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Detection of a Coherent Magnetic Field in the Magellanic Bridge through Faraday Rotation PDF

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Preview Detection of a Coherent Magnetic Field in the Magellanic Bridge through Faraday Rotation

Mon.Not.R.Astron.Soc.000,000–000(0000) Printed24January2017 (MNLATEXstylefilev2.2) Detection of a Coherent Magnetic Field in the Magellanic Bridge through Faraday Rotation J. F. Kaczmarek,1(cid:63) C. R. Purcell,1,2 B. M. Gaensler,1,3 N. M. McClure-Griffiths,4 J. Stevens5 1SydneyInstituteforAstronomy,SchoolofPhysics,TheUniversityofSydney,NSW2006Australia 2ResearchCentreforAstronomy,Astrophysics,andAstrophotonics,MacquarieUniversity,NSW2109,Australia 3DunlapInstitute,UniversityofToronto,50St.GeorgeStreet,Toronto,ONM5S3H4,Canada 4ResearchSchoolofAstronomyandAstrophysics,AustralianNationalUniversity,Canberra,ACT2611,Australia 5CSIROAstronomy&SpaceScience,1828YarrieLakeRoad,Narrabri,NSW2390Australia 7 1 24January2017 0 2 n ABSTRACT a WepresentaninvestigationintothemagnetismoftheMagellanicBridge,carriedoutthrough J the observation of Faraday rotation towards 167 polarized extragalactic radio sources span- 1 ningthecontinuousfrequencyrangeof1.3−3.1GHzwiththeAustraliaTelescopeCompact 2 Array. Comparing measured Faraday depth values of sources ‘on’ and ‘off’ the Bridge, we find that the two populations are implicitly different. Assuming that this difference in pop- ] ulations is due to a coherent field in the Magellanic Bridge, the observed Faraday depths A indicate a median line-of-sight coherent magnetic-field strength of B (cid:39) 0.3µG directed (cid:107) G uniformly away from us. Motivated by the varying magnitude of Faraday depths of sources . ontheBridge,wespeculatethatthecoherentfieldobservedintheBridgeisaconsequenceof h thecoherentmagneticfieldsfromtheLargeandSmallMagellanicCloudsbeingpulledinto p thetidalfeature.Thisisthefirstobservationofacoherentmagneticfieldspanningtheentirety - o oftheMagellanicBridgeandwearguethatthisisadirectprobeofa‘pan-Magellanic’field. r t Keywords: galaxies:MagellanicClouds,galaxies:magneticfields s a [ 1 v 1 INTRODUCTION Tidaltails,streamsandbridgesplayanimportantroleinthe 2 evolutionoftheparentgalaxiesaswellasthehostenvironment,as 6 TheLargeMagellanicCloud(LMC)andSmallMagellanicCloud theyserveasasiphonforgalacticmaterialtobedispensedintothe 9 (SMC) are a highly-studied galaxy pair. Due to their close prox- diffuseintergalacticmedium.Itcanbepositedthatapre-existing 5 imity to the Milky Way (MW), the Magellanic Clouds allow as- magneticfieldcouldfollowthemovementofneutralgasintothe 0 tronomers to study galaxy interactions and evolution in unprece- intergalactic medium. The stretching and compressing of tidally 1. dented detail. The on-going interaction between the galaxy pair, strippedgasmaythenserveasamechanismfortheamplificationof 0 and possibly the MW, have led to the creation of the Magellanic anyexistingmagneticfields(Kotarbaetal.,2010).Thus,thestrip- 7 Bridge (MB), the Magellanic Stream, and the Leading Arm (see pingoftidaldebrismaybepartiallyresponsibleforthedistribution 1 Beslaetal.2010andD’Onghia&Fox2016foracompletereview). ofmagneticfieldsoverlargevolumes.Whatremainsunclearisthe : Eachofthesetidalfeaturescanbeidentifiedthroughthepresence v importanceandroleofmagneticfieldswithintidalfeatures. Xi poefrlhaarpgsetahmeoMunBts(oHfinHdImgaans.eMt aols.t1p9r6o3m)in–eantcoofnttihgeusoeufse,agtuasreesouiss The association between tidal remnants and magnetic fields hasbeenstudiedfornearlytwodecades.Classically,theradiocon- r tidalfeaturethatspanstheregionbetweentheLMCandSMC.We