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

8Ivisonetal.

Table4.Mid-IRpropertiesofSMGsintheSXDFSHADESSourceCata-logue.

Nickname

Positionat24µmSa24µm

Off

P

b

αJ2000δJ2000

/µJy

-set

hms ′′′

′′

SXDF850.01021729.59 045936.6485±47(14.1)(0.109)SXDF850.02021803.54 045526.9313±470.580.001SXDF850.04021738.69 050339.2488±472.010.005SXDF850.05021802.83 050031.0956±471.880.002SXDF850.06

021729.77 050319.6873±477.210.017021729.91 050333.3179±476.820.060021730.15 050324.2532±476.260.023SXDF850.07021738.86 050529.1325±475.460.031SXDF850.08021743.98 045552.1221±477.260.056SXDF850.10021825.61 045559.2153±475.780.057021824.88 045603.3177±47(8.21)(0.132)SXDF850.11021725.16 045935.0195±472.520.017SXDF850.12021758.60 050503.8397±47(11.5)(0.101)SXDF850.14021819.58 050232.2256±47(13.0)(0.161)021818.77 050249.0240±47(8.70)(0.110)SXDF850.16021814.41 045749.0247±47(10.7)(0.136)SXDF850.17021755.11 045250.5174±47(12.5)(0.195)SXDF850.19021827.83 045836.7536±475.400.019SXDF850.21021742.54 050425.86,844±474.370.001SXDF850.24021734.87 050432.7381±476.640.034SXDF850.27021807.93 050144.8334±473.830.018SXDF850.28

021806.32 045914.3176±47(10.9)(0.175)021806.43 045920.3477±47(10.4)(0.075)021806.87 045912.4877±474.040.007SXDF850.29021816.49 045508.2971±473.630.005SXDF850.30021740.00 050115.1523±474.690.016SXDF850.31

021736.75 045610.4452±47(14.6)(0.120)021735.83 045556.7594±477.100.025021736.37 045603.4251±476.030.043SXDF850.32021722.58 050044.4168±477.800.066SXDF850.35021800.86 045306.6215±474.660.036SXDF850.36

021831.92 045959.1162±47(13.0)(0.205)021831.95 045953.2177±477.690.065021833.04 045941.4181±47(12.9)(0.195)021831.86 045937.3182±47(11.7)(0.181)SXDF850.37021724.41 045842.0183±472.140.015SXDF850.45021830.11 050535.4157±47(12.8)(0.206)SXDF850.47021734.37 045859.9298±477.560.048021733.72 045858.7250±472.690.015SXDF850.52021805.09 050452.7151±473.080.029SXDF850.56021751.23 050630.5299±47(8.34)(0.086)SXDF850.69021751.77 050258.6157±47(9.59)(0.168)021751.06 050302.8724±47(13.0)(0.068)SXDF850.71021821.28 045858.8404±474.470.019SXDF850.76021756.32 050625.5183±47(8.86)(0.140)SXDF850.77021736.02 050428.2726±477.320.021021736.51 050425.6295±476.650.042SXDF850.86021816.66 050400.0208±47(9.13)(0.131)SXDF850.88021801.54 050442.1446±47(10.4)(0.079)SXDF850.91021734.24 045714.3203±47(12.9)(0.184)SXDF850.94021740.26 045824.0187±476.830.059021739.24 045813.1198±47(13.4)(0.192)SXDF850.96021800.40 050201.5478±47(12.7)(0.097)SXDF850.119

021756.20 045302.1784±477.200.019021755.65 045258.0202±47(10.8)(0.158)021756.24

045250.9

275±474.620.029

a)Objectsmissinghere,butlistedin

Table2,haveupperlimitsof5σ<235µJyat24µm.

b)Pwascalculatedusingasearchradiusof8arcsec.Forpossiblecounterpartswith8–15-arcsecoffsets,Pwascalculatedusingasearchradiusof15arcsec—thesevaluesarelistedinparentheses.Reliableidenti cations(P 0.05)within8arcsecarelistedinbold.

Wecanquantifythismorepreciselyintwoways.First,wecanusethedistributionofradialoffsetsforallradioidenti ca-tioncounterpartsandattempttocorrectstatisticallyforbackgroundcontamination:thedashedlineinFig.2representsthedistributionandabsolutelevelofarandomlydistributedradiopopulationwiththecountsseenintheLHradioimage(§2.1).Thenumberofradioidenti cationswithina6-arcsecradiusofthesubmmpositionsisseentoexceedtherandomlevelbyalmosttwoordersofmagnitude,whichgivesus(additional)con dencethatthevastmajorityoftheradioidenti cationsaretrulyassociatedwiththeSMGs.The nite

Table5.AlternativenamesfortheSHADESSourceCatalogue.

SHADES8-mJyaMAMBObBolocamcChapmandLOCKJ—LOCK–LE850.–LE1200.–

LE1100.–

SMMJ–105201+572443850.010100514105201.25+572445.7

105257+572105850.02–00401–

105238+572436850.030200108105238.30+572435.8

105204+572658850.0414003––105204+572526850.0604–––105153+571839850.0827104––105216+572504850.0929042––

105227+572513850.121600616105227.58+572512.4105230+572215850.140601005105230.73+572209.5105151+572637850.1607096–105151.69+572636.0105158+571800850.1703011–105158.02+571800.2105227+572217850.18–009–105227.77+572218.2

105200+572038850.2432–––105203+571813850.27–00704–105130+572036850.2911–––

105207+571906850.3012––105207.49+571904.0105155+572311850.3318012–105155.47+572312.7

105202+571915850.4021–––

105159+572423850.410801417105200.22+572420.2

105148+572838

850.76

–

–

15

–

a)Scottetal.(2002).

b)Greveetal.(2004);Ivisonetal.(2005).c)Laurentetal.(2005).d)Chapmanetal.(2005).

Figure2.HistogramsofpositionaloffsetsbetweenthepositionsoftheSMGsandthoseofthecounterparts(left:radio;right:24µm),inR.A.(α,thickblue),Dec.(δ,red)andbothtogether(black).Thedashedlinesshowtheexpecteddistributionandabsolutelevelforarandomlydistributedpopu-lationwiththeaveragecountsseenintheLHandSXDFimages.ThedottedlinesshowGaussian tswithσ=3.2arcsecwhichwereconstrainedtobecentredatα=δ=0arcsec.

searchradiuswithinwhichwehavehuntedforradiocounterpartsexplainswhytheobservednumberofcounterpartsfallsbelowthatpredictedforarandompopulationintheoutermostbinsofFig.2.NotethatFig.2usesalltheradioidenti cations,ratherthanjustthosewiththelowestPvalues,soanybiaspresentisdueonlytothe nitesearchradiiusedto ndradioemittersforthisanalysis(12.5arcsec).

Havingcorrectedtheobserveddistributionsfortheexpectedunrelated‘ eld’radiosources(thoseinthebackgroundandfore-ground),aGaussian tcentredatα=δ=0arcsec,showninFig.2,yieldsaFWHMof7.5±0.7arcsec(7.4±0.6arcsecifthecentroidisunconstrained).Thistranslatesinto α= δ=FWHM/2.354=3.2arcsec.Ourcorrectionfortheexpected‘ eld’sourcesshouldhavedealtwithanybroadeningduetoradiosourcesunrelatedtotheSMGs.ThemedianSNRoftheradio-detectedsam-pleusedinthisanalysisis3.0,aftercorrectionforMalmquist-typebias,whichimpliesthat α= δ=0.66θ(SNR) 1,adoptingθ=14.5arcsec,i.e.10percenthigherthanexpected.

c0000RAS,MNRAS000,000–000