The bias of the submillimetre galaxy population: SMGs are poor tracers of the most massive structures in the z ~ 2 Universe

2.5 MB·English

by  Tim B. Miller

Mon.Not.R.Astron.Soc.000,1–6(2015) Printed3August2015 (MNLATEXstylefilev2.2)
The bias of the submillimetre galaxy population: SMGs are poor
tracers of the most massive structures in the z 2 Universe
∼
Tim B. Miller1(cid:63), Christopher C. Hayward2,3 , Scott C. Chapman1 and Peter S.
†
Behroozi4
‡
1DepartmentofPhysicsandAtmosphericScience,DalhousieUniversity,6310CoburgRoad,Halifax,NSB3H4R2,Canada
2TAPIR350-17,CaliforniaInstituteofTechnology,1200E.CaliforniaBoulevard,Pasadena,CA91125,USA
3Harvard–SmithsonianCenterforAstrophysics,60GardenStreet,Cambridge,MA02138,USA
4SpaceTelescopeScienceInstitute,3700SanMartinDrive,Baltimore,MD21218,USA
5
1
0
2 AcceptedforpublicationinMNRAS

l
u
J ABSTRACT

1 It is often claimed that overdensities of (or even individual bright) submillimetre-selected
3 galaxies (SMGs) trace the assembly of the most-massive dark matter structures in the Uni-
verse. We test this claim by performing a counts-in-cells analysis of mock SMG catalogues

] derivedfromtheBolshoicosmologicalsimulationtoinvestigatehowwellSMGassociations
A
trace the underlying dark matter structure. We find that SMGs exhibit a relatively complex
G bias: some regions of high SMG overdensity are underdense in terms of dark matter mass,
. and some regions of high dark matter overdensity contain no SMGs. Because of their rar-
h
ity, Poisson noise causes scatter in the SMG overdensity at fixed dark matter overdensity.
p
Consequently,richassociationsofless-luminous,more-abundantgalaxies(i.e.Lyman-break
-
o galaxyanalogues)tracethehighestdarkmatteroverdensitiesmuchbetterthanSMGs.Even
r on average,SMG associationsare relatively poortracers of themost significant darkmatter
st overdensities because of ‘downsizing’: at z (cid:46) 2.5, the most-massive galaxies that reside in
a
thehighestdarkmatteroverdensitieshavealreadyhadtheirstarformationquenchedandare
[
thusnolongerSMGs.Atagivenredshift,ofthe10percentmost-massiveoverdensities,only

2 25percentcontainatleastoneSMG,andlessthanafewpercentcontainmorethanone
∼
v SMG.
5
Key words: cosmology: theory – cosmology: large-scale structure of Universe – galaxies:
0
1 clusters:general–galaxies:high-redshift–methods:numerical–submillimeter:galaxies.
4
0
.
1
0 1 INTRODUCTION the highest-redshift proto-clusters (e.g. Capak et al. 2011; Walter
5 etal.2012).Thus,observationsofbrightSMGsshouldprobetheir
1 Submillimetre-selectedgalaxies(SMGs;seeCaseyetal.2014for
environment and trace significant overdensities that can be inter-
iv: a5×re1c0en12trLe(cid:12)vi,erwep),rewseitnhtttyhpeircaarlesintfarnadremdo(IsRte)xlturmemineoesxitaimespolefsLoIfRst(cid:38)ar pSrMetGedsisnetthcerictiocnatlecxotnosftlraarignets-socnalceosstmruocltougreicsailmmuloadtieolsn.s.Therefore,
X forminggalaxies.TheLIRofanSMGimpliesanimmensestarfor-
r mationrate,typicallySFR∼500−1000M(cid:12)yr−1,assumingthat InterestinSMGassociationshasgrowninrecentyearsasin-
a thereisnotasignificantcontributiontoLIRfromdeeplyobscured creasing numbers of SMG associations have been detected (e.g.
AGN. SMGs allow us to probe the mechanisms behind most in- Blainetal.2004;Chapmanetal.2005;Chapmanetal.2009;Geach
tense star formation events in the Universe and can elucidate the etal.2005;Daddietal.2009;Dannerbaueretal.2014;MacKen-
highestSFRssustainableinagalaxy.Becauseoftheirextremena- zie et al. 2014; Smail et al. 2014). Furthermore, Clements et al.
ture,SMGsprovidelaboratoriestotestthelimitsofhydrodynam- (2014)havedemonstratedthatsomePlancksourcestraceoverden-
icalsimulationsofgalaxies(e.g.Narayananetal.2010;Hayward sitiesofdustystar-forminggalaxies,andtheysuggestedthatsuch
etal.2011;Hayward2013). observations can be used to investigate the epoch of galaxy clus-
Massivestarburstgalaxiesappeartogrowinthemostmassive ter formation. However, this claim relies on the assumption that
halos(Hickoxetal.2012),thusmakingthempotentialtracersfor overdensitiesofdustystar-forminggalaxiescorrespondtogalaxy
clustersintheprocessofformation.