a tinuumtidalbridgeconnectingthe‘Taffy’galaxies(Condonetal., assumethattheMBislocatedatadistanceof55kpc,themeandis- 1993)wasestimatedashavingasimilarmagnetic-fieldstrengthto tancetotheLMCandSMC(Walker,1999).Wealsoassumethat thepre-collisiongalaxiesandthefieldlinesappearedtobestretch- thebulkoftheHIemissionintheMBhasaradialvelocityinthe ingacrossthespacebetweenthegalaxypair.Morerecently,tidal range+100kms−1 ≤ v ≤ +300kms−1(Putmanetal.,2003; LSR dwarfs within the Leo Triplet and Stephan’s Quintet have been Mulleretal.,2003).Thetidalremnantisthoughttohaveformed showntopossesscoherentmagneticfieldsandhavetotalmagnetic- ∼200MyragowhentheLMCandSMCwereattheirclosestap- fieldstrengthsofB = 3.3 ± 0.5µGandB = 6.5 ± 1.9µG, proach to one another (Gardiner & Noguchi, 1996; Besla et al., T T respectively (Nikiel-Wroczyn´ski et al. 2013a, Nikiel-Wroczyn´ski 2012). etal.2013b). Decades of research using optical polarized starlight has (cid:63) email:[email protected] shown that polarization vectors in the plane of the sky trace out (cid:13)c 0000RAS 2 J.F.Kaczmareketal. apathfromtheSMCalongthewesternBridgeorientedinthedi- rectionoftheLMC(Mathewson&Ford,1970a,b;Schmidt,1970, 1976; Magalhaes et al., 1990; Wayte, 1990; Lobo Gomes et al., LMC 2015).Duetothelimitednumberofstarswithwhichonecancarry North outopticalpolarimetrystudies,allpreviousclaimsoftheexistence ofacoherentmagneticfieldspanningtheentireMagellanicSystem West havehadtobespeculativeduetothelackofinformationstemming fromthediffuseMB. -2m) Studies of Faraday rotation of background polarized radio c sources towards the LMC have determined that the galaxy has a 18(10 Join I coherentmagneticfieldofstrength∼1µG(Gaensleretal.,2005). Maoetal.(2008)observedtheSMCusingbothFaradayrotation measuresandpolarizedstarlight.Throughcarefulconsiderationof theGalacticforegroundtheyconstructed3Dmodelsforthemag- SMC South neticfieldandshowedthattheorientationofthefieldhasapossible Wing alignmentwiththeMB. A similar investigation into Faraday rotation towards ex- tragalactic polarized sightlines has shown that a high-velocity cloud(HVC)intheLeadingArmhostsacoherentmagneticfield Figure 1. Neutral hydrogen column density for the velocity range of (McClure-Griffiths et al., 2010). In such an instance, a magnetic +100 ≤ vLSR ≤ +300kms−1oftheMBregionfromtheGASSsur- fieldcouldworktoprolongthestructurallifetimeoftheHVCasit vey(McClure-Griffithsetal.2009,Kalberlaetal.2010),over-plottedwith thepositionsofobservedradiosources.Eachpointingisassociatedwitha isaccretedontotheMWdisk.Whiletheexactoriginofthemag- regionnamedenotedbythetextintheenclosedareas.Redcircles(point- neticfieldinthisHVCremainsunclear,itisplausiblethattheHVC ingsenclosedbyasolidline)aresourceswheretheMBisconsideredto fragmented from a magnetized Leading Arm. Therefore, the ob- intersectthebackgroundsource’sline-of-sight,whereassourcesmarkedby servedmagneticfieldintheHVCwouldbeaconsequenceofthe blackcircles(pointingsenclosedbyadashedline)areconsideredashav- initialseedfieldfollowedbycompressionandamplificationdueto inglines-of-sightthatarenotcontaminatedbytheMB.Theselattersources theMWhalo. wereobservedinordertosubtracttheFaradayrotationcontributionfrom AlthoughmagneticfieldshavebeenfoundintheSMC,LMC, foregroundsandbackgrounds. andsomeHVCs,noneofthepreviousinvestigationsofmagnetism intheMagellanicSystemhavedirectlyconfirmedtheexistenceof the Pan-Magellanic Field – a coherent magnetic field connecting (B ,inµG)accordingto (cid:107) thetwoMagellanicClouds. (cid:90) 0 φ(L) = 0.812 n B dl, (3) e (cid:107) L whereListhedistancethroughthemagneto-ionicmaterialinpar- 1.1 FaradayRotation