxies,avoidingtheplanar regions.Thistype thatgalaxiesfallintoclustersanisotropically.Furthertotheirwork,
1
of polar alignment is also seen in the Milky Way (Kroupa et al. the idea that satellites are preferentially (not randomly) accreted
:
v 2005;Metzetal.2009)andwasprobablyfirstnotedover3decades andretainamemoryofthelargescalesfromwhichtheycamehas
Xi ago(Lynden-Bell1982),anadequateexplanationofwhichisstill also recently been suggested (Knebe et al. 2004; Libeskind et al.
lacking. 2011;Vera-Ciroetal.2011).
r
a External galaxies (for example in the SDSS) often exhibit a Onlargerscalesanumberofobservationalstudieshavehinted
spatialalignmentofsatelliteswiththelongaxisofthehost(Sales thatgalaxiesseparatedbyasmuchas∼30Mpc(or100softimes
& Lambas 2004; Brainerd 2005; Yang et al. 2006; Agustsson & theirvirialradii)mayalsoexhibitalignmentsalbeitwiththelarge
Brainerd 2010) although this alignment is strongest for the older scale distribution of matter (Hirata & Seljak 2004; Hirata et al.
reddersatellites-youngerbluesatellitegalaxiesexhibitnosignifi- 2007; Mandelbaum et al. 2006; Okumura et al. 2009). On these
cantalignment.ItsnotclearwhethertheMilkyWay’spolaralign- scales,matterclustersintoa“cosmicweb”definedeithergeomet-
mentisatoddswiththeseresults,asthesurfacebrightnessofmany rically (e.g. Sousbie et al. 2008) or dynamically (e.g. Hahn et al.
oftheMilkyWay’sultrafaintsatellitegalaxiesismanyordersof 2007;Forero-Romeroetal.2009).
magnitudelowerthanwhatcanbeobservedextra-galactically.
Yetwhatlacksfromtheabovestudiesisaclearlinkbetween
In addition to their anisotropic spatial distribution at least 5 thelargescalecosmicweb,theorientationofcentralgalaxiesand
of the Milky Way’s satellites (the Large and Small Magellanic thepreferentialbiasinsatelliteentrypoints,angularmomentaand
(cid:13)c 0000RAS
2 Libeskindetal.
Figure1.A0.25h−1Mpcslicethroughthesimulationsboxofsidelength
64h−1Mpc.Intheleftpanel,weshowthemeshcellsassociatedwithknots
(black),filaments(lightgray)andsheets(darkgray).Ontherightweshow
thedistributionofDMhaloesinthesamesimulationslice.
z = 0position.Somestudies,suchasArago´n-Calvoetal.(2007)
andHahnetal.(2007)haveusedmethodsbasedonthetidalfield
ortheHessianofthedensityfieldtocorrelateintrinsichaloproper-
tieswiththecosmicweb.Arago´n-Calvoetal.(2007)foundamass
dependenceforthe(perpendicular)correlationbetweenhalospins
andcosmicstructure.Hahnetal.(2007)examinedhowanycorrela-
tionvariedwithredshift,extendingtheirworkinHahnetal.(2010),
where they attempted to establish a link between central galactic
discs and the cosmic web. In that paper they found an alignment
betweenthespinofgaseousdiscsandtheintermediateaxisofthe
ofthelargescaletidalfield,consistentwithlineartidaltorquethe-
ory(e.g.Navarroetal.2004;Lee&Erdogdu2007).Howevernone
ofthesestudiesexaminedtheorbitsofsatellitegalaxies.
InthisLetterweextendandcomplementtheworkofHahnet
al.(2007,2010)andArago´n-Calvoetal.(2007)intwoways.First
weexaminingtheorientationofthehalowithrespecttothevelocity
shear tensor instead of the tidal tensor. This method allows us to
obtain much higher spatial resolution for our web classification.
Secondly,welookattheorientationwithrespecttothecosmicweb
ofsubstructureangularmomentum,inabidtounderstandhowthe
Figure2.Normalizedhistogramsofthecosineoftheanglebetweenthe
internal dynamics of haloes and the substructures resident within
spinaxisofthehalo(LDM,left),theorbitalangularmomentumofsub-
themareeffectedbyandreflectiveofthelargescalecosmicweb.
structures(Jsub right)andtheprincipalaxesofthecosmicwebinsheets
(top),filaments(middle)andinknots(bottom).Weshowtheangleformed
withthelong(eˆ1,black),intermediate(eˆ2,red)andshort(eˆ3,blue)axesof
thecosmicweb.Auniformdistributionofanglesisshownbytheflatline
2 METHODS atP(|cosφ|)=1.
We use a DM only N-body cosmological simulation run assum-
ing the standard ΛCDM concordance cosmology (e.g. WMAP5,
Komatsu et al. 2009). These assume a flat universe with cos- available halo finder AHF (Knollmann & Knebe 2009) is run on
mological constant density parameter Ω = 0.72, matter den- theparticledistributiontoobtainahalocatalogue.AHFidentifies
Λ
sity parameter Ω = 0.28, a Hubble constant parameterized by haloes and subhaloes in the simulation by searching the particle
m
H = 100hkms−1 Mpc−1 (withh = 0.7),aspectralindexof distribution for local density by maxima and checking that parti-
0
primordialdensityfluctuationsgivenbyn =0.96,andmassfluc- cles within the virial radius are gravitationally bound to the host
s
tuationsgivenbyσ =0.817. structure.Substructuresareidentifiedashaloeswhosecenterislo-
8
The simulations span a box of side length 64h−1Mpc with catedwithinthevirialradiusofamoremassiveparenthalo.
10243 particles, achieving a mass resolution of ∼ 1.89 × A grid based velocity field is constructed by the “clouds in
107h−1M and a spatial resolution of 1h−1kpc. The publicly cells” (CIC) algorithm. The velocity of each cell is computed by
(cid:12)
(cid:13)c 0000RAS,MNRAS000,000–000
Haloesinthecosmicweb 3
summingthemomentumofalltheparticlesineachcellandthen Knots Filaments Sheets Voids
dividingbythetotalmassinthatcell.Anormalizedsheartensor
isdefinedateachgridcellpointbyΣ = − 1 (cid:0)∂vα + ∂vβ(cid:1), Vff 0.5% 4.5% 26% 69%
αβ 2H0 ∂rβ ∂rα Nf 6% 28% 45% 21%
whereαandβarethex,y,andzcomponents.TheH0normaliza- Mf 25% 44% 26% 5%
tionisusedtomakethetensordimensionlessandtheminussignis N 17 6.1 1.7 0.3
introducedtomakethepositiveeigenvectorscorrespondtoacon- ρ 72 9.4 0.96 0.08
vergingflow.Thesheartensorisdiagonalizedateachgridpointto
obtain the eigenvalues λ and the corresponding eigenvectors eˆ, Table1.Propertiesofhaloesandthecosmicweb.Wepresent:thevolume
i i
(wherei = 1,2,3andλ1 > λ2 > λ3).Thewebclassificationat fillingfractionVff (thefractionofthetotalvolumeoccupiedbyeachweb
eachgridcellisdonebycountinghowmanyeigenvaluesareabove type),thenumberfractionNf (thefractionofhaloesassignedtoagiven
athresholdλ =0.07,(choseninHoffmanetal2011tovisually web type), the halo mass fraction Mf (the fraction of all halo mass, in
th haloesofeachwebtype),thenumberdensityofhaloesN (thenumberof
reproducethecosmicweb).If0,1,2,or3eigenvaluesareabove
haloesinagivenwebtypedividedbythevolumeoccupiedbythatwebtype,
λ weclassifythegridcellasavoid,sheet,filamentorknotre-
th normalizedbythemeannumberdensityofhaloes),andthemassdensityof
spectively.TheCICvelocityfieldisthengriddedinto2563 cells, haloesρ(thetotalmassofhaloesineachwebtypedividedbythevolume
eachwithalengthof0.25h−1MpcandisthenGaussiansmoothed occupiedbythatwebtype,normalizedbythemeanhalomassdensity).
with a kernel of 0.25 h−1Mpc so as to suppress numerical arti-
factsandspuriouspreferreddirectionsintroducedbythecartesian
grid.NotethattheCICalgorithminherentlysmoothesthediscrete webclassificationsandthehaloesinvoidstendtobelowmass-
particle distribution across eight cells, two for each of the three littleofthemassboundtohaloesatz=0isinvoids.
dimensions. This intrinsic smoothing allows us to use a gaussian
smoothing of 1 grid cell while still suppressing artificial grid ef-
fects.
