Determining an accurate position for a submm galaxy (SMG) is the crucial step that enables us to move from the basic properties of an SMG sample - source counts and 2-D clustering - to an assessment of their detailed, multi-wavelength properties, their con

Identi cationofsubmillimetregalaxiesintheSHADESSourceCatalogue

9

Table6.Identi cationsummary.

NicknameRobustidenti cation?

NicknameRobustidenti cation?

LOCK850.01 SXDF850.01 LOCK850.02 SXDF850.02 LOCK850.03 SXDF850.03 LOCK850.04 SXDF850.04 LOCK850.05SXDF850.05 LOCK850.06 SXDF850.06 LOCK850.07 SXDF850.07 LOCK850.08 SXDF850.08 LOCK850.09 SXDF850.09LOCK850.10 SXDF850.10 LOCK850.11SXDF850.11 LOCK850.12

SXDF850.12 LOCK850.13SXDF850.14 LOCK850.14SXDF850.15LOCK850.15 SXDF850.16 LOCK850.16 SXDF850.17LOCK850.17 SXDF850.18 LOCK850.18 SXDF850.19 LOCK850.19 SXDF850.20LOCK850.21 SXDF850.21 LOCK850.22 SXDF850.22LOCK850.23SXDF850.23 LOCK850.24 SXDF850.24 LOCK850.26

SXDF850.25LOCK850.27SXDF850.27 LOCK850.28SXDF850.28 LOCK850.29 SXDF850.29 LOCK850.30 SXDF850.30 LOCK850.31 SXDF850.31 LOCK850.33 SXDF850.32LOCK850.34

SXDF850.35 LOCK850.35SXDF850.36LOCK850.36SXDF850.37 LOCK850.37 SXDF850.38 LOCK850.38 SXDF850.39LOCK850.39SXDF850.40 LOCK850.40 SXDF850.45LOCK850.41 SXDF850.47

LOCK850.43 SXDF850.48LOCK850.47SXDF850.49LOCK850.48 SXDF850.50 LOCK850.52 SXDF850.52 LOCK850.53 SXDF850.55

LOCK850.60SXDF850.56LOCK850.63

SXDF850.63LOCK850.64SXDF850.65LOCK850.66SXDF850.69LOCK850.67 SXDF850.70LOCK850.70 SXDF850.71 LOCK850.71 SXDF850.74 LOCK850.73 SXDF850.76LOCK850.75SXDF850.77

LOCK850.76 SXDF850.86LOCK850.77 SXDF850.88LOCK850.78SXDF850.91LOCK850.79 SXDF850.93LOCK850.81SXDF850.94LOCK850.83 SXDF850.95LOCK850.87 SXDF850.96 LOCK850.100

SXDF850.119

indicatesarobust(P 0.05)radioidenti cation. indicatesarobustidenti cationat24µm.

coincidentradioand24-µmemission(bothP 0.1)yieldsreliableidenti cation. indicatesmultiplerobust(P 0.05)identi cations.

closevisualinspectionofthedatarevealsmorethanonegoodidenti cation.

This

procedurewasreplicatedforthe24-µmcounterpartslistedinTables3and4,correctingforblank- eld,backgroundsourcedensitiesof4.5and1.2arcmin 2tolimitsof50and150µJy,respectively.Theresult,shownintherightpanelofFig.2,isawiderdistribution,borneoutbythebest- tGaussian:aFWHMof10.7±1.0arcsec,whenconstrainedtobecentredatα=δ=0arcsec,or α= δ=4.5arcsec.Thelowaccuracyofthe24-µmpositionsrelativetothosedeterminedat1.4GHzcanaccountformostoftheextrawidth.

c0000RAS,MNRAS000,000–000Figure3.Left:Cumulativedistributionofradialoffsetsbetweentheradioandsubmmpositionsforthe62statisticallysecure(P 0.05)radioidenti- cations.Thedashedlineshowsthepredicteddistribution(1 e r2/2σ2

)assumingthatthepositionaluncertaintyinR.A.orDec.isgivenbyσ=0.6θ/SNR,asdiscussedinAppendixB,wherewehaveusedthemeanSNRsforthesample.AKStestyieldsaprobabilityof0.57thatthedataareconsistentwiththemodel.Right:Thesamepredictedprobabilitydis-tribution(dashedline),thistimecomparedwiththecumulativedistributionforall83sourceswithcandidateradioidenti cations(i.e.includingthoseforwhichP>0.05).Thepoor tintheright-handplot–aKStestyieldsaprobabilityof0.0003thatthedataareconsistentwiththemodel–demon-stratestheimportanceofusingthePstatisticto lterthecandidatelistofassociations.

Asasecondwayofquantifyingthisapproach,wecancon-sideronlythesubsetof‘robust’radioidenti cations(P 0.05)

onthebasisthatthisshouldprovidethemostsecuremeasureofthetruedistributionofuncertaintyinthesubmmpositions.Thera-dialoffsetdistributionforthissubsetof62sourcesisshownintheleft-handpanelofFig.3,whereitiscomparedwiththepredicted

cumulativedistribution(1 e r2/2σ2

),usingσ=0.6θ(SNR) 1asdiscussedinAppendixB.Forthiscalculationwehaveadoptedθ=14.5arcsecandSNR=3.17(theaverageSNRforthedeboosted850-µm uxdensitiesofthese62sources).Itisclearfromthisplotthatthepredicteddistributionisinexcellentagreementwiththatobservedforthissecuresubsetofidenti edsources;indeed,aKolmogorov-Smirnov(KS)testyieldsa57-per-centprobabilitythatthedataareconsistentwiththemodel.Forcompleteness,theright-handpanelinFig.3showsthesamepredictedprobabilitydis-tribution,thistimecomparedwiththecumulativedistributionforall83sourceswithcandidateradioidenti cations,i.e.includingthoseforwhichP>0.05.ThesameKStestnowyieldsaproba-bilityoflessthan0.1percent.Theseplotsgivecon dencethattheradialoffsetdistributionofsecureidenti cationsisconsistentwiththatexpectedgiventheJCMT’sbeamandthedeboosted850-µm uxdensitiesoftheSHADESsourcesandthatthereisnoaddi-tionalsigni cantsourceofastrometricerrorinthesubmmmaps.TheyalsodemonstratetheimportanceofusingthePstatisticto lterthecandidatelistofassociationsforrobustidenti cations.

Inconclusion,thereisnoevidenceforsigni cantadditionalsourcesofpositionalerror.ForanSMGdiscoveredinasubmmsurveywhereaMalmquist-typebiascorrectionhasnotbeenap-plied,wecanparameteriseitspositionaluncertaintyasfollows.Itspositionhavingbeendeterminedaftersmoothingwiththebeam,a

circleofradius0.91θ(SNR2app 1/2

,forpower-lawcountsoftheformN(>f)∝f (2β

,βhas+a4))

68percentchanceofcontainingthesubmmemitter(whereSNRappistherawSNR,un-correctedfor uxboosting–seeAppendixB),or0.91θ(SNR) 1ifacorrectionhasbeenapplied.Thesecorrespondtoconventional1-σerrorcircles.