secs.ThesignoftheFaradaydepthisindicativeoftheorientation Complexlinearpolarizationisanobservablequantityandcanbe ofthemagneticfieldwithapositiveφsignifyingthefieldtobeori- definedas entedtowardstheobserverandanegativeφimplyingafieldthatis pointingaway. P = Q+iU =p e2iΨ, (1) 0 Themeasuredφ foraextragalacticsourcebehindtheMB obs whereQ,andU aretheobservedlinearlypolarizedStokesparam- isasummationofthevariousFaradaydepthcomponentsalongthe eters,p isthepolarizationfractionintrinsictothesourceandΨis line-of-sightandcanbebrokendownintoitsconstituentpartsas 0 theobservedpolarizationangle,alsodefinedas: follows: 1 U φobs = φintrinsic + φIGM + φMB + φMW, (4) Ψ= arctan . (2) 2 Q whereφ istheFaradaydepththatisassociatedwiththepo- intrinsic Thepolarizationangleisrotatedfromitsintrinsicvalue(Ψ )any larizedemittingsource,φ isanyrotationduetotheintergalac- 0 IGM time the emission passes through a magneto-ionic material. This ticmedium,φ isourtargetedFaradaydepthduetotheposited MB effectisknownasFaradayrotation.ThetotalobservedFaradayro- MB magnetic field and φ is the Faraday rotation due to the MW tation,defined∆Ψ/∆λ2,isknownastherotationmeasure(RM). foreground MW.Although φ ,φ andφ are present intrinsic IGM MW Whentherotatingmaterialislocatedalongtheline-of-sight, along all sightlines, φ is likely to dominate the observed sig- MW Faraday rotation can serve as a powerful tool to analyse mag- nal.ThisassumptionappearstohavebeenwelljustifiedinTaylor netism.Inthesimplecaseofathermalplasmathreadedbyasin- etal.(2009),wherebymappingtherotationmeasuresofextragalac- gle magnetic field, the intrinsic polarization angle is rotated by ticpolarizedsourcesfromtheNRAOVLASkySurvey(NVSS)re- ∆Ψ = RMλ2 radians.However,recentstudieshaveshownthat vealedlocalstructuresintheGalaxy.Therefore,byobservingpo- theRMmayofferanincomplete,ormisleadingdiagnosticofthe larizedsourceswithsightlinesthatdonotintersecttheMB,wewill actual polarization properties along the line-of-sight (O’Sullivan be able to correct for the Galactic foreground, leaving the resid- etal.,2012;Andersonetal.,2016)andthatmanysourcescannotbe ualφtorepresenttheintrinsicpropertiesofthebackgroundsource describedbyasingleRM.Itisthereforemorerobusttodiscussthe andtheMBcontribution.Theintrinsicpolarizedpropertiesofeach polarizedsignalintermsofitsFaradayDepth(φ),asfirstderived polarized source are random and considered to have a negligible by Burn (1966). The Faraday depth encodes the electron density effectontheoverallstatisticsforalargesample. (n , in cm−3) and magnetic-field strength along the line-of-sight IfthereexistsacoherentmagneticfieldthreadingtheMB,ob- e (cid:13)c 0000RAS,MNRAS000,000–000 DetectionofaCoherentMagneticFieldintheMagellanicBridgethroughFaradayRotation 3 Table1.Summaryoftheobservations.Column1givesthearrayconfiguration;Column2givestheregionstargeted(asdefinedin§2);Column3liststhe lengthoftheobservingrunandColumn4givesanapproximationforthetotalintegrationtimepersource.Column5givestheUTdateofthecommencement oftheobservations. ArrayConfig. Obs.Targets Obs.Length TimeOn-Source Obs.Date (hrs) (min) 6C Wing,West 12 2.5 2015Mar14 6A Wing,West 15 1.5 2015Apr30 6A Join,North,South 15 3 2015Apr30 1.5B Wing(subset) 3 5 2016Jun11 servationsoflinearlypolarizedbackgroundradiosourcesmayhold in order to improve uv-coverage. Phase calibrators were ob- the key to its discovery. In this work, we use detailed measure- served at least every 40 minutes. The bandpass and flux calibra- mentsoftheFaradaydepthofbackground,extragalacticpolarized torPKSB1934-638wasobservedon14March2015and30April sources to investigate the existence of a coherent magnetic field 2015 and PKSB0823-500 was observed as