(cid:63) E-mail:[email protected] Thereissomeobservationalevidencethatcallsthisclaiminto
† MoorePrizePostdoctoralScholarinTheoreticalAstrophysics question: in their study of the GOODS-N field, Chapman et al.
‡ GiacconiFellow (2009)foundanassociationof8SMGsatz ≈ 1.99.Theassoci-
(cid:13)c 2015RAS
2 Miller,Hayward,Chapman&Behroozi
atedstructurewasonlyatypicaloverdenseregion,asindicatedby
thewell-sampledopticalspectroscopyinthisregion,thatwouldnot 8
SMG
formavirializedclusterbyz = 0.Moreover,Blainetal.(2004)
6 RandomLBG
foofuenvdoltvheadt t‘heextrcelumsetelyrinrgedleonbgjethctso’f(SEMROGss)iastczon∼sist1enatnwdizth=tha0t alaxy 4 LBG
g
clusters,whichwouldsuggestthatthedescendantsofSMGswould δ 2
tendtobefoundinrichclusterenvironments;however,thisinter- 0
pretation implies a comoving space density of clusters that is at
50
least an order of magnitude greater than that observed. These re-
40
sultssuggestthatperhapsassociationsofSMGstraceparticularly
active phases in relatively modest-mass overdensities rather than galaxy 2300
thehighestoverdensitiesandthushavearelativelycomplexclus- δ
10
teringbias. 0
To test this possibility, we have performed a counts-in-cells
analysis on the Hayward et al. (2013a, hereafter H13) simulated 2 0 2 4 6 8 10
−
SMGcataloguestoinvestigatetherelationshipsofSMGsandmore δmass
modestlystar-forminggalaxiestotheunderlyingdarkmatterstruc-
ture.WefirstinvestigatetheclusteringbiasesofSMGsandLyman- Figure1.Top:OverdensityofLBGs(0.1mJy<S850 <1mJy)vs.over-
break-galaxy(LBG)analogues.Wethenstudythepropertiesofin- densityofdarkmatter,δmass,fortherandomcells.Thereisaclearcorrela-
dividualassociationsofSMGsandLBGanalogues. tionbetweenδgalaxyandδmass,whichindicatesthattheclusteringofthe
LBGstracestheclusteringofthedarkmatterwell.Bottom:Similartothe
toppanel,butforSMGs(S850 >3mJy;redcircles)andarandomsubset
ofLBGsselectedtohavenumberdensityequaltothatoftheSMGs(blue
2 METHODS
diamonds).(TheSMGpointshavebeenshiftedupwardsby5forclarity.)
ToanalyzethebiasintheSMGpopulation,weusethemockSMG TheSMGsandrandomsubsetofLBGsexhibitalargescatterinδgalaxy
atagivenδmass.ThisresultindicatesthatbecauseoftherarityofSMGs,
cataloguesofH13,whichweregeneratedbyassigninggalaxyprop-
PoissonnoisecausesSMGoverdensitiestobepoortracersofdarkmatter
ertiestodarkmatterhaloesfromacosmologicalcollisionlessdark
overdensities.
