The clustering and evolution of H-alpha emitters at z~1 from HiZELS

2.8 MB·English

by  David Sobral

Mon.Not.R.Astron.Soc.000,1–13(2009) Printed15January2010 (MNLATEXstylefilev2.2)
The clustering and evolution of Hα emitters at z ∼ 1 from HiZELS(cid:63)
David Sobral1†, Philip N. Best1, James E. Geach2, Ian Smail2, Michele Cirasuolo3,
Timothy Garn1, Gavin B. Dalton4,5 and Jaron Kurk6
1SUPA,InstituteforAstronomy,RoyalObservatoryofEdinburgh,BlackfordHill,Edinburgh,EH93HJ,UK
0
2InstituteforComputationalCosmology,DurhamUniversity,SouthRoad,Durham,DH13LE,UK
1
3AstronomyTechnologyCentre,RoyalObservatoryofEdinburgh,BlackfordHill,Edinburgh,EH93HJ,UK
0
4Astrophysics,DepartmentofPhysics,KebleRoad,Oxford,OX13RH,UK
2
5SpaceScienceandTechnology,RutherfordAppletonLaboratory,HSIC,Didcot,OX110QX,UK

n 6Max-Planck-Institutfu¨rExtraterrestrischePhysik,Postfach1312,85741Garching,Germany
a
J

5
1
Accepted2010January18.Received2010January15;inoriginalform2009December21

]
O
ABSTRACT
C
. The clustering properties of a well-defined sample of 734 Hα emitters at z = 0.845±
h
p 0.015, obtained as part of the Hi-z Emission Line Survey (HiZELS), are investigated. The
- spatial correlation function of these Hα emitters is very well-described by the power law
o ξ =(r/r )−1.8,withareal-spacecorrelation,r ,of2.7±0.3h−1Mpc.Thecorrelationlength
0 0
tr r0increasesstronglywithHαluminosity(LHα),fromr0 ∼2h−1Mpcforthemostquiescent
s galaxies(star-formationratesof∼4M yr−1),uptor >5h−1Mpcforthebrightestgalax-
a (cid:12) 0
[ ies in Hα. The correlation length also increases with increasing rest-frame K-band (MK)
luminosity,butther -L correlationmaintainsitsfullstatisticalsignificanceatfixedM .
0 Hα K
2 Atz =0.84,star-forminggalaxiesclassifiedasirregularsormergersaremuchmoreclustered
v
thandiscsandnon-mergers,respectively;however,oncethesamplesarematchedinL and
Hα
8
M ,thedifferencesvanish,implyingthattheclusteringisindependentofmorphologicaltype
8 K
at z ∼ 1 just as in the local Universe. The typical Hα emitters found at z = 0.84 reside in
8
dark-matter haloes of ≈ 1012M , but those with the highest SFRs reside in more massive
3 (cid:12)
. haloes of ≈ 1013M(cid:12). The results are compared with those of Hα surveys at different red-
2 shifts: although the break of the Hα luminosity function L∗ evolves by a factor of ∼ 30
1 fromz =0.24toz =2.23,iftheHαluminositiesateachredHsαhiftarescaledbyL∗ (z)then
9 Hα
the correlation lengths indicate that, independently of cosmic time, galaxies with the same
0
(L )/L∗ (z)arefoundindarkmatterhaloesofsimilarmasses.Thisnotonlyconfirmsthat
: Hα Hα
v thestar-formationefficiencyinhighredshifthaloesishigherthanlocally,butalsosuggestsa
i fundamentalconnectionbetweenthestrongnegativeevolutionofL∗ sincez =2.23andthe
X Hα
quenchingofstar-formationingalaxiesresidingwithindark-matterhaloessignificantlymore
ar massivethan1012M(cid:12)atanygivenepoch.
Keywords: galaxies:high-redshift,galaxies:cosmology:observations,galaxies:evolution.
1 INTRODUCTION masses(Mo&White1996;Shethetal.2001)andtosuggestlinks
betweenpopulationsfoundatdifferentepochs.
InaUniversedominatedbycolddarkmatter,galaxiesarefoundin
Wide surveys of the nearby Universe (e.g. 2dF, SDSS; Col-
darkmatterhaloeswithastructuredeterminedbyuniversalscaling
lessetal.2001;Yorketal.2000)havenowassembledextremely
relations(e.g.Navarroetal.1996).Sincebaryonstracetheunder-
largesamplesofgalaxieswhichcanbeexploredtostudytheirclus-
lying distribution of dark matter, measurements of the clustering
tering properties in great detail. Using those data, several studies
ofbaryonicmattercanbeusedtoextracttypicaldark-matterhalo
have found that the amplitude of the two-point correlation func-
tionrisescontinuouslywithgalaxyluminosity(e.g.Norbergetal.
2001;Zehavietal.2005;Lietal.2006).Theyalsorevealthatthe
mostrapidincreaseoccursabovethecharacteristicluminosity,L∗.
(cid:63) ThisworkisbasedonobservationsobtainedusingtheWideFieldCAm-
Red galaxies are found to be more clustered than blue galaxies,
era(WFCAM)onthe3.8mUnitedKingdomInfraredTelescope(UKIRT),
aspartoftheHi-zEmissionLineSurvey(HiZELS). butthecorrelationamplitudeofthelatterpopulationalsoincreases
† E-mail:[email protected] continuously with blue or near-infrared luminosities (e.g. Zehavi
(cid:13)c 2009RAS
2 D.Sobraletal.
et al. 2005). This seems to indicate that both star-formation rate fectedbysystematicuncertainties,butalsoallowsthestudyofvery
(SFR,tracedbyultraviolet/bluelight)andstellarmass(tracedby well-definedcosmicepochs.Additionally,theselectionfunctionis
near-infraredlight)areimportantfordeterminingtheclusteringof well-understood and easy to model in detail, a feature that con-
differentpopulationsofgalaxies.Otherstudieshaveusedmorpho- trastsdeeplywiththatofcurrentlargehigh-redshiftspectroscopic
logicalclassifications.Skibbaetal.(2009),forexample,tookad- surveys.Narrow-bandsurveysalsopopulatetheredshiftslicesthey
vantageofthelargestsampleofvisuallyclassifiedmorphologiesto probewithhighcompletenessdowntoaknownfluxlimit,incon-
date(fromSDSS)toclearlyrevealthatalthoughearly-typegalax- trasttospectroscopicsurveyswhichareusuallyveryincompleteat
iesclustermorestronglythandiscs,oncetheanalysisisdoneata anysingleredshiftandpresentthetypicalpencil-beamdistribution
fixedcolourandluminositynosignificantdifferenceisfound;this problems.Finally,narrow-bandsurveyscanselectequivalentpop-
confirmspreviousresults(e.g.Beisbart&Kerscher2000;Balletal. ulations at different redshifts, making it possible to really under-
2008)forthenearbyUniverse. stand the evolution with cosmic time, avoiding the biases arising
Understandingwhenthesetrendswerecreatedandhowthey fromcomparingpotentiallydifferentpopulations.
evolvedwithcosmictimeisakeyinputtogalaxyformationmod- Thispaperpresentsadetailedclusteringstudyofthelargest
elsandtoourgeneralunderstandingofhowgalaxiesformedand sampleofnarrow-bandselectedHαemittersatz ∼ 1(c.f.S09),
evolved. The first clustering studies of different populations of obtainedafterconductingdeepnarrow-bandimagingintheJband
galaxies beyond the local Universe (e.g. Efstathiou et al. 1991; over∼ 1.3deg2,aspartoftheHiZELSsurvey.Itisorganisedin
Fisher et al. 1994; Brainerd et al. 1995; Le Fe´vre et al. 1996), thefollowingway.§2outlinesthedata,thesamplesandtheiron-
althoughpioneering,weremostlylimitedbythelackofinforma- skydistribution.§3presentstheangulartwo-pointcorrelationfunc-
tionontheredshiftsfortheirsamples.Fortunately,thoseproblems tion,carefullyestimatingtheerrorsandotherpotentialbias,along
arenowstartingtobeeffectivelytackledbylargeranddeepersur- with the exact calculation of the real-space correlation. §4 quan-
veys.Suchsurveyshaverecentlyledtorobustclusteringstudiesof tifies the clear clustering dependences on the host galaxy proper-
specificpopulationsofsourcesatmoderateandhighredshiftsuch ties.§5presentsthefirstdetailedcomparisonbetweenthecluster-
asAGN(e.g.daAˆngelaetal.2008),sub-mmgalaxies(e.g.Blain ingpropertiesofHαemittersfromz = 0.24uptoz = 2.23.Fi-
etal.2004;Weißetal.2009),luminousredandmassivegalaxies nally,§6presentstheconclusions.AnH0 =100hkms−1Mpc−1,
(e.g.Wakeetal.2008),orstar-forminggalaxiessuchasHαemit- ΩM = 0.3andΩΛ = 0.7cosmologyisusedand,exceptwhere
ters,Lyman-breakgalaxiesorLyman-αemitters(e.g.Geachetal. otherwisenoted,magnitudesarepresentedintheVegasystemand
2008; McLure et al. 2009; Shioya et al. 2009). A dependence of h=0.7.