the bandpass calibra- spanningtheMB.Wedescribeoursourceselectionprocessandob- toron11June2016.polarizationleakagecalibrationswerecarried servationsinSection2,followedbydatareductionandprocessing outusingtheaforementionedprimarycalibrators.Onaverage,each inSection3.WepresentourresultsinSection4,whichincludethe pointingwasobservedforatotalof3minutes.Duetothenatureof fittingandsubtractionoftheMWforeground.Section5motivates thesourceselectionassociatedwiththe‘Wing’andthepossibility differentdistributionsofionizedgasandthesubsequentlyderived thatsourcescouldbeweakintotalintensity,theinitial3minutesof magnetic-fieldstrengths.InSection6wediscussthepossibleori- observationwassometimesnotenoughtoreachasufficientsignal- ginsandimplicationsofthepan-MagellanicField.Asummaryis to-noise.Additionalobservationsweremadeasasinglehour-angle presentedinSection7. uv-cuton11June2016inordertoimproveoursensitivitylimits forpointsthatwerenotbrightenoughinpolarizationnortotalin- tensitytobeconfidentlydetectedwithourinitialobservations.A summaryoftheobservationsislistedinTable1andtherepresen- 2 OBSERVATIONS&DATA tativeuv-coverageforanysourceineachregionisshowninFigure 2.1 SourceSelection 2. For this investigation, we observed a subset of polarized sources that were originally identified through the reduction and re- processing of archival continuum data of the western MB (see 3 DATAREDUCTIONANDEXTRACTION Muller et al. (2003) for a summary of observations). In the liter- Observationswerecalibratedandimagedinthe MIRIADsoftware ature,thisregionhasbeenreferredtousuallyaseitherthe‘Wing’ package(Saultetal.,1995)usingstandardroutines.Flaggingofthe or‘Tail’(Bru¨nsetal.,2005;Lehneretal.,2008),andwemakeref- datawasdonelargelywiththeautomatedtaskPGFLAG,withminor erence to this region as the ‘Wing,’ exclusively (See Figure1 for manualflaggingbeingcarriedoutwithtasksBLFLAGandUVFLAG. location). The HI observations of the ‘Wing’ had simultaneously Naturally-weightedStokesI,Q,U andV mapsweremadeusing observedthecontinuumemissionassociatedwiththisregion.The theentire2GHzbandwidth.Deconvolutionofthemulti-frequency source-findingalgorithmAegean(Hancocketal.,2012)wasusedto datasetwasperformedonthedirtymapswiththetaskMFCLEAN. identifypolarizedsourcesinthefinal,deconvolvedcontinuumim- Cleaningthresholdsweresettobe3timesthermsStokesV levels ages.Fromthisoriginalsample,wetargeted101polarizedsources (3σ )forStokesQandU,and5σ forStokesI.Imageswerecon- V V forfollow-upobservations. volvedtoacommonresolutionof8arcseconds,whichcorresponds Anadditional180radiosourcesweretargetedinordertoex- toalinearscaleof2pcattheassumeddistancetotheMBof55kpc. tendtheinvestigationacrosstheentiretyoftheMBandsurround- Fromthebroadband2GHzimages,imagesoflinearlypolar- ing area. Motivated by the changing morphology and kinematics izedintensity(P)weremadewiththetaskMATH.Thetotalpolar- of the Bridge, we separate these additional sources into regions ized flux of a target was extracted from an aperture 8arcseconds ‘West’,’Join’,‘North’,and‘South’.Theseadditionalradiosources indiametercentredonthepeakpolarizationpixelwithnoiseesti- were selected from the Sydney University Molonglo Sky Survey mates(σ )measuredasthermsresidualsfromasource-extracted P (SUMSS,Mauchetal.2003)ashavingaStokesIflux≥ 100mJy image.Atargetwasconsidered‘polarized’iftheintegratedpolar- at843MHzfortheregionlabelled‘West’and≥ 150mJyforre- izedfluxwasgreaterthan8σ .Thismethodofimagingwillleadto P gions ‘Join,’ ‘North’ and ‘South’. Figure 1 gives a summary of bandwidthdepolarizationforsourceswithabsoluteFaradaydepths thepointingregionsobservedoverlaidonamapofneutralHydro- greater than ∼ 90radm−2; however, we consider the number of gen(HI)oftheregionfromtheGalacticAllSkySurvey(GASS; sourcesrejectedduetohighFaradayrotationtobenegligibleand McClure-Griffithsetal.2009;Kalberlaetal.2010). hasnoimpactonourfinalsciencegoals. Imagingwithnarrowbandwidthsdecreasesthesignal-to-noise inadditiontoreducingtheresolutioninFaradaydepthspace,while 2.2 Observations broadbandwidthsdecreasethemaximumobservablescaleinFara- Observationsofthe281radiosourcesweretakenover3dayswith dayspace,aswellasthemaximumobservableFaradaydepth.Inor- theAustraliaTelescopeCompactArrayunderprojectC3043.Tak- dertominimisethebandwidthdepolarizationandmaintainadesir- ingadvantageoftheinstantaneousbroadbandwidthsoftheCom- ablesignal-to-noiseratio,StokesI,Q,U imagesweremadeevery pact Array Broadband Backend (CABB, Wilson et al. 2011), the 64MHz-resultingin27channelmapsspanning1312-3060MHz. observations spanned the continuous frequency range of 1100– AswiththebroadbandP images,integratedfluxeswereex- 3100MHz. Each pointing was observed as a series of snapshots tractedfromeachmapfromanequivalentbeamareacentredonthe (cid:13)c 0000RAS,MNRAS000,000–000 4 J.F.Kaczmareketal. (a) WingandWestregions (b) Join,NorthandSouthregions Figure2.Typicaluv-coverageofasingleradiosourceassociatedwith(a)the‘Wing’and‘West’and(b)‘Join’,‘North’,‘South’. Region Observed Polarized Acceptedfraction 3.1 qu-fittingandφdetermination (%) Wing 101 69 68 We adopt the fractional notation such that q = Q/I and u = West 83 40 48 U/I,wheretheobservablepolarizedfractioncanbeexpressedas Join 23 15 65 (cid:112) p = q2+u2. (5) North 34 22 65 South 40 21 53 In working with fractional Stokes parameters the wavelength de- 281 167 59 pendent depolarization effects are decoupled from spectral index Table2.Summaryoftotalnumberofpointsobservedperregionandtotal effects. number of polarized sources accepted. In order to be accepted, a source Tocreateourfractionalpolarizedspectra,theQandUspectra must be detected to at least 8σ in the full bandwidth polarized intensity aredividedbyamodelfittotheStokesI spectrum.Thisapproach image.The‘Wing’regionreturnsahigherfractionofpolarizedsourcesdue avoidscreatingnon-Gaussiannoiseandthepropagationofsmall- toourpreviousknowledgeofthepolarizationinthisregion. scalespectralerrorsthatmaybepresentintheStokesI spectrum. Usingabootstrapapproachwith10,000iterations,wefitasecond- orderpolynomialtotheStokesIspectrumofeachpolarizedsource andcalculatethestandarddeviationoftheresultantqanduvalues foreachfrequencychannel.Thetotalerrorisconsideredtobethe standarddeviationofthebootstrappedvaluesofq anduaddedin quadraturetothemeasurednoisefromthecleanedStokesQand pixelcorrespondingtothepeakinP.Errormeasurementswerees- U maps.Thebootstrapmethodisnecessarytocorrectlypropagate timatedastherms-noiselevelfromimagescreatedfromtheresid- theuncertaintyduetothefitandhastheoveralleffectofincreasing ualoftheStokesmapsafterthesourceaperturewasblanked.With themagnitudeoftheerrorsfromwhatcanbemeasuredfromthe theexceptionofsourcesassociatedwiththe‘Wing’,alltargetsare Stokesmaps. expectedtobebrightintotalintensity.Afurther10σ cut-offwas InordertoextracttheobservedFaradaydepthfromourpolar- imposed,andextractedspectrawithfewerthan10channelswere izedsignal,wemustmotivateapolarizationmodelfortheMBen- discarded. vironment.ExternalFaradaydispersion(Burn,1966)canbeused The procedures described above result in 167 sources with as a proxy to measure fluctuations in the free-electron density or spectra in I, Q and U. Table2 has a summary of the fraction of magnetic-fieldstrength.Thismodelhasbeenusedinnumerouspast sourcesacceptedperregion.The‘Wing’regionhasanadvantage studiesofthepolarizationofