The SCUBA HAlf Degree Extragalactic Survey (SHADES) - III. I(18)

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

18Ivisonetal.

SXDF850.16:Faintradioemissionisoffsetfromaseeminglydis-tortedopticalcounterpartby～1arcsec.

SXDF850.21:AlocalgalaxyliesclosetothisSMG–VLA0077inthecatalogueofSimpsonetal.(2006),atz=0.044;thismustbeviewedasthemostlikelyidenti cation–arareexampleofanearbygalaxyinablank-skysubmmsurvey.SXDF850.23:AsSXDF850.16.

SXDF850.24:Tworobustradioidenti cations,onenear-coincidentwithfaint24-µmemission.

SXDF850.28:Animmenselycomplexregionwithatleastthreeradio-detectedcomponents,eachwithdifferent24-µmproperties.SXDF850.29:Abrightradioidenti cation–VLA0225inthecat-alogueofSimpsonetal.(2006)–offsetsigni cantlyfromthecen-troidofabrightz=0.264opticalgalaxy.Thecorrectidenti ca-tionbecomesobviousinthenear-IR(Clementsetal.,inprepara-tion).

SXDF850.30:ThisSMGisbetrayedby24-µmand1.4-GHzemis-sion;anearbyopticalgalaxymaybetheunobscuredcomponentofalargersystem.

SXDF850.31:Tworobust24-µmidenti cations,onecoincidentwithradioemission,bothwithbrightopticalcounterparts.

SXDF850.37:OpticallyfaintSMGwithnear-coincident24-µmand1.4-GHzemission.

SXDF850.47:Acomplexregionwiththreeradio-detectedcompo-nents,eachwithnear-coincident24-µmemission.

SXDF850.52:Tworobustradioidenti cationswithverydifferentopticalproperties,onebright,oneinvisible;thebrightestoftheop-ticalgalaxiesisnotwellalignedwithitsradioemission.

SXDF850.77:AcomplexSMGwithtworadioemitters,neitherofwhichisalignedwellwiththetwo24-µmemittersintheregion.SXDF850.119:Twoplausibleidenti cations,eachwithverydif-ferentopticalproperties–onebrightandpresumablyrelativelylo-cal;theotheropticallyinvisible,likelyathighredshift.

APPENDIXB:POSITIONANDFLUXERRORSUncorrelatednoise

MuchofthetheoryneededforanunderstandingofSCUBAposi-tionerrorscanbefoundinCondon(1997),whichtreatsthegeneralcaseof ttingaGaussianellipsoidtomapdata,forwhichtherearesixfreeparameters:sourcecoordinates,total ux,twoprincipalaxesandapositionangle.Forthepresentapplication,wegenerallyprefertoassumethatSCUBAsourceswillnotberesolvedbythebeam,althoughresolvedorblendedsourcesarecertainlyknown(Ivisonetal.2000;Stevensetal.2003;Popeetal.2005).Themapshouldthereforeconsistofascaledandshiftedreplicaofthebeam,plusnoise.Thisleavesjustthreefreeparameters.

WefollowCondonandassumethatthebeamisasingle2DGaussianwithanr.m.s.‘width’σ( FWHM/2.354)ineachco-ordinate.Letthecoordinatesofthecentroidbe(α,δ)andassumethatthemapisdigitisedona( ne)gridwherethepixelspacingishandthenoisevalueateachpixelisanindependentzero-meanGaussiandeviatewithr.m.s.value,µ;theunitsofµarethoseofsurfacebrightness.Thepeakvalueofthe ttedpro leisA;strictly,thisisasurfacebrightnessvalueandthetotalintegrated uxden-sitywillbeS=2πσ2A.However,normallythefactor2πσ2willbeabsorbedintomapunitsofmJybeam 1orequivalent,sothatAhasthenumericalvalueofthe uxdensityofa ttedunresolvedsource.Withthisnotation,Condon’ssolutionforther.m.s.errors( )onthethree-parameter tis

A=

hπ(B1)

2Ah.

Forapracticalformula,itmakessensetocombinethesebyde ningthe uxsignal-to-noiseratio:SNR=A/ A:

α= δ=

√