theclusteringongalaxyluminosityhasalsobeenidentifiedbeyond
thelocalUniverse(e.g.Giavalisco&Dickinson 2001). Inpartic-
ular,Kongetal.(2006),Hayashietal.(2007)and,morerecently,
2 DATAANDSAMPLES
Hartleyetal.(2008)foundacleardependenceoftheclusteringam-
plitudeonnear-infraredluminosityforz ∼1−2“BzK”selected 2.1 ThesampleofHαemittersfromHiZELS
galaxies, indicating that already in the young Universe the most
This paper takes advantage of the HiZELS large sample of Hα
massivegalaxiesweremuchmoreclusteredthantheleastmassive
emittersatz=0.845presentedinS09(thereaderisreferredtothat
ones.Theseresultsmeanthatalthoughdifferentstudieshavebeen
paperforfulldetailsofhowthesamplewasconstructed).Briefly,
combinedtosuggestlinksbetweenthesamepopulationatdifferent
the sample was obtained from data taken through a narrow-band
redshifts,orbetweendifferentpopulationsatdifferentepochs,in-
J filter(λ = 1.211±0.015µm)usingtheWideFieldCAMera
terpretingtheserequiresagreatdealofcare,sinceluminositylim- eff
(WFCAM) on the United Kingdom Infrared Telescope (UKIRT),
itstypicallyincreasesignificantlywithredshiftandaredifferentfor
andreachesaneffectivefluxlimitof8×10−17ergs−1cm−2over
differentpopulations.
∼ 0.7deg2 in the UKIDSS Ultra Deep Survey (UDS, Lawrence
Narrow-bandHαsurveysarenowaveryeffectivewaytoob-
etal.2007)field,and∼ 0.8deg2 intheCosmologicalEvolution
tainrepresentativesamplesofstar-forminggalaxies.SincetheGal-
Survey(COSMOS,Scovilleetal.2007)field.Thedataallowedthe
lego et al. (1995) wide-area study in the local Universe, tremen-
selectionofatotalof1517lineemitterswhichareclearlydetected
dousprogresshasbeenachieved,withrecentnarrow-bandstudies
inNB (signal-to-noiseratio>3)withaJ-NB colourexcesssig-
(e.g. Ly et al. 2007; Shioya et al. 2008; Geach et al. 2008; Shim J J
nificanceofΣ>2.5andobservedequivalentwidthEW>50A˚.
etal.2009;Sobraletal.2009a)takingadvantageofstate-of-the-art
Asthedetectedemissionmayoriginatefromseveralpossible
wide-field cameras and obtaining large samples of typically hun-
emission lines at different redshifts, photometric redshifts1 were
dreds of Hα emitters from z = 0 to z = 2.23, down to limit-
usedtodistinguishbetweenthemandselectthecompletesample
ingstar-formationrates(SFRs)of≈1-10M yr−1.Inparticular,
(cid:12) of743Hαemittersoveraco-movingvolumeof1.8×105Mpc3
HiZELS, the Hi-z Emission Line Survey (c.f. Geach et al. 2008,
atz =0.84.Ofthese,477arefoundinCOSMOS(0.76deg2)and
Sobraletal.2009a;hereafterG08andS09,respectively),isobtain-
266inUDS(0.54deg2;thereductioninareaisdrivenbytheover-
ingandexploringuniquesamplesofstar-forminggalaxiespresent-
lapwiththehigh-qualityphotometriccatalogueused–c.f.S09for
ingHαemission(andothermajoremissionlines,e.g.Sobraletal.
moredetails)).Thecompletenessandreliabilityofthissamplewere
2009b),redshiftedintotheJ,H andK bands.Byusingasetof
studiedusingthe∼ 104 availableredshiftsfromzCOSMOSData
existingandcustom-madenarrow-bandfilters,HiZELSissurvey-
Release2(Lillyetal.2009),spectroscopicallyconfirming∼ 100
ingHαemittersatz =0.84,z =1.47andz =2.23overseveral
Hαemitterswithinthephotometricredshiftselectedsample;this
squaredegreeareasofextragalacticsky.
Narrow-band surveys have a great potential for determining
theclusteringpropertiesoflargesamplesofgalaxiesandtheirevo- 1 PhotometricredshiftsusedinS09forCOSMOSpresentσ(∆z)=0.03,
lutionwithcosmictime.Suchsurveysproberemarkablythinred- where∆z=(zphot−zspec)/(1+zspec);thefractionofoutliers,defined
shiftslices(∆z ≈ 0.02),whichnotonlyprovidesanundeniable assourceswith∆z>3σ(∆z),islowerthan3percent,whileforUDS,the
advantage over photometric surveys that can be significantly af- photometricredshiftshaveσ(∆z)=0.04,with2percentofoutliers.
(cid:13)c 2009RAS,MNRAS000,1–13
TheclusteringandevolutionofHα emittersatz ∼ 1fromHiZELS 3
Figure1.Theon-skydistributionoftheHαemittersfoundatz=0.84intheUDS(leftpanel)andCOSMOS(rightpanel)fields,togetherwithaphotometric
redshiftselectedsampleatthesameredshift.Bothpanels/boxescoverthesameangular/physicalarea,correspondingto≈29×29Mpcatz=0.84.TheHα
emittersareplottedin3differentsymbolscorrespondingtodifferentstar-formationrates(seekeyinleftpanel).
allowedtoestimatea> 95percentreliabilityand> 96percent a distance modulus of 43.649. Rest-frame K luminosities (M )
K
completeness for the sample in COSMOS. Hα fluxes, Hα lumi- are computed following Cirasuolo et al. (2009) by assuming the
nosities and Hα-based star-formation rates were obtained for all sameluminositydistanceandinterpolatingusingdeep3.6µmand
HαcandidatesusingHiZELSdata–thedetailsonhowthesewere 4.5µmSpitzerdata.
computedarefullydetailedinS09. Furthermore, the COSMOS field has been imaged by
SincetheworkpresentedinS09,improvedphotometricred- ACS/HST,andthesampleofHαemittershasbeenmorphologically
shifts forCOSMOS and UDShave been produced, incorporating classifiedbothautomatically,withZEST(Scarlataetal.2007),and
visually,asdetailedinS09.Thegalaxieswereclassifiedintoearly-
ahighernumberofbands,deeperdataandaccountingforpossible
types,discsandirregularsand,independently(visually-only),into
emission-linefluxcontaminationofthebroad-bands(c.f.Cirasuolo
non-mergers,potentialmergersandmergers(c.f.S09).Thesample
etal.2009;Ilbertetal.2009,Cirasuoloetal.inprep.);thesefurther
hasalsobeeninvestigatedforAGNcontaminationbothinS09,us-
confirmtherobustnessandcompletenessoftheselectiondonein
ingemission-linediagnostics,andinGarnetal.(2009)makinguse
S09.Nevertheless,theHαsampleusedfortheanalysisinthispaper
ofawidevarietyoftechniques.