3 RESULTS
Note that the number of positive eigenvalues corresponds to
thenumberofeigenvectorsalongwhichmassismoving“inwards” Fig.1showsa0.25h−1 Mpcslicethroughthecentreofoursim-
orcollapsing,whilethenumberofnegativeeigenvaluesindicates ulation box. Since each point (grid cell) in space is given a web
expansion.Inthisworkweassumethatif0<λi <λththeeigen- classification,wecanvisualizethecosmicwebbydividingitinto
vectoriscollapsingsoslowlyastobeconsideredexpanding.Thus its constituent components. Fig. 1 reveals the nature of the cos-
knotsandvoidsarecollapsingandexpandinginallthreedirections mic web: knots are fragmented over dense clumps in the puffier
respectively.Filaments,expandalongtheirlongaxis,eˆ3,whilecol- filaments,whichthemselvesinhabitthecentersofevenlessdense
lapsingalongeˆ1andeˆ2whilesheetscollapsealongtheirshortaxis sheets. The filamentary appearance of sheets in Fig. 1 is a result
eˆ1,andexpandintheplanedefinedbyeˆ2andeˆ3. oftheplanarcutofthetwodimensionalmanifold.Althoughitap-
Wefocusontheorientationofhaloangularmomentum(LDM) pears that sheets dominate the environment of haloes this is only
andtheorbitalangularmomentumofsubhaloes(Jsub)withrespect duetotheirlargevolume.InTable1wepresentthepropertiesof
to the cosmic web. Often the word “orientation” is used to mean thecosmicwebintermsofvariousfillingfactors.
theorientationofthesevectors.ForthestudyofLDM onlyvirial- Thistablerevealsthenatureofthehalodistribution-forex-
izedhaloesmoremassivethat109.5M(cid:12)areconsidered;thisreturns ample,althoughvoidsoccupy69%ofthesimulationvolume,only
∼106haloes.Ofthese,∼2.7×104haloescontain∼1.2×105 21% of the haloes are found in voids. Furthermore, these haloes
substructures more massive than 30 particles, that are then used tendtobesmall,makingupjust5%ofthemassboundtohaloes.
inthestudyofJsub.Onlysubhaloeswith>30particlesareused Finallysincethevolumeoccupiedbyvoidsissolarge,thenumber
here (AHF returns converged results for haloes above this limit, densityofhaloeshereis0.3timesthemeanwhilethemassdensity
seeKnebeetal.2011),butnotethatincreasingordecreasingour isjust0.08timesthemeanmassdensityofthehaloesintheuni-
subhaloresolutionto20or200particles,hasnoeffectonourre- verse.Converselyforknots,weseethatalthoughtheyoccupyjust
sults. 0.5%ofthesimulation’svolume,theycontainaquarterofthemass
ThealignmentofLDM andJsub ismeasuredwithrespectto boundtohaloesandare72timesdenserthenthemeandensity.
theeigenvectorsofthesheartensor.Toeachhosthaloacosmicweb Fig.2showsthenormalized(differential)distributionofthe
classificationcanbeassignedbyfindingwithinwhichgridcellthe anglesformedbetweentheprincipalaxesofthecosmicwebwith
haloislocated.Itistheorientationofhalopropertieswithrespect thehaloandsatelliteorbitalangularmomentaL andJ for
DM sub
tothatgridcell’sorthonormalbasisoftheV-webthatisexamined haloesinavarietyofdifferentcosmicwebenvironments.Weper-
here. formedKolmogorov-Smirnoff(KS)teststocheckthenullhypoth-
For the purpose of this Letter we examine only haloes that esis that the distributions are consistent with being drawn from a
arefoundatz = 0withinsheets,filamentsandknots.Weignore random (uniform) distribution. With the exception of the Knots,
theorientationofhaloeswithrespecttovoidsfortworeasons(see thenullhypothesiscanberuledoutathigh(>99.99%)confidence
table1anddiscussioninsection3fordetails):thenumberdensity levels.Weexaminethesepanelsindetailbelow.
ofhaloesinvoidsisexceedinglysmallwhencomparedtotheother In Fig. 2a-c, we show the alignment of L with the three
DM
(cid:13)c 0000RAS,MNRAS000,000–000
4 Libeskindetal.
principleaxesofthecosmicweb.Insheets(Fig.2a)weseeaclear haloestendtoalignwitheˆ andeˆ insheetsandfilamentsandjust
1 3
alignmentwitheˆ anda(slightlyweaker)perpendicularalignment witheˆ inknots.
3 1
witheˆ andeˆ .Thisindicatesthatahalo’sspinaxisliesinthesheet
1 2
alongtheaxisthatiscollapsingslowest(eˆ )andperpendicularto
3
the sheet’s short (normal) axis (eˆ ). KS tests rule out uniformity
1
at a high confidence level for all three axes. When we examine 4 DISCUSSIONANDCONCLUSIONS
the orientation of L in filaments (Fig. 2b) we find a general
DM WehaveexaminedtheorientationofDMspinaxis(L )andthe
DM
weakening of the alignments found in sheets, but the same over
orbitalangularmomentumofsubstructures(J )withrespectto
sub
allpictureprevails-thehalospinaxispointsalongthelongaxis
thecosmicwebinsheets,filamentsandvoids.Ourmainfindings
ofthefilament(eˆ ).Again,KStestsruleoutuniformityatahigh
3 are
confidencelevel.Thealignmentweakensfurtherinknots(Fig.2c)
where the distribution of L is fully consistent with a random • Substructuresorbitsuchthattheirangularmomentatendtobe
DM
orientationwithrespecttoallthreeprincipalaxes(KSprobabilities alignedwiththeintermediateaxisofthewebstructuretheyarein.
of∼20%). If the second axis of the web is parallel to the intermediate axis
ofthematerialthatcollapsedtoformthehaloatturnaround,then
Haloes that live in sheets are aligned perpendicular to the
ourresultisconsistentwithtidaltorquetheory(e.g.Navarroetal.
sheet’sshortaxis,whilefilamenthaloesarealignedparalleltothe
2004).Thisoccursbecausethevelocitysheariscloselyrelatedto
filamentaryaxis,aresultconsistentwithpreviouswork(e.g.Hahn
theinitialconditions.
etal.2007;Arago´n-Calvoetal.2007).Insheets,thisisbecausethe
• InsheetsandfilamentsJ tendstobeperpendiculartothe
shortaxisistheaxisofcollapse,hencetheaxisfromwhichmat- sub
short(eˆ )andlong(eˆ )axisofthecosmicweb,whileinknotsitis
ter is being gravitationally pulled along. If the sheet is squeezed 1 3
perpendicularonlytothelongaxis.Thisindicatesthatinsheetsand
alongthisaxis,itfollowsthattheangularmomentumwillbeper-
filaments,substructuresmoveinjustoneplane(theeˆ -eˆ )whilein
pendicular to eˆ . Yet this interpretation weakens in filaments (as 1 3
1
knotstheplaneoftheirorbitisallowedanyconfigurationparallel
therearetwo“shortaxes”)anddisappearsinknots.Ashaloesare
tothe longaxis,eˆ .This transitionis most likelydue totheran-
drawnintofilamentsandthenknots,theirangularmomentumbe- 1
domizationoforbitsinthehighlynonlinearhalointeriors.
comesrandomized,mostlikelyduetothehighlynonlinearchaotic
• ThespinaxisofaDMhalotendstoalignwiththeshortaxisof
motionspresentindenserenvironments.
thecosmicwebinsheetsandinfilaments,butisconsistentwitha
Fig.2d-fshowsthealignmentofJ ,theorbitalangularmo-
sub randomorientationinhaloesassociatedtoknots.Sinceinsheetsthe
mentum of substructures with the cosmic web. It is immediately
spinaxisliesintheplane,andassumingthatinsheetsthelongand
clear that that J is always aligned parallel to the intermediate
sub intermediateaxesaredegenerate,thisresultisalsoconsistentwith
axis of the cosmic web - this alignment is strongest in filaments
Navarroetal.(2004)(giventhatthereissomecorrelationbetween
yetseeninallwebclassificationsatsignificantKSconfidencelev-
galaxyandhalospin).
elsandisindicativeofsimilarfindingsbyNavarroetal.(2004).In
bothsheetsandfilamentshowever,thereisadditionallya(slightly Ourresultsindicatethatthelargescalevelocitysheartensoris
weaker)perpendicularalignmentwiththesmallandlongaxesof stilladeterminingfactorintheorientationoftheangularmomenta
theweb.Thisindicatesthatsubstructuresareaccreted(andarethus ofsubstructures.AlthoughKnebeetal.(2004)alreadyclaimedthat
moving)inaplanefairlywelldefinedbyeˆ (thesheet’sshortaxis) thepositionofasubhaloatapocenterrecalleditsfilamentaryaccre-
1
andeˆ (thesheet/filamentslongaxis). tionevenafterseveralorbits,thislinkwasnotquantitativelyestab-
3
lishedbythem.Thisresultisalsoconsistentwithanumberofre-
Remarkablytheperpendicularalignmentwitheˆ radicallyand
3
centstudies(Libeskindetal.2011;Vera-Ciroetal.2011)thathave
significantly flips in knots (Fig. 2i). This indicates that although
arguedthatamemoryofthelargescaleenvironmentisimprinted
substructuresareaccretedintheeˆ -eˆ plane,bythetimetheyland
1 3
onz = 0subhaloorbitsandDMhaloes.Yetnoneofthesestud-
inknotstheplanehasnutatedsuchthatJ isperpendiculartojust
sat
ieswereabletodrawadirectparallelbetweenthelargescalesand
eˆ ,themainaxisoftheknot.Theplaneofaccretioninfilaments
1
satelliteorbitsatz = 0,insteadtheyreliedontyingz = 0prop-
iswelldefined-theeˆ -eˆ ,whileinknotsthisplaneisallowedto
1 3
erties of satellite galaxies to the merger history of the host halo.
nutateabouteˆ .
2
Indeedourresultissurprisingsincewedonosuchtrackingbackin
Itisimportanttonotethatthesignificantperpendicularalign-
time.Insteadourresultindicatesthatthelargescalevelocityfield
ment of J with eˆ in knots is strong evidence that the cosmic
sub 1 isreflectedintheorbitsofsubhaloesatz=0.
webiswelldefinedinknots.Thisindicatesthattheuniformdistri-
Sinceasubhaloesz = 0positionisperpendiculartoitsan-
butionofanglesseenbetweenthecosmicwebandL inknots
DM gularmomentum,ourfindingshelpunderstandtherelationshipbe-
(Fig.2c)isindeedduetoarandomizationofL .
DM tweentheanisotropicz = 0spatialdistributionofsatellitegalaxy
Weclosethissectionbynotingthatwealsoexaminedtheori- insimulations(Knebeetal.2004;Libeskindetal.2005;Zentner
entation of substructure position with the cosmic web. Since the etal.2005;Libeskindetal.2007)andobservations(e.g.Sales&
positionvectorisbyconstructionperpendiculartoJ wefinda Lambas 2004; Kroupa et al. 2005, among others) with their ap-
sub
mirror image panels (d)-(e), in otherwords, the positions of sub- parent coherent motion (Metz et al. 2008, 2009; Libeskind et al.
(cid:13)c 0000RAS,MNRAS000,000–000
Haloesinthecosmicweb 5
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nous satellite galaxies that do not enter the halo randomly but in HinshawG.,et.al.2009,ApJS,180,330
somecorrelatedway(e.g.Tormen1997;Li&Helmi2008;Knebe KroupaP.,TheisC.,BoilyC.M.,2005,A&A,431,517
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randomlyaccretedsubhaloesisdeterminedbythecosmicwebat LiY.,HelmiA.,2008,MNRAS,385,1365
z = 0,thusconnectingthelargescalesheets,filamentsandknots Libeskind N. I., Cole S., Frenk C. S., Okamoto T., Jenkins A.,
withthesub-virialradiusscaleofsubhaloorbits.Insummary,The 2007,MNRAS,374,16
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