mattersimulationusingsubhaloabundancematchingandthenas-
signingsubmmfluxdensitiesusingafittingfunctionderivedfrom
the results of performing radiative transfer on idealized hydrody- mJy is ∼ 140 M(cid:12)yr−1) and those with 0.1 < S850 < 1
namical simulations. We will summarize the H13 methodology
mJy as LBGs (this range corresponds to median SFR values of
here,andwereferthereadertoH13forfulldetails. ∼10−50M(cid:12)yr−1).WestudythebiasofSMGsandLBGsand
Using halo catalogues from the Bolshoi simulation (Klypin,
identifySMGandLBGassociations(orredshiftspikes;e.g.Chap-
Trujillo-Gomez, & Primack 2011; Behroozi et al. 2013b,c), we
man et al. 2005; Chapman et al. 2009) using a simple counts-in-
constructedmocklightconesbystartingateightrandomlocations
cellsanalysis(e.g.Adelbergeretal.1998).Specifically,wedivide
within the simulation and selecting haloes along a randomly ori-
eachofthe8mockcataloguesintocellswithangulardimensions
ented sightline with an 84’ x 84’ (1.96 deg2) field of view from 10arcmin×10arcminanddepthdz=0.05;theresultsaresimilar
z = 0.5toz = 8.Wecalculatedcosmologicalredshifts,includ-
ifweusecellswithsidelengthsequaltotwicethesevalues.Weuse
ingtheeffectsofhalopeculiarvelocities.Wethenassignedstellar
asubsetof10,000ofthesecellsforcalculatingtheclusteringbias
masses(M(cid:63))andSFRsusingtheredshift-dependentstellarmass– and for making comparisons to the properties of SMG and LBG
halomassandSFR–halomassrelationsofBehroozi,Wechsler,&
associations;werefertothesecellsas‘randomcells’.Toidentify
Conroy(2013a),whichincludescatteratfixedhalomassandred-
associations,westartwiththesamecells.However,toensurethat
shift.Weincludedasimplemodelforsatellitequenching:satellite
we do not divide potential associations by using a fixed grid, we
SFRswerereducedbyafactorequaltotheircurrentsubhalomass
shiftthecellsby1-arcminintervals10timesanddefineanSMG
dividedbythepeakmassintheirsubhalo’smassaccretionhistory.
(LBG)associationasthegalaxiescontainedinthecellthatcontains
Weassigneddustmasses(Md)tothehaloesusingtheempirically themaximumnumberofSMGs(LBGs).Weensurethatwedonot
basedmethodofHaywardetal.(2013b).Finally,weassigned850-
countasingleassociationmultipletimes.Wecalculatetotaldark
µmfluxdensities(S850)usingthefollowingfittingfunction,which mattermassesforeachcellbysummingthedarkmattermassesof
wasderivedbasedontheresultsofperformingdustradiativetrans- allhaloesofmass> 1010 M(cid:12) (becausetheBolshoisimulationis
fer on hydrodynamical simulations of idealized disc galaxies and
incompletebelowthishalomass)containedinthecell.
mergers(Haywardetal.2011,2013b):
As discussed in detail in H13, the H13 model does not in-
(cid:18) (cid:19)0.43(cid:18) (cid:19)0.54 clude the effect of starbursts (i.e. the extended tail to high SFR
SFR M
S850 =0.81mJy 100 M yr−1 108Md , (1) at a given stellar mass and redshift). Because one would expect
(cid:12) (cid:12)
thatinteraction-inducedstarburstswouldmostaffecttheSFRsof
whereweincorporatedthescatterintherelationof0.13dex(Hay- SMGsinhighlyoverdenseregionsandthuspotentiallyalterourre-
ward et al. 2011) when assigning S850. Note that because S850 sults,wehaveextendedtheH13modelbyincludingamodelfor
scalessublinearlywithbothSFRandMd,thepredictedS850 val- interaction-inducedstarbursts.Foreachgalaxy,wecheckwhether
uesarerelativelyinsensitivetothemodeldetails.Furthermore,the ithasaneighboringgalaxywithstellarmasswithinafactorof3of
S850–M(cid:63) relation predicted in this manner agrees well with that itsown(suchthatthepairwouldconstitutea‘major’merger)that
observed(Daviesetal.2013). is located within a physical distance of dweak. If so, the SFRs of
Throughoutthiswork,werefertomockgalaxieswithS850 > bothgalaxiesareboostedbyafactorofbweak.Iftheseparationis
3 mJy as SMGs (the median SFR for sources with S850 ∼ 3 lessthandstrong < dweak,weinsteadboosttheSFRsbyalarger
(cid:13)c 2015RAS,MNRAS000,1–6
SMGsastracersoflarge-scalestructure 3
10 10
Mass=1.9z9=⇥21.30914(M�/h) SMGs Mass=8.6z1=×21.30313(M(cid:12)/h) SMGs
5 5
n) n)
mi mi
c c
ar 0 ar 0
( (
C C
E E
D D
5 5
� −
10 10
� 10 5 0 5 10 − 10 5 0 5 10
� � − −
RA(arcmin) RA(arcmin)
Figure2.Spatialdistributionsofgalaxiesnearthe2richestSMGassociations(whicheachcontain6SMGs;thecellsaremarkedwithdashedlines).The
SMGs(LBGs)aredenotedwithred(blue)points,thesizesofwhichareproportionaltoS850.Thespatialdistributionsofthegalaxiesreflectthefilamentary
structureofthedarkmatterdistribution.
factor,bstrong >bweak.Weexperimentedwithdifferentreasonable Table1.DemographicsofSMGassociations
parametervalues,asjudgedbasedontheresultsofidealizedhydro-
dynamicalsimulationsofmergers(e.g.Coxetal.2008;Torreyetal. NSMGa Percentageb Massc Separationd
2012;Haywardetal.2014),andfoundthattheresultswerequal- (1013M(cid:12)) (Mpc)
itativelyunaffectedevenfortheextremescenarioofdweak = 15
kpc,bweak =10,dstrong =5kpc,anddstrong =100.However,it 1 64 5.9±3.0 –
2 23 7.7±3.6 7.6
isimportanttonotethatthecataloguesareincompleteformergers
3 10 9.1±4.7 6.1
withsmallseparations(Behroozietal.2013b),whichwouldresult
4 2 10.3±2.8 5.2
inanunderestimateofthenumberofinteractinggalaxies.Never-
5 0.8 12.6±2.6 4.3
theless, this incompleteness likely does not affect our results be-
6 0.2 14.1±5.6 4.6
causealthoughinteractionscouldboostthesubmmfluxesofsome
galaxiesandincreasetheclusteringsignalon(cid:46)10kpcscales,the aNumberofSMGsinacell. bPercentageofSMGsinsuchas-
clusteringonlargerscalesshouldbeunaffected.Inallfigures,we sociations. cMedianmassofsuchassociationsat2<z <3.
showtheresultsfortheoriginalH13model,butthecorresponding dMedianpairwiseseparationsofSMGsinsuchassociations.
plotsfortheboostedmodelsaresimilar.
blendNinogteotfhamtuulntilpikleegHa1la3x,iweseihnatvoeanositnignlceosrpuobrmatmedstohuerceeffeinctsthoisf δmass = MDM<−M<DMM>DM >, (3)
work,althoughtheoreticalarguments(Haywardetal.2011,2012, whereMDMisthemassofdarkmatterinacelland<MDM >is
2013b;H13)andobservations(e.g.Karimetal.2013;Hodgeetal. themeandarkmattermasspercell.
2013) suggest that blending significantly affects the single-dish- Fig.1showstheoverdensityδgalaxyofSMGs(S850 >3mJy;
detectedSMGpopulation.Thereasonisthatthesizesoftheassoci- redcircles),LBGs(0.1mJy<S850 <1mJy;blackdiamonds)and
ationsaremuchgreaterthanthebeamsizesofsingle-dishsubmm arandomsubsetofLBGsselectedtohavenumberdensityequalto
telescopes (see below). Thus, although the detailed results could thatoftheSMGs(bluediamonds)vs.overdensityofdarkmatter,
be affected by blending, our conclusions would be unchanged if δmass,fortherandomcells.ForthetotalLBGpopulation,δgalaxy
blendingwereincorporated.Furthermore,wewishtoanalyzehow and δmass are tightly correlated, which indicates that LBG over-
well individual submm-bright galaxies, which would be resolved densitiesaregoodtracersofdarkmatteroverdensities.Theslope
by e.g. the Atacama Large Millimeter Array, rather than blended ofthebest-fittinglinearrelation(i.e.thebias,b ≡ δgalaxy/δmass)
submmsources(whichdependonthebeamsizeoftheinstrument is0.98±0.01,andthemeansquarederror(MSE)is0.1.Forthe
usedtodetectthemandarethusalessgeneralpopulationthanre- SMGsandrandomsubsetofLBGs,thereisacorrelationbetween
solvedsources)tracedarkmatterstructures. δgalaxyandδmass,butitexhibitssignificantscatter.Thebiasvalues
are1.3±0.1and1.0±0.1fortheSMGsandLBGs,respectively,
andtheMSEvaluesare17and16.ThefactthattheSMGsandran-
domLBGsexhibitsimilarscatterindicatesthatPoissonnoisedue
3 RESULTS
to the rarity of SMGs is the reason for the complicated relation-
For each cell, we calculate the number overdensity of SMGs shipbetweenδgalaxyandδmassforthispopulation.Thus,although
(δSMG)andLBGs(δLBG)usingthefollowingequation: SMGsareslightlymorebiasedthanLBGs,SMGoverdensitiesare
poortracersoftheunderlyingdarkmatteroverdensities.Thisef-
N −<N >
δgalaxy = gala<xyN ga>laxy , (2) fectmayexplaintheresultsofBlainetal.(2004)discussedabove.
galaxy We now investigate the properties of individual SMG and
whereNgalaxyisthenumberofgalaxiesinacelland<Ngalaxy > LBG redshift associations in detail. Table 1 presents the fraction
isthemeannumberofgalaxiespercell.Wealsocalculatethedark ofSMGsinassociationsandthemedianseparationoftheSMGs
mattermassoverdensityofeachcell, inthedifferenttypesofassociations.TypicalSMGsarenotinas-
(cid:13)c 2015RAS,MNRAS000,1–6
4 Miller,Hayward,Chapman&Behroozi
15 10
Random Random
N 150 ≥≥100519LS5MBLGGBssGs N 5 134-SS2MMSMGGssGs
5SMGs
1015 1015 6SMGs
h) h)
/ /
(cid:12) �
M M
( (
s s
s s
a a
m 1014 m 1014
er er
att att
m m
k k
ar ar
D D
1013 1013
1.5 2.0 2.5 3.0 3.5 3 6 9 12 1.5 2.0 2.5 3.0 3.5 5 10
z N z N
Figure3.Left:totaldarkmattermassinacellversusredshiftofthecellforcellsthatcontain(cid:62)5SMGs(redcircles),cellswith(cid:62)195LBGs(thisnumberwas
selectedtoyieldthe10richestLBGassociations;blackcircles),cellsthatcontainexactly100LBGs(greencircles)andrandomlyselectedcells(bluepoints).
Theredshiftanddarkmattermassdistributionsareshownnexttotherespectiveaxes.ComparedwiththerichestLBGassociations,theSMGassociations
traceless-massive,higher-redshiftstructures.Associationsof100LBGstracelower-massdarkmattersubstructuresthatspanthefullredshiftrangeconsidered.
Right:similartotheleftpanel,butwithcellsclassifiedaccordingtothenumberofSMGsthattheycontain.CellswithlowernumbersofSMGstendtoinclude
lessdarkmatter.Notably,someofthemostoverdenseregionscontainnoSMGs.
sociations,butasubstantialminority(36percent)are.Onlyafew thanthevaluesfortheSMGassociations,whereastherichestLBG
percentofSMGsarelocatedinrichassociationsoffourormore associations more faithfully trace the cells with the largest dark
SMGs. The richer associations exhibit lower median separations, mattermasses.
whichsuggeststhattheseassociationscorrespondtohigherover- Forcomparison,weshowmore-modestLBGassociationsthat
densities(whichwillbeconfirmedbelow).Fig.2showsthespatial containexactly100LBGs(greencircles).Asexpected,theseLBG
distributions of the SMGs and LBGs in two mock SMG associ- associationstracelessmassivesubstructuresthantherichestLBG
ations.Theassociationseachcontain6SMGs.Thespatialdistri- associations.Themediandarkmattermassofthe100-LBGassoci-
butionsofthegalaxiesexhibitclearfilamentarystructures,which ationsissimilartothatoftheSMGassociations,9.1×1013 M(cid:12),
reflecttheunderlyingstructureofthe‘cosmicweb’.Notethatin- butthe100-LBGassociationsspanabroaderrangeofredshifts.
corporatingblending(usingatypicalbeamof(cid:46)30arcsec)would The right panel of Fig. 3 shows the total dark matter mass
tendtoincreasethesubmmfluxesoftheLBGsandblendtheSMGs in a cell versus redshift of the cell for cells that contain one or
withLBGs,butitwouldnotblendanyofthebrightSMGs.Thus,a moreSMGs(colouredaccordingthenumberofSMGs).Thisfigure
blendedversionwouldpotentiallycontainadditionalbrightSMGs demonstratesmultipleinterestingresults:first,manyofthehighest
and therefore be comparable to observed SMG associations (e.g. darkmatteroverdensitiesatagivenredshiftcontainnoSMGs(the
Chapmanetal.2009;Dannerbaueretal.2014). bluepointswithdarkmattermass(cid:38)2×1014M(cid:12)).Atagivenred-
OurgoalistounderstandhowwellSMGassociationstracethe shift,ofthe10percentmost-massiveoverdensities,only∼25per
highestdarkmatteroverdensities.Todoso,itisinstructivetocom- centcontainatleastoneSMG,andlessthanafewpercentcontain
parethetotaldarkmattermassinindividualcellsthatareidentified morethanoneSMG.Consequently,findingdarkmatteroverdensi-
asSMGorLBGassociationswiththevaluesforrandomlyselected tiesusingSMGsassignpostswillcauseonetomissmanyofthe
cells.IfSMGassociationstracethemostsignificantoverdensities, highestoverdensities.Second,cellswithlowernumbersofSMGs
thesecellsshouldcontainmoredarkmattermassthanothercells tendtohavelessdarkmatter.Finally,theminimummassnecessary
at a given redshift. The left panel of Fig. 3 shows the total dark foracelltohostanSMGis∼1013M(cid:12),whichisconsistentwith
matter in a given cell versus the redshift of the cell for cells that theresultsofinferencesfromtheclusteringofrealSMGs(Hickox
contain(cid:62) 5SMGs(redcircles),the10richestLBGassociations etal.2012).
((cid:62)195LBGsinacell;blackcircles),cellsthatcontainexactly100
LBGs(greencircles),andasubsetofrandomlyselectedcells(blue
points).Theredshiftanddarkmattermassdistributionsareshown
4 SUMMARYANDDISCUSSION
nexttotherespectiveaxes.
ItisimmediatelyclearthattheSMGassociationsdonottrace WehaveusedmockSMGcataloguestodemonstratethatSMGas-
the most significant dark matter overdensities, although they do sociationsarepoortracersofthehighestoverdensitiesofdarkmat-
tracerelativelyhighoverdensities.ComparedwiththerichestLBG ter. At higher redshifts (z (cid:38) 2.5), the richest SMG associations
associations, which should be considered analogous to observed tracesomeofthehighestoverdensitiesbecausethemost-massive
associations (i.e. redshift spikes) of LBGs, the SMG associations galaxiesinthoseregionsarestillformingstarsrapidly.However,
tendtohavelowerdarkmattermasses(amedianof1.2×1014M(cid:12) such associations are rare, and the majority of the highest over-
fortheSMGassociationscomparedwith2.2×1014 M(cid:12) forthe densitiesdonothostasingleSMG,letaloneanSMGassociation.
(cid:62) 195−LBGassociations)andarelocatedathigherredshifts(the Consequently,SMGassociationsarehighlyincompletetracersof
medianvaluesfortheSMGandLBGassociationsare2.4and2.0, thehighestoverdensitiesevenatz (cid:38) 2.5.Thesituationisworse
respectively).Furthermore,therearemanyrandomlyselectedcells at z (cid:46) 2.5: many of the most-massive galaxies, which reside in
thathavedarkmattermassesthatarecomparabletoorevengreater the highest dark matter overdensities, have already had their star
(cid:13)c 2015RAS,MNRAS000,1–6
SMGsastracersoflarge-scalestructure 5
formationquenched.(Independentlyofredshift,thehaloswiththe anisotropies Cowley et al. (2015b) than did the previous model,
highest ratio of SFR to halo mass are those with halo masses of whichsuggests(perhapsunsurprisingly)thattheCIBmayprovide
∼ 1012 M(cid:12) at that redshift; e.g. Behroozi et al. 2013a; Moster moreinsightintothenatureofSMGsthanclusteringdoes.
et al. 2013; Sparre et al. 2015.) Consequently, the z (cid:46) 2.5 dark Granatoetal.(2014)performeddustradiativetransferonsim-
matteroverdensitiesarelesslikelytocontainSMGs. ulated (proto-)clusters at z (cid:38) 1 to determine whether they could
In our model, galaxy SFRs are assigned using a redshift- reproducethepropertiesofthePlanck sourcesofClementsetal.
dependent SFR–halo mass relation and a model for satellite (2014).Theyfoundthattheirsimulated(proto-)clustershadlower
quenching. The parameters of the model are constrained by fit- totalSFRsthaninferredfromobservations.Thistensionsuggests
ting to a wide range of observations (Behroozi et al. 2013a). that associations of dusty galaxies should be investigated further
Consequently, the fact that some fraction of massive galaxies are bothintermsoftheoryandobservation.
quenched even at z ∼ 2 is not a prediction. The utility of our It is worthwhile to clarify why we have claimed that SMGs
model is that it can be used to determine the consequences of are ‘poor tracers’ of high overdensities. In our model, the (cid:62) 5-
quenching/downsizing for the clustering of the SMG population. SMGassociationseachlieinoneofthemost-massivecellsattheir
Furthermore, because we determine the submm flux densities of respectiveredshifts.Inthissense,SMGassociationsdotracehigh
ourgalaxiesself-consistentlyusingafittingfunctionderivedfrom overdensities.However,suchassociationsareuncommon(thereare
radiative transfer calculations, there is not a monotonic mapping 11inour∼16−deg2mockcatalogue),whichisconsistentwiththe
betweenSFRandsubmmfluxdensity(agalaxywitharelatively factthatonlyafewoverdensitiesof(cid:62) 5brightSMGshavebeen
modest SFR can still be submm-bright if it has sufficiently high reportedintheliterature(Tamuraetal.2009;Chapmanetal.2009;
dust mass). Thus, the results are specific to the SMG population Dannerbaueretal.2009;Maetal.2015).Moreover,atz (cid:46) 2.5,
rather than just the most rapidly star-forming galaxies (cf. Dave´ almostnoneofthehighestoverdensitiescontain>3SMGsdespite
etal.2010).Finally,ourmodelexplicitlyaccountsforthestochas- alargefractionoftheSMGpopulationbeinglocatedatz (cid:46) 2.5.
ticitythatisinherentintheSMGselectionbecausebrightSMGsare Thus,searchingforhighoverdensitiesusingSMGassociationsas
anextremepopulation;thus,onemayselectagalaxyasanSMG beaconswouldresultinaveryincompletesampleatbest.
because it is in a short-lived phase of elevated SFR (perhaps due Overall,ourresultsurgecautionwheninterpretingSMGas-
toaninteraction)orbecauseithasanespeciallyhighsubmmflux sociationsinthecontextoflarge-scalestructure.Becauseoftheir
densityforitsSFRanddustmass(becauseofe.g.anespeciallyex- rarity,PoissonnoisecausessignificantscatterintheSMGoverden-
tendedgeometry).GN20couldbeareal-Universeexampleofthe sityatfixeddarkmatteroverdensity(i.e.SMGsstochasticallysam-
latter.Consequently,Poissonnoisecontributestothescatterinthe plethehighestoverdensities).Consequently,althoughthehighest-
valueofδSMG atagivenδmass andcausessomeofthemostsig- redshift SMG associations trace some of the highest dark matter
nificantoverdensitiestocontainfewornobrightSMGs.Moreover, overdensities at those redshifts, most of the highest overdensities
ourmodelsuggeststhatsomethebrightestSMGsintheUniverse do not host SMG associations. At lower redshifts (z (cid:46) 2.5), the
maylieinrelativelyisolatedmassivedarkmatterhalos,consistent situationisworse:thehighestoverdensitiestendtocontainonlya
withobservationalfindings(Chapmanetal.2015). fewSMGsatmost,andthemajoritydonotcontainasingleSMG.
A few other theoretical works have investigated the cluster- Thus,ifonewishestoidentifyprotoclusters,thecomplicatedbias
ingoftheSMGpopulation.Dave´ etal.(2010)studiedtheproper- ofSMGsmakesthemless-than-idealbeacons.
tiesofthemostrapidlystar-forminggalaxies,whichtheyconsid-
ered SMG analogues, in a cosmological hydrodynamical simula-
tion.Becauseofthetight,monotonicSFR–stellarmassrelationfor
star-forminggalaxiesintheirsimulation,theyeffectivelyselected ACKNOWLEDGEMENTS
themost-massivestar-forminggalaxiesintheirsimulation.Conse-
We thank Neal Katz for useful discussion and Phil Hopkins
quently, they found that their simulated SMGs were highly clus-
teredandbiased,withacorrelationlengthr0 ≈ 10h−1 comoving forcommentsonthemanuscript.Wethanktheanonymousreferee
foraconstructivereportthathelpedimprovethemanuscript.CCH
Mpcandbiasof∼6.
isgratefultotheGordonandBettyMooreFoundationforfinancial
Cowleyetal.(2015b)analyzedtheclusteringofSMGsinthe
supportandacknowledgesthehospitalityoftheAspenCenterfor
currentDurhamsemi-analyticalmodel(Cowleyetal.2015a;Lacey
Physics, which is supported by the National Science Foundation
etal.,inpreparation).Inthismodel,bright(S850 >4mJy)SMGs
atz ∼ 2.5exhibitacorrelationlengthofr0 = 5.5h−1 Mpcand Grant No.PHY-1066293. PSB was supportedby a Giacconi Fel-
lowship provided through the Space Telescope Science Institute,
a bias of ∼ 2.5. Both the correlation length and bias are almost
whichisoperatedbytheAssociationofUniversitiesforResearch
independentofS850(atleastforS850 >0.25mJy),whichisqual-
inAstronomyunderNASAcontractNAS5-26555.
itativelyconsistentwithourresults(i.e.galaxiesinhighoverden-
sitiesarenotnecessarilysubmm-bright).Interestingly,similarre-
REFERENCES
sults were obtained for a previous version of the model in which
the physical nature of the SMGs was qualitatively very different AdelbergerK.L.,SteidelC.C.,GiavaliscoM.,DickinsonM.,PettiniM.,
(Almeidaetal.2011).1However,thecurrentmodelbettermatches KelloggM.,1998,ApJ,505,18
theangularpowerspectrumofcosmicinfraredbackground(CIB) AlmeidaC.,BaughC.M.,LaceyC.G.,2011,MNRAS,1312
BehrooziP.S.,WechslerR.H.,ConroyC.,2013a,ApJ,770,57
BehrooziP.S.,WechslerR.H.,WuH.-Y.,2013b,ApJ,762,109
BehrooziP.S.,WechslerR.H.,WuH.-Y.,BushaM.T.,KlypinA.A.,
1 Inthecurrentmodel,SMGsarepredominantlystarburstsdrivenbydisk PrimackJ.R.,2013c,ApJ,763,18
instabilities,andamildlytop-heavyinitialmassfunctionisusedinstar- BlainA.W.,ChapmanS.C.,SmailI.,IvisonR.,2004,ApJ,611,725
bursts. In the previous model, SMGs were predominantly very gas-rich CapakP.L.etal.,2011,Nature,470,233
galaxiesundergoingstarburstsdrivenbyminormergers,andaflatIMFwas CaseyC.M.,NarayananD.,CoorayA.,2014,PhysRep,541,45
assumedforstarbursts. ChapmanS.C.etal.,2015,arXiv:1503.02195
(cid:13)c 2015RAS,MNRAS000,1–6
6 Miller,Hayward,Chapman&Behroozi
ChapmanS.C.,BlainA.,IbataR.,IvisonR.J.,SmailI.,MorrisonG.,
2009,ApJ,691,560
ChapmanS.C.,BlainA.W.,SmailI.,IvisonR.J.,2005,ApJ,622,772
ClementsD.L.etal.,2014,MNRAS,439,1193
CowleyW.I.,LaceyC.G.,BaughC.M.,ColeS.,2015a,MNRAS,446,
1784
CowleyW.I.,LaceyC.G.,BaughC.M.,ColeS.,2015b,ArXive-prints
CoxT.J.,JonssonP.,SomervilleR.S.,PrimackJ.R.,DekelA.,2008,
MNRAS,384,386
DaddiE.etal.,2009,ApJ,694,1517
DannerbauerH.,DaddiE.,RiechersD.A.,WalterF.,CarilliC.L.,Dick-
insonM.,ElbazD.,MorrisonG.E.,2009,ApJL,698,L178
DannerbauerH.etal.,2014,A&A,570,A55
Dave´R.,FinlatorK.,OppenheimerB.D.,FardalM.,KatzN.,KeresˇD.,
WeinbergD.H.,2010,MNRAS,404,1355
DaviesL.J.M.,BremerM.N.,StanwayE.R.,LehnertM.D.,2013,MN-
RAS,433,2588
GeachJ.E.etal.,2005,MNRAS,363,1398
GranatoG.L.,Ragone-FigueroaC.,Dominguez-TenreiroR.,ObrejaA.,
BorganiS.,DeLuciaG.,MuranteG.,2014,arXiv:1412.6105
HaywardC.C.,2013,MNRAS,432,L85
HaywardC.C.,BehrooziP.S.,SomervilleR.S.,PrimackJ.R.,Moreno
J.,WechslerR.H.,2013a,MNRAS,434,2572(H13)
HaywardC.C.,JonssonP.,KeresˇD.,MagnelliB.,HernquistL.,CoxT.J.,
2012,MNRAS,424,951
HaywardC.C.,KeresˇD.,JonssonP.,NarayananD.,CoxT.J.,Hernquist
L.,2011,ApJ,743,159
HaywardC.C.,NarayananD.,KeresˇD.,JonssonP.,HopkinsP.F.,Cox
T.J.,HernquistL.,2013b,MNRAS,428,2529
Hayward C. C., Torrey P., Springel V., Hernquist L., Vogelsberger M.,
2014,MNRAS,442,1992
HickoxR.C.etal.,2012,MNRAS,421,284
HodgeJ.A.etal.,2013,ApJ,768,91
KarimA.etal.,2013,MNRAS,432,2
KlypinA.A.,Trujillo-GomezS.,PrimackJ.,2011,ApJ,740,102
MaC.-J.etal.,2015,ArXive-prints
MacKenzieT.P.etal.,2014,MNRAS,445,201
MosterB.P.,NaabT.,WhiteS.D.M.,2013,MNRAS,428,3121
Narayanan D., Hayward C. C., Cox T. J., Hernquist L., Jonsson P.,
YoungerJ.D.,GrovesB.,2010,MNRAS,401,1613
SmailI.etal.,2014,ApJ,782,19
SparreM.etal.,2015,MNRAS,447,3548
TamuraY.etal.,2009,Nature,459,61
TorreyP.,CoxT.J.,KewleyL.,HernquistL.,2012,ApJ,746,108
WalterF.etal.,2012,Nature,486,233
(cid:13)c 2015RAS,MNRAS000,1–6