isslightlymodifiedfromthatinS09onthebasisofthenewpho-
Figure1presentsthedistributionoftheHαemittersatz =
tometricredshifts.Inparticular,thesampleinUDSnowcontains
257Hαemittersover0.52deg2.Theverysmallreductioninarea 0.84fortheUDSandCOSMOSfields.Thepanelsvisuallyindi-
catehowtheseemittersclusteracrossthesetworegionsofthesky
simplyresultsfromtheoverlapwithdeepmid-infrareddataused
relativetoasimplephotometricredshiftselectedpopulationatthe
forderivingthenewimprovedphotometricredshifts–thisreduc-
sameredshift,selectedwith0.82<z <0.87.
tionplaces3sourcesfromtheinitialsampleoutsidethecoverage. photo
The remaining 6 sources excluded from the S09 sample were re-
movedonthebasisthatthenewphotometricredshiftsclearlyplace
thosesourcesatz ≈ 2.2(2)andz ≈ 1.45(4)(theyaretherefore
identifiedascandidate[OII]3727and[OIII]5007/Hβemitters,re- 2.2 Therandomsample
spectively).ForCOSMOS,thesampleofHαemittersisthesame
Randomcataloguesareessentialforrobustclusteringanalysisand
asinS09(477emittersover0.76deg2),sincethenewphotometric
an over- or under-estimation of the clustering amplitude can eas-
redshiftsdonotchangeanyoftheclassifications(notingthatspec-
ilybeobtainedifonefailstoproduceaccuraterandomcatalogues.
troscopicdatahadalreadybeenusedtoproduceacleanersample
These are produced by generating samples with 100 times more
inS09).
sources than the real data and by distributing those galaxies ran-
As the samples were obtained in two of the best studied domly over the geometry corresponding to the survey’s field-of-
square degree areas, a wealth of multi-wavelength data are avail- view.Thistakesintoaccountboththegeometryofthefieldsand
able.Theseincludedeepbroad-bandimagingfromtheultra-violet the removal of masked areas (due to bright stars/artefacts) – see
(UV) to the infrared (IR) – including deep Spitzer data. These discussionofmaskedregionsinS09formoredetails.
data make it possible to compute rest-frame luminosities for the While the survey is fairly homogeneous in depth, there are
sampleofHαemittersatz = 0.84.Here,rest-frameB luminosi- somesmallvariationsfromchiptochipandfieldtofieldreaching
ties(M )areestimatedbyusingi+-banddata(probing4152.6A˚ amaximumof∼0.2mag(NB of21.5to21.7mag).Thiscorre-
B J
atz=0.84)obtainedwiththeSUBARUtelescopeinbothUDSand spondstoamaximumvariationinluminosity[inlog(L)]of∼0.1.
COSMOS.Thisisobtainedbyapplyinganaperturecorrectionof TheobservedluminosityfunctionpresentedinS09showsthatgo-
-0.097mag(torecoverthetotalfluxformagnitudesmeasuredin3 ingdeeperby0.1inlog(L)increasesthenumbercountby∼20per
arcsecapertures)andagalacticextinctioncorrectionof-0.037to cent.Thiscanhaveaneffectonestimatingtheclustering,although
i+ magnitudes(Capaketal.2007).Itisassumedthatallsources simulationsindicatethatthisissmallerthanthemeasurederrors.
areataluminositydistanceof5367Mpc(z = 0.845);thisyields Thefinalrandomcatalogueswerecreatedreproducingsourceden-
(cid:13)c 2009RAS,MNRAS000,1–13
4 D.Sobraletal.
sitiesvaryinginaccordancewiththemeasureddepthsandtheS09
numbercounts.
3 THECLUSTERINGPROPERTIESOFHαEMITTERS
3.1 Thetwo-pointω(θ)correlationfunctionatz=0.84
Inordertoevaluatethetwo-pointangularcorrelationfunction,the
minimumvarianceestimatorsuggestedbyLandy&Szalay(1993)
isused:
(cid:16)N (cid:17)2 DD(θ) N DR(θ)
ω(θ)=1+ R −2 R , (1)
N RR(θ) N RR(θ)
D D
where DD(θ) is the number of pairs of real data galaxies within
(θ,θ+δθ),DR(θ)isthenumberofdata-randompairsandRR(θ)
isthenumberofrandom-randompairs.N andN arethenumber
R D
of random and data galaxies in the survey. Errors are computed Figure2.Thetwo-pointangularcorrelationfunctionfortheentiresample
usingthePoissonestimate(Landy&Szalay1993): andfortheCOSMOSandUDSfieldsseparatelyforangularseparationsup
to600arcsec,andthe1σ,2σand3σco-variancecontourswhenfittingboth
1+ω(θ)
∆ω(θ)= (cid:112) . (2) Aandβfortheentiresamplecomparedtotheresultsofeachfield.These
DD(θ) resultsshowaverygoodagreementbetweenCOSMOSandUDS,reveal-
ingthatHαemittersincompletelydifferentregionsoftheskyclusterwith
The angular correlation function is computed for the entire
comparableamplitudesandpower-lawslopes.Theresultsalsoshowthat
sampleofHαemitters2,aswellasforCOSMOSandUDSsepa-
thereisnocleardeparturefromthepower-lawforthissampleofHαemit-
rately, and it is found to be very well-fitted by a power-law with tersdownto5(cid:48)(cid:48),implyingthatthe2-halocontributiontoω(θ)isdominant
the form Aθβ with θ in arcsec. The power-law fit is obtained by forscaleslargerthan∼50kpc,butthereistentativeevidenceofasignificant
determiningω(θ)2000timesusingdifferentrandomsamplesand 1-halocontributiontoω(θ)forsmallerscales.
arangeofbinwidths(∆logθ = 0.1−0.3,randomlypickedfor
each determination) and by performing a χ2 fit to each of these
(over5 < θ < 600arcsec,correspondingto38.2kpcto4.5Mpc Table1.Thepower-lawfitparameterswhichbestdescribeω(θ)forHα
at z = 0.845; these correspond to angular separations for which emittersatz = 0.84,resultingfromcomputingω(θ)2000times.These
fittingω(θ)withonesinglepower-lawisappropriate;seedetailsin were obtained over 5 < θ < 600 arcsec, corresponding to 38kpc to
Section3.2.2).TheresultsareshowninFigure2andpresentedin 4.5Mpcatz=0.84,avoidingboththepossibleone-haloclusteringcontri-
bution(atthesmallestscales)andthebreakoftheLimber’sapproximation
Table1;theyimplyA = 14.1±3.9andβ = −0.79±0.06for
(atthelargestscales).NotethedegeneracybetweenAandβinFigure2.
theentiresample(theerrorspresentthe1σdeviationfromtheav-
erage).Thisrevealsaverygoodagreementwiththefiducialvalue, Aβ=−0.8isobtainedbyfixingβ =−0.8,thefiducialvalueandinexcel-
lentagreementwithwhathasbeenfoundfortheentiresamplewithorwith-
β =−0.8.
outpossible/likelyAGNcontamination.Anerrorof20percentisaddedin
Recentstudies(e.g.Ouchietal.2005)havefoundatransition quadraturetorandomerrorin∆Aβ=−0.8toaccountforcosmicvariance
between small and large-scale clustering (corresponding to one- fortheentiresample(or25percentwhenconsideringjustonesub-field–
andtwo-haloclustering,respectively)athighredshift,manifested COSMOSorUDS,c.f.Section3.1.1).
as a clear deviation from the power-law at small scales (smaller
than≈ 50kpcforLyman-breakgalaxiesatz ∼ 4,forexample). Sample Number A β Aβ=−0.8
Whilethereisnodefinitiveevidencefortheone-halotermforthe (z=0.84) # (θinarcsec) (θinarcsec)
Hα sample presented here (especially for separations larger than
AllEmitters 734 14.1±3.9 −0.79±0.06 14.2±3.1
∼5(cid:48)(cid:48)–correspondingto38kpc),forsmallerseparationstheresults
point towards a departure from the power-law, but only at ≈ 1σ NoAGN 660 13.6±4.4 −0.78±0.07 14.1±3.0
level.Therefore,alargersampleisrequiredtoreliablydetermine NolikelyAGN 700 15.4±4.0 −0.81±0.06 14.6±3.2
ω(θ)downtothesmallestscalesandconstrainthecontributionof
COSMOS 477 11.1±3.0 −0.75±0.08 13.8±3.7
theone-haloterm. UDS 257 19.2±8.9 −0.84±0.15 18.4±5.5
The best power-law fit seen in Figure 2 also reveals a good
agreement both at small and larger scales between the COSMOS
andUDSfields(seealsoTable1);theUDSfieldpresentsaslightly These results are consistent with ∼ 0.6−0.8 deg2 fields being
higherclusteringamplitude,butconsistentwithin1σ (fixingβ = sufficienttoovercomemostoftheeffectsofcosmicvariancewhen
−0.8). Note that the Hα luminosity function derived in S09 for conductingclusteringanalysiswithnarrow-bandsurveysatz ∼ 1
eachfieldalsorevealedagoodagreementbetweenthetwofields. –althoughtheagreementcouldbecausedbychance.
2 Duetothefiniteareaprobed,themeasuredclusteringamplitudewillbe 3.1.1 Robusterrorestimationandtheeffectofcosmicvariance
underestimatedbyanamountC(knownastheintegralconstrain;c.f.Roche
Thesurveycovers1.3deg2 intwocompletelyindependentfields;
etal.2002)whichdependsontheassumedtruepower-lawandtheprobed
area.ThisisestimatedasC=0.0023fortheentiresurveyareaanditonly this is a fundamental advantage over smaller surveys which only
represents≈ 0.01percentchangeinA,butitisstillincluded,sincethis probeonesinglefield,asitallows,inprinciple,areliableestimate
becomessignificantforobtainingω(θ)atlargeseparations;c.f.Figure4. ofpossibleerrorsduetocosmicvariance.Inordertoachievethis,
(cid:13)c 2009RAS,MNRAS000,1–13
TheclusteringandevolutionofHα emittersatz ∼ 1fromHiZELS 5
tering amplitude; this will be added in quadrature to the directly
calculatederrorsinA.
3.1.2 AGNcontamination
Some of the Hα emitters are likely to contain an AGN. By us-
ingemission-lineratiodiagnosticsforasmallsubsetofemittersin
zCOSMOS,S09estimatedacontaminationof∼15percentAGN
inthesample.Morerecently,Garnetal.(2009)performedanex-
tendedsearchforAGNwithinthesampleusingseveralmethodsfor
identifying those sources, such as radio, X-rays and mid-infrared
colours. This resulted in the identification of a maximum of 74
AGN(40inCOSMOSand34inUDS).Fromthese,34areclas-
sifiedaslikelyAGNandtheremaining40aspossibleAGN–this
correspondstoanestimated∼ 5-11percentAGNcontamination
withinthesample.
TheAGNmaywellhavedifferentclusteringpropertiesfrom
thestar-formingpopulation.However,thenatureofthesepotential
Figure 3. The uncertainty in A (per cent; ∆A = σ/A × 100, with
β = −0.8)derivedfrom100-1000ω(θ)measurementsonsub-samples AGN contaminants is very unclear, particularly the origin of the
spanningdifferentareaswithinthecomplete1.3deg2 (upto0.5deg2)– detectedHαemission.Forexample,theyaremostlymorphologi-
whichisconsideredtobemostlyduetocosmicvariance.Thisrevealsthat callyclassifiedasirregularsandmergersandtheyspantheentire
∆Adecreaseswithincreasingareaandthistrendisverywellfittedbya luminosityrange;itthusseemsthatalthoughsomeofthemmight
simplepower-law(20×θ−0.35 percent,withθ indeg2,shownbythe have their Hα emission powered by the AGN, they may well be
dashedline).ThesimplestandarddeviationbetweenresultsfromtheCOS- undergoing significant star-formation. Indeed, recently, Shi et al.
MOSandUDSfieldsisalsoshownforcomparison.Theerrorestimated (2009)presentedastudyofunambiguousAGNatz ∼1,showing
fromthebootstrapanalysisandthatgivenbyextrapolatingthefittedpower-
that at least half of the sample shows clear signatures of intense
lawarealsoshownforthefullarea.
star-formation.
In order to understand how AGN contaminants might affect
theclusteringmeasurements,theangularcorrelationfunctionwas
ω(θ) is estimated over randomly picked square areas of different calculatedafterremovingallthepotentialAGNcontaminants.This
sizes (from 0.05 deg2, corresponding to the area probed by one resultsinnostatisticalchangeineitherAorβfortheentiresample
WFCAMchip,upto0.5deg2)inCOSMOSandUDS.Themini- (seeTable1).RemovingonlythelikelyAGNleadstoanidentical
mumnumberofemittersrangesfrom15to65withinthesmaller result.However,thetrueAGNcontaminants(andthepossiblebias
areasused(0.05deg2).Either100and1000randomlychosenre- theymayintroduce)mightwellhavealargereffectontheresults
gionsareconsideredforeacharea(100for0.3-0.5deg2 and1000 whenstudyingtheclusteringasafunctionofhostgalaxyproperties
forsmallerareas)andapowerlawisfittedtoeachω(θ)determi- (presentedinSection4),sinceforcertainhostgalaxypropertiesthe
nationbyfixingβ = −0.8.Foreacharea,thestandarddeviation AGNcontaminationmaybesignificantlyhigherthaninthesample
ontheamplitudeAisusedtoquantifytheuncertainty.Theresults asawhole.
areshowninFigure3anddemonstratethatthemeasuredstandard ToensurethattheanalysisisreallytacklingtheAGNcontam-
deviationiseffectivelyreducedwitharea.TheerrorinA(percent) inationandtorobustlydeterminetheclusteringpropertiesofeach
canbeapproximatedbyapowerlawoftheform20×θ−0.35with sample being studied (and test trends), all the clustering proper-
θ indeg2;extrapolatingthissuggestsanerrorslightlylowerthan tiesinthispaper(forthez = 0.84sampleandsub-samples)are
∼20percentforthetotalareaofthesurvey,andalsoagreeswith derived from a combination of measurements from samples with
thesmalldifferencefoundbetweenCOSMOSandUDS(seeFigure andwithoutpossibleAGNcontaminants.Inpractice,ω(θ)iscom-
3).Furthermore,thissuggeststhatonerequiresareasof∼ 7deg2 puted 500 times each using i) all the emitters in the sample, ii)
(theHiZELSsurveytarget)ormoretoreducetheeffectsofcosmic removinglikelyAGN,andiii)removingall(likelypluspossible)
variancetolessthan10percent. AGN.χ2 fitsareobtainedforeachrealizationofeachsampleand
These estimates could still slightly underestimate the errors, the total resulting distribution is used for the analysis. This also
mostlybecauseatlargerareasthenumberofapproximatelyinde- allows to carefully confirm that there is a good degree of consis-
pendent areas is strongly reduced. An alternative estimate of the tency between the 3 different distributions and in no case is the
clustering uncertainty can be derived using a bootstrap analysis. differencebetweensampleswithandwithoutAGNlargerthanthe
Since this often leads to a slight over-estimation of the errors, it 1σerrors.Thismostlyresultsinestimatinglargererrorsthanthose
canbecombinedwiththepreviousanalysistogiveanapproximate which would be obtained from either simply excluding all AGN
rangefortheexpectederror.Theanalysisisdonebynaturallydi- ornotdealingwithAGNcontamination,andthereforerepresentsa
viding the complete sample into 26 regions of ∼0.05 deg2 each conservativeapproach.
(thesearetheminimumindividualprobedareasasthesearecov-
eredbyoneWFCAMchip)andcomputingω(θ)with26randomly
picked regions each time for 10000 times. Fitting all realizations 3.2 Real-spacecorrelation
withapowerlaw(fixingβ = −0.8)resultsinadistributionwith
3.2.1 Firstorderapproximation:Limber’sequation
astandarddeviationof23percentintheclusteringamplitude,A.
Whencomparedandcombinedwiththepreviousestimation(≈18 The real-space correlation, r , is a very useful description of the
0
per cent error), it suggests an error of ∼ 20 per cent in the clus- physical clustering of galaxies when the spatial correlation func-
(cid:13)c 2009RAS,MNRAS000,1–13
6 D.Sobraletal.
tioniswell-describedbyξ = (r/r )γ.TheinverseLimbertrans-
0
formation(Peebles1980)canbeeasilyusedtoobtainanapprox-
imation of the spatial correlation function3 from the angular cor-
relationfunction,providedtheredshiftdistributionisknown.For
narrow-band surveys, the expected redshift distribution depends
solely on the shape of the narrow-band filter profile; this can be
well approximated by a Gaussian4, which, for the Hα emission-
line,correspondstoaredshiftdistributioncenteredatz = 0.845
withσ=0.0075.Thiscanbecomparedwiththeredshiftdistribu-
tionfromHαemittersconfirmedbyzCOSMOS(93sources)which
hasameanredshiftof0.844andσ =0.0076;theexcellentagree-
mentrevealsthattherealredshiftdistributionshouldbeveryclose
totheoneassumed.
Inordertocalculatetherealspacecorrelationlength,r ,and
0
whenperformingthede-projectionanalysis,itisassumedthatthe
redshifts are drawn from this Gaussian distribution and that the
real-spacecorrelationfunctionisindependentofredshift(c.f.G08;
Kovacˇetal.2007)overtheredshiftrangeprobed;thisisaverygood
approximation,sincetheredshiftdistributionisextremelynarrow.
Figure4.Thetwo-pointangularcorrelationfunctionfortheentiresam-
ContaminationbysourceswhicharenotHαemittersatz = 0.84
ple,comparedwiththesimplepower-lawfitexpectedfromtheLimber’s
couldhaveasignificanteffectonr0,sincetherealredshiftdistribu- approximation.Thesearecomparedwiththebest(fromaχ2 fit–shown
tionwillbedifferentfromtheoneassumed.Nevertheless,inS09 inthefigure)exactangularcorrelationfunctionobtainedwiththenarrow-
thesamplewasstudiedtofindthatonly2outof90sourceswith bandfilterprofileforaspatialcorrelationfunctiongivenbythepower-law
spectroscopic redshifts that had been photometrically selected as ξ = (r/r0)γ,withγ = −1.8andr0 = 2.61±0.13h−1Mpc(notcor-
Hα emitters were not real Hα emitters (one [SII]6717 emitter at rectedforcontamination;errorsdirectlyfromχ2),revealinganexcellent
z = 0.79anda[OIII]5007emitteratz = 1.42,whichwerethen agreementwiththedata.ThisalsorevealstheregimeforwhichtheLimber’s
removedfromthesample).Thisconclusionisdrawnfromtheanal- approximationbreaksforthisparticularcase(∼600arcsecfora∼15per
ysisoflimited spectroscopic data(∼ 20percentof theHiZELS centdifference;c.f.Simon2007forageneralanalysisofthetypicalsepa-
rationatwhichLimber’sapproximationbreaksdown).
sampleinCOSMOS),butcontaminationatthatlevelwillonlylead
to underestimating r by a maximum of 6 per cent5. Throughout
0
thispaper,a5percentcorrectionisappliedwhencomputingr to
0
accountfortheexpectedcontamination.
slopesβ =γ+1forsmallscalesandβ =γforlargeangularsep-
Computingr foreachrealizationofω(θ)fittedwithapower-
0
law with β = −0.8 results in r = 2.5±0.3h−1Mpc for the arationswhenusinganarrowfilter–seefulldiscussioninSimon
0
entiresample,orr = 2.6±0.3h−1Mpcwhenaccountingfor5 (2007).
0
Here,itisassumedthatthespatialcorrelationfunctionisgiven
per cent contamination. Note that the 20 per cent error in A due
by the power-law ξ = (r/r )γ (as this is able to reproduce the
tocosmicvarianceresultsinanerrorof11percentinr ,andthis 0
0
observedω(θ)verywellwithγ =−1.8),andthatthenarrow-band
is added in quadrature. However, as mentioned before, Limber’s
filterprofileisdescribedbyaGaussianasdetailedinSection3.2.1.
equationisonlyanapproximationwhichcanpotentiallyresultin
Thefollowingisthennumericallyintegratedforthesameangular
significanterrorsfornarrow-bandsurveysathighredshift.Section
separationsasforthedataandaχ2fitisdoneforω(θ)aroundthe
3.2.2describeshowr isrobustlycalculatedbyfullyde-projecting
0
valueofr obtainedinthepreviousSection:
ω(θ). 0
(cid:90) +∞(cid:90) 2s 2f (s−∆)f (s+∆)
∆ω(θ)=ψ−1 S S dRds, (3)
3.2.2 Accuratedeterminationofr fornarrow-bandsurveys √ R−γ−1rγ∆
0 0 s 2φ 0
The errors introduced by the Limber’s approximation are tack-
(cid:112)
led by numerically integrating the exact equation connecting the whereψ=1+cosθ,φ=1−cosθ,∆= (R2−2s2φ)/(2ψ)
spatialandangularcorrelationfunctions(followingSimon2007). andfS istheprofileofthefilterbeingusedinco-movingdistance
Thisrelationimpliesthatspatialcorrelationfunctionsdescribedby (assumed to be a Gaussian distributed value with an average of
ξ = (r/r )γ are projected as angular correlation functions with 2036.3h−1Mpc and σ = 14.0h−1Mpc). The χ2 fitting results
0
inamuchmorerobustestimateofr andallowstheuseofω(θ)up
0
tolargerangularseparationsthan600arcsec,aregimeforwhicha
3 Limber’sequationisanapproximationthatbreaksdownforlargeangular singlepower-lawstartstobecomeinadequate(asβ changesfrom
separationswhenoneusesanarrowfilter,butcanstillbeusedtoobtainat γ + 1 to γ, c.f. Figure 4). For the entire sample, however, this
leastafirstapproximationofr0 within≈ 15percentfortheNBJ filter leadstolittlechange:r0 = 2.7±0.3h−1Mpc(thisincludesa5
used;seeSection3.2.2fordetails. percentcorrectionforcontamination,whiletheerrorsalsoinclude
4 Asimplerwaytomodelthenarrow-bandfilteristoassumeitisatop-
cosmicvariance–thiserrorestimationhasbeendiscussedinSec-
hat;thisresultsinaHαredshiftdistributionof0.845±0.015.Thetwo
tion3.1.1).Indeed,whilstLimber’sequationbreaksdownforlarge
approachesproduceresultsfordifferentr0 determinationswhicharecon-
galaxyseparations,itisshowntodowellaslongasonlysmaller
sistentwithin5percent.
5 Assumingthatcontaminantswillnotclustersignificantly,thecontamina- angulardistancesareconsidered.Notethatreal-spacecorrelations
tionfractionoff willresultinamaximumunderestimationofAgivenby fordifferentsamples(seeTable2)arecomputedinthefollowing
(1-f)2,andanunderestimationofr0givenby∼(1-f)2/|γ|. sectionsusingthesameproceduredescribedhere.
(cid:13)c 2009RAS,MNRAS000,1–13
TheclusteringandevolutionofHα emittersatz ∼ 1fromHiZELS 7
3.2.3 Thedependenceoftheredshiftdistributiononlimitingline
luminosityfornarrow-bandsurveys
Sincethenarrow-bandfilterprofileisnotaperfecttop-hat,emitters
withdifferentHαluminositiesaredetectedoveraslightlydifferent
range of redshifts. As the exact relation between ξ(r) and ω(θ)
dependsontheredshiftdistribution(givenbythefilterprofile),as-
sumingthesameredshiftdistributionfordifferentluminositylimits
canleadtobiases,especiallywhenlookingatapossiblerelation-
shipbetweentheclusteringamplitudeandHαluminosity.
This potential bias is studied by performing the same sim-
ulations described in S09. Briefly, the Hα luminosity function
presented in S09 is used to generate a fake population of emit-
tersequallydistributedoverawiderrangeofredshiftsthanthose
probedbythenarrow-bandfilterandthisisusedtolookatthere-
coveredredshiftdistributionofsourcesasafunctionofmeasured
luminosity. The redshift distribution is found to become continu-
ouslynarrowerwithincreasingHαluminositylimit6,althoughall
Figure5.Thetwo-pointangularcorrelationfunctionforsub-samplesob-
thedistributionscanbeequallywell-fittedbyaGaussian.Thevari- tainedbysplittingthesamplein2halvesbasedon Hαluminosity/SFR.
ationcanbewrittenasafunctionofobservedHαfluxas: Theseclearlyshowthattheclusteringamplitudeishigherforgalaxieswith
higherHαluminosities,implyingthatthemostactivestar-forminggalaxies
σ=−η×(logFHα(limit)−logF0)+σ0, (4) aremoreclusteredthantheleastactive.Linesshowthebestχ2totheexact
relationbetweenξ(r)andω(θ)byfixingγ=−1.8;which(afterapplying
whereF isa fluxlimit atwhich theredshift distributionis rela-
tivelywe0llunderstoodandσ isthewidthoftheredshiftdistribu- allcorrectionsalreadydetailed)resultinr0 = 4.84±0.58h−1Mpcfor
0 thebrightestemittersand2.52±0.41h−1Mpcforthefaintesthalf(inHα
tionatthatfluxlimit;fortheNB filter,η = 0.00117,asderived
J luminosity)ofthesample.
fromsimulations.
Overtheluminosityrangeofthesample(andfortheassumed
luminosityfunctionandtherealfilterprofile),neglectingthiseffect ordertoinvestigatetheclusteringasafunctionoffundamentalob-
results in over-estimating r0 by a maximum of 8 per cent; this is servable host galaxy properties. These include i) Hα luminosity
onlyfoundwhencomputingr0forasamplecontainingthebrightest correctedforextinctionasinS09(1mag),ii)rest-frameK lumi-
5 per cent emitters (the ≈ 40 brightest emitters, for which σ ≈ nosity(M ),iii)rest-frameB luminosity(M )andiv)morpho-
K B
0.0065). Nevertheless, narrow-band surveys which span a much logical class (discs, irregulars; non-mergers, mergers). The ω(θ)
wider luminosity range will be much more sensitive to this and correlationfunctioniscomputedforeachsub-sample(asingleex-
line-luminositytrendscouldnaturallyarisefromthisbias. ampleisshowninFigure5,presentingω(θ)forthebrightestand
Thisluminositydependenceisfullytakenintoaccountwhen faintesthalvesofthesamplewithrespecttoHαluminosity).The
computing r0 for sub-samples defined by different Hα luminos- approach detailed in the previous sections is then used by firstly
ity/SFR limits. For the analysis of other sub-samples, if the Hα computingr usingLimber’sapproximationpower-lawfittoω(θ)
0
luminositydistributiondoesnotpresentanyclearoff-setfromthat (fixing β = −0.8 and restricting the analysis to 5 < θ < 600
oftheentiresurvey,itisassumedthattheredshiftdistributionof arcsec),andthenusingtheexactrelationbetweenthespatialand
thosesub-samplesisverywellapproximatedbythecompletered- angular correlation functions to improve the r estimation. This
0
shiftdistribution. analysisalsoaccountsforthepotentialAGNcontaminationinthe
sample, following the procedures described at the end of Section
3.1.2(computingω(θ)withandwithoutthepossibleAGNcontam-
inants and using the combined distribution). The results obtained
4 THECLUSTERINGDEPENDENCESONHOST whensplittingthesampleintodifferentsub-samplesarepresented
GALAXYPROPERTIES inTable2,Figure6andFigure7.Forsub-samplesobtainedfrom
the complete survey area, an error of 11 per cent in r is added
AsdiscussedintheIntroduction,inthelocalUniversethecluster- 0
inquadraturetothe1σ errors(seeSection3.1.1),whileforsub-
inghasbeenshowntodependonseveralhostgalaxyproperties.At
samplesderivedbasedonmorphologya14percenterrorisadded
z = 0.24,Shioyaetal.(2008)haveshownthattheclusteringof
inquadratureto∆r (fortheCOSMOSfieldonly).
Hαemittersseemstobestrongerforthemostluminoussourcesin 0
Hα,butsofartestingandquantifyingthatclusteringdependence
at higher redshifts for Hα emitters has not been possible, as sur-
4.1 Hαluminosity/star-formationrate
veyshavelackedareaandsamplesize.TheHiZELSsampleislarge
enoughtoachievethis. Followingpreviousstudies,suchasShioyaetal.(2008),onecan
The complete sample is divided into several sub-samples in do a simple splitting of the sample in two halves with the same
numberofemitters(367with41.95 <logL < 43.18ergs−1
Hα
and equal number with 41.61 < log L < 41.95 ergs−1), and
Hα
studytheclusteringpropertiesofeachofthosesamples.Figure5
6 Althoughintrinsicallymoreluminoussourcesaredetectableoverawider
presents the angular correlation function obtained for the bright-
redshiftrange,theirdetectioninthewingsofthefilterleadstoanunder-
estimationoftheirluminosity;galaxiesareonlymeasuredtobeluminous est and faintest halves of the sample, revealing that the bright-
inHαwhentheemissionlineisbeingdetectednearthepeakofthefilter est Hα emitters are much more clustered than the faintest ones.
profile. This is also very clear when one compares the spatial correla-
(cid:13)c 2009RAS,MNRAS000,1–13
8 D.Sobraletal.
Table2.Thecorrelationlength(fixingγ = −1.8andcorrectedby5per
centforcontamination)forHαemittersatz = 0.84.Sampleswithfixed
MK have−24.44<MK <−22.68(AB)andthosewithfixedlogLHα
have41.76 < logLHα < 42.22(ergs−1).Hαluminositiesaregivenin
ergs−1,MKandMBareABrest-frameluminosities.Unclassifiedsources
orwithnodataavailablewerenotconsidered.Errorsincludecosmicvari-
ance(11percentofr0fortheentiresampleand14percentofr0forsamples
ofeachindividualfield).
Sub-sample Number r0
(Hαz=0.84) # (h−1Mpc)
AllEmitters 734 2.74±0.29
PureStar-forming 660 2.61±0.28
COSMOS 477 2.67±0.37
UDS 257 3.13±0.52
41.95<logLHα<43.18 367 4.84±0.58
41.61<logLHα<41.95 367 2.52±0.41
42.40<logLHα<42.80 46 5.24±1.01
Figure6.Thedependenceoftheclusteringlength,r0,withHαluminosity 42.25<logLHα<42.40 55 5.03±0.96
atz =0.84.ThisclearlyrevealsthatgalaxiespresentinghigherHαlumi- 42.10<logLHα<42.25 92 4.55±0.72
nosities/SFRsaremoreclustered,andthatgalaxiesabovethebreakinthe 41.88<logLHα<42.10 243 2.50±0.45
Hαluminosityfunction(L∗ )aremuchmoreclusteredthanthosebelow. 41.75<logLHα<41.88 173 2.26±0.42
ThisdependenceisnotareHsuαltofthecorrelationbetweenSFR(Hαlumi- 41.62<logLHα<41.75 125 2.13±0.55
nHoαsiltuym)ainnodssittyelflaorrmsuabs-ssa(mMpKle,ssweeithFitghuerseam8)e,aMsKr0.correlatesaswellwith 444211...298083<<<lllooogggLLLHHHααα<<<444221...429408(((fififixxxeeedddMMMKKK))) 11512675 432...288074±±±000...855685
41.71<logLHα<41.83(fixedMK) 117 1.70±0.51
tionsobtainedforeachsample:whilethebrightestemittersinHα −26.1<MK <−24.5 82 3.74±0.69
presentr0 =4.8±0.6h−1Mpc,forthefaintestemittersonefinds −24.5<MK <−24.0 116 4.24±0.63
2.5±0.4h−1Mpc.Itshouldalsobenotedthatbecauseγisfixed, −24.0<MK <−23.5 145 3.08±0.51
thesignificantdifferenceinr0forthetwosamplesisnotaresultof −23.5<MK <−23.0 145 2.72±0.43
thedegeneracybetweenγandr0(seeFigure2forasimilardegen- −23.0<MK <−22.5 117 2.65±0.54
eracybetweenβandA),contrarilytostudiessuchasShioyaetal. −22.5<MK <−20.5 116 2.31±0.49
(2008),whichallowforbothγ andr tovary;suchnoteisvalid −24.96<MK <−24.00(fixedlogLHα) 116 3.99±0.56
throughoutthispaper. 0 −24.00<MK <−23.40(fixedlogLHα) 108 2.52±0.62
WiththelargesampleofHαemittersobtainedbyHiZELSat −23.40<MK <−22.84(fixedlogLHα) 112 2.81±0.54
−22.84<MK <−21.81(fixedlogLHα) 111 2.48±0.50
z=0.84,itispossibletoperformamuchmoredetailedinvestiga-
tionintotherelationbetweenr0 andHαluminositybyseparating −23.23<MB <−21.61 96 4.47±0.77
theemittersintoalargernumberofsub-samples.Figure6andTa- −21.61<MB <−21.11 186 2.97±0.44
ble2showthatr increasesbyafactorofalmost3fromthefaintest −21.11<MB <−20.61 246 2.25±0.30
0
Hαgalaxiestothemostactivestar-forminggalaxiesfoundabove −20.61<MB <−20.11 145 3.92±0.63
thebreakintheHαluminosityfunction,L∗ (1042.2ergs−1,S09). −20.11<MB <−18.71 59 2.54±0.92
Hα
Whilst the increase of r0 with LHα can be reasonably well- Discs(COSMOS) 363 2.52±0.32
describedbyastraight-linefit(χ2=1.4),therearehintsthatthere Irregulars(COSMOS) 68 5.12±0.88
mightbeastrongerincreaseinr0aroundL∗Hα.Thisprovidesade- Discs(SFR&MKmatch) 109 2.59±0.45
scription which is in line with previous studies, but gives an un- Irregulars(SFR&MKmatch) 46 2.96±0.80
precedented degree of detail of the relation between r0 and Hα Non-mergers(COSMOS) 298 2.30±0.31
luminosity/star-formation rate. Moreover, the robustness of these Mergers(COSMOS) 111 3.75±0.50
results is also increased by including the small correction for the Non-mergers(SFR&MKmatch) 128 2.35±0.42
factthatsampleswithdifferentluminositylimitswillpresentadif- Mergers(SFR&MKmatch) 100 2.87±0.56
ferentredshiftdistributionjustfromconsideringthefilterprofile.
Bulge-dominateddiscs(COSMOS) 97 2.72±0.54
Recently,Orsietal.(2009)madepredictionsforthecluster-
Disc-dominateddiscs(COSMOS) 204 2.51±0.39
ing properties of Hα emitters using two different versions of the
GALFORMgalaxyformationmodel.Atz = 0.84andfortheflux
limitofS09,Orsietal.(2009)predictsr ≈ 4−5h−1Mpc.This
0 4.2 Rest-framecontinuumluminosity
showsthatthedisagreementbetweenthedataandthemodelsfound
at z = 0.24 and z = 0.4 in Orsi et al. (2009) is also found at Hα emitters presenting the highest rest-frame K band luminosi-
z = 0.84. The models predictions would be consistent with the ties (M < −24) are strongly clustered, and a general trend of
K
dataforfluxlimits2timeshigherduetothestrongclusteringde- anincreasingr withKbandluminosityisfound(seeleftpanelof
0
pendencewithHαluminosityatz = 0.84;however,noneofthe Figure7),similarlytowhathasbeenfoundforotherpopulations
models is able to fully reproduce this r -L relation at the mo- ofgalaxiesatdifferentredshifts.Thissuggeststhatthiscorrelation
0 Hα
ment. mustbevalidregardlessofthepopulationbeingobserved–atleast
(cid:13)c 2009RAS,MNRAS000,1–13
TheclusteringandevolutionofHα emittersatz ∼ 1fromHiZELS 9
Figure7.Thereal-spacecorrelationlengthasafunctionofrest-frameKluminosity(leftpanel),rest-frameBluminosity(middlepanel)andvisualmorphology
(rightpanel).Theseresultsshowthatstar-forminggalaxiesclustermorewithincreasingrest-frameKluminosity(whichtracesstellarmass),withthistrend
beingmaintained(butslightlyweakened)evenwhenoneusessub-samplesthathavethesameHαluminositydistribution.Nostatisticallysignificantcorrelation
betweenr0withrest-frameBluminosityisfound.Morphologicallyclassifiedirregularsandmergersclustermorestronglythandiscsandnon-mergers,but
thisisduetoadifferentHαluminosityandMKdistributionwithineachpopulation;matchingthesedistributionsresultsinasimilarr0.
fortherangeofluminositiesprobed–andseemstosimplyimply rectlycomparethesepopulationsonthebasisofthemorphological
thatgalaxieswiththehigheststellarmasses(astheseareexpected classonly.
tocorrelateverycloselywithKluminosity,althoughthecontribu- Thereisnosignificantdifferenceinr forthematchedsam-
0
tionfromthethermallypulsingasymptoticgiantbranch(TP-AGB) plesofirregularsanddiscs(seeFigure7–filledcircles)within1σ.
phaseofstellarevolutioncanleadtosomescatterintheM versus Ther differencebetweenmergersandnon-mergersisalsogreatly
K 0
stellarmassrelation;c.f.Marastonetal.2006)resideinthemost reduced,althoughmergersarestillfoundtobeslightlymoreclus-
massivehaloes.However,itisalsoclearthattheincreaseofr with teredthannon-mergersat∼1σlevel.
0
rest-frameK luminosity,whilstcontinuous,isnotaspronounced Thesample ofHα emitterswith discmorphologieshas also
astheincreasewithstar-formationrate. beenclassifiedaccordingtohowmuchdisc/bulgedominatedeach
InthelocalUniverse,galaxieswithhigherB bandluminosi- galaxyis(withZEST;c.f.Scarlataetal.2007).Bycomputingthe
ties(M )aremoreclusteredthangalaxieswithlowerM .How- correlation length for disc dominated discs and bulge dominated
B B
ever,studyingtheclusteringpropertiesofHαemittersatz=0.845 discs, one finds that they present reasonably the same r (2.7±
0
asafunctionofrest-frameBluminosityrevealsnostatisticallysig- 0.5h−1Mpcfordiscdominatedand2.5±0.4h−1Mpcforbulge
nificanttrend(<1σ)(seemiddlepanelofFigure7).Theseresults dominatedgalaxies).Therefore,thebulge-diskratioofthestudied
areinreasonableagreementwithrecentstudies(e.g.Meneuxetal. star-formingdiscgalaxiesdoesnothaveanysignificanteffecton
2009), which did not find any significant dependence of galaxy howthesegalaxiesclusteratz∼1.
clusteringonBluminosityforasimilarredshiftrange. TheseresultsshowthatHαluminosityandM (probingstel-
K
larmass)arethekeyhostgalaxypropertiesdrivingtheclustering
ofstar-forminggalaxiesatz ∼ 1andmorphologyisunimportant
4.3 Morphologicalclass fortheclusteringofgalaxiesathighredshift,justashasbeenfound
inthelocalUniverse(e.g.Skibbaetal.2009).
By splitting the sample into morphological classes (only for the
COSMOSfield[c.f.S09]),onefindsthatgalaxiesclassifiedasir-
regularsaremoreclusteredthanthoseclassifiedasdiscs;mergers
4.4 Hαluminosityversusrest-frameKluminosity
haveameasuredr whichliesbetweenthesepopulations,butsig-
0
nificantly above the non-mergers (see Table 2 and right panel of Ithasbeenshownthatr isverywellcorrelatedwithbothHαlumi-
0
Figure 7 – open circles). However, S09 found that irregulars and nosity(orstar-formationrate)andrest-frameK luminosity(trac-
mergers are typically brighter in Hα and M than discs (which ingstellarmass).Ontheotherhand,star-forminggalaxiesbothin
K
completelydominatethefaint-endoftheHαluminosityfunction thelocalUniverseandathighredshiftrevealacorrelationbetween
at z ∼ 1). Therefore, in order to understand if the clustering re- both, with star-formation rate typically being higher for galaxies
ally does depend on the morphological class or if this is simply with higher stellar masses (see Figure 8). Thus, how much is the
a secondary effect driven by star-formation rate and stellar mass correlationbetweenr andHαluminositydrivenbydifferentrest-
0
dependencies, one needs to compare samples which are matched frameKluminositydistributions,andvice-versa?
inlogL andM .ThisisdonebyusingthedistributionofHα In order to clearly test if both relations hold – or whether
Hα K
emitters in the log L -M plane and matching irregulars with theyarearesultofasinglestrongrelationbetweenr andeither
Hα K 0
discs and mergers with non-mergers. A ∆log L < 0.02 & Hαluminosityofrest-frameK luminosity–newsub-samplesare
Hα
∆M <0.02criteriaisused:thesevalueswerechosentoensure derived.Todothis,twosub-regionsaredefinedinthe2-DL –
K Hα
thatthesamplesareverywell-matchedinbothHαluminosityand M space(seeFigure8).Totestther -L correlationatafixed
K 0 Hα
M whilestillretainingthesamplesizesrequiredfortheanalysis. M , the region −24.44 < M < −22.68(AB) and 41.71 <
K K K
Thepopulationmatchusedstillresultsinaseverereductionofthe logL < 42.44ergs−1 (correspondingto4.1 < SFR < 21.8
Hα
largerdiscandnon-mergersamples(alongwithasmallerreduction M yr−1) is considered (see Figure 8). This region contains 409
(cid:12)
ofthenumberofirregularsandmergers),butbymatchingtheseon Hαemitters,whichcanbedividedinto4sub-samplesonthebasis
thebasisofM andlog L distribution,itisthenpossibletodi- of Hα luminosities with the same distribution of M (means of
K Hα K
(cid:13)c 2009RAS,MNRAS000,1–13
10 D.Sobraletal.
Shioyaetal.(2008)usedgalaxycolourstoidentify∼ 1000
candidate z = 0.24 Hα emitters within their narrow-band ex-
cess sample. For this analysis, the sample is restricted to 492
sourcesbylimitingittoaveryrobustcompletenesslimit(L >
Hα
1039.8ergs−1, corresponding to SFR > 0.05M yr−1). The ro-
(cid:12)
bustnessofthissamplecanbetestedandimprovedtakingadvan-
tage of a large set of spectroscopic data recently made available
intheCOSMOSfieldbythezCOSMOSproject.Thereare75Hα
candidateswithaspectroscopicredshiftavailablefromzCOSMOS
and 69 are identified as Hα emitters at 0.236 < z < 0.252.
The remaining 6 sources are identified as [SII]6717 emitters at
0.229 < z < 0.231(contaminationbySII emittersisevenmore
significantatlowerlinefluxes,aspointedoutrecentlybyWestra
etal.2009).Withtherobustluminositycutusedhere,thiscorre-
sponds to a contamination of 8 per cent, and by removing the 6
confirmedcontaminantsfromthesampleofHαemitters,thecon-
taminationisestimatedtobe7percentfortheremainingsample
Figure8.Thecomplete2-DMK-logLHαspace,showingthecorrelation of486emitters.Thisresultsinunderestimatingr0 byamaximum
betweenrest-frameKluminosityandHαluminosity,comparedtothere- of 8.4 per cent and r0 will be corrected by 7 per cent to account
gionsusedtoselectsub-sampleswiththesameMK orLHαdistributions. for contamination in the sample at z = 0.24; this is 80 per cent
Thisclearlyshowsthatwithoutusingsub-regionsofthis2-Dspace,sam- ofthemaximumcorrection,consistentwiththeapproachusedfor
plesdefinedonlyoneitherLHα orMK willpresentdifferentMK and z=0.84.
LHαdistributions,respectively,sincethesequantitiesarecorrelated. Finally,inordertoobtainr (followingthesameprocedures
0
asforthez =0.84sample,exceptAGNcontamination),twored-
−23.6,−23.7,−23.6and−23.7withstandarddeviationsof0.5 shiftdistributionsareconsidered:theoneassumedinShioyaetal.
in all instances; ordered from highest to lowest in respect to Hα (2008;atop-hatcharacterizedbyz = 0.242±0.009),andared-
luminosity).Similarly,inordertotestther -M correlation,the shift distribution derived from the distribution of the 69 spectro-
0 K
sample is restricted to Hα emitters within the region defined by scopicallyconfirmedHαemitters,whichcanbewell-describedby
−24.96 < M < −21.81(AB)and41.76 < logL < 42.22 aGaussianwithanaverageofz =0.245andastandarddeviation
K Hα
ergs−1 (see Figure 8) in which sub-samples split on the basis of ofσ = 0.006.Inpractice,thevaluesderivedfrombothdistribu-
theirMKhavethesameLHαdistributions(meansof41.97,41.95, tionsagreewell,butforconsistencyindeterminingr0,theGaussian
41.95 and 41.97 and standard deviations of 0.12 in all instances; distributionwillbeassumed.
orderedfromhighesttolowestinMK)–c.f.Table2.Theangular Thecorrelationlengthresultsinr0 =1.8±0.2h−1Mpc,with
correlationfunctionsofthesematchedsub-samplesarethencom- theerrorincludingrandomerrors(fromthestandarddeviationob-
putedandvaluesofr derivedasfullydescribedbefore. tainedafter1000measurementsofω(θ))andcosmicvariance(as-
0
The results are presented in Table 2 and in Figures 6 and 7. sumedtoaffectr0by11percentforthisarea).Onlyseparationsof
TheserevealthatbothHαluminosityandrest-frameK luminos- 5 < θ < 800arcsecareusedwhenobtainingapower-lawfit:an-
ity are relevant for the clustering of star-forming galaxies, since gularseparationslowerthan5arcsecarenotusedasω(θ)becomes
forafixeddistributionofoneofthese,avariationintheotherone steeper,deviatingfromthepowerlaw;thisissimplyinterpretedas
leadstoachangeinr .However,itshouldbenotedthatthecorre- thetransitionbetweenthetwo-haloandone-haloclustering,hap-
0
lationbetweenr andHαluminosity(forafixedM distribution) peningat≈ 20kpc.ItshouldalsobenotedthattheLimberequa-
0 K
ismaintainedashighlystatisticallysignificant,whilethestatistical tion works well for this case, with the differences between using
significanceofthecorrelationbetweenr andM atafixedL suchapproximationandintegratingthefullrelationbetweenω(θ)
0 K Hα
distributionisslightlyreduced. andξ(r)beinglowerthan5percentforθ<800arcsec.
5.2 TheclusteringofHαemittersatz=2.23
5 THECLUSTERINGOFHαEMITTERSACROSS
COSMICTIME IthasbeenmentionedthatLimber’sequationbreaksdownforlarge
angularseparationsandforverynarrowfilters.Indeed,atz=2.23
The clustering properties of the Hα emitters at z = 0.84 can be the co-moving space width of the filter is extremely narrow, pre-
compared with those of the HiZELS sample at z = 2.23 (G08) senting σ = 7.3h−1Mpc, and representing only ≈ 0.2 per cent
andwithresultsderivedfromlowerredshiftsurveysofHαemitters of the total co-moving distance to z = 2.23; this means that if
at z = 0.24 and z = 0.4 (Shioya et al. 2008; Nakajima et al. thespatialcorrelationfunctionoftheHαemittersisapower-law
2008). This can then be interpreted in the context of the ΛCDM ξ =(r/r )−1.8,thenω(θ),measuredat5<θ <1000arcseccan
0
cosmologicalmodel. notbewell-fittedbyapower-lawwithβ =−0.8,sincethisregime
isprobingtheexactchangebetweenβ =γ+1andβ =γ.
The correlation length r is therefore re-computed. This is
5.1 TheclusteringofHαemittersatz=0.24 0
done by using the ω(θ) data points presented in G08 and by do-
Withthemotivationofreliablycomparingtheclusteringmeasure- ing a χ2 fit to the obtained ω(θ) from Equation 3. This assumes
mentsatdifferentredshifts,andsincetheShioyaetal.(2008)sam- thatthespatialcorrelationfunctionisapower-lawwithγ =−1.8
ple is publicly available, ω(θ) is carefully re-computed for this (whichisshowntoreproducethedataverywell)andonlyr isal-
0
sample. lowedtovary.Thisprocedureresultsinr = 2.6±0.5h−1Mpc,
0
(cid:13)c 2009RAS,MNRAS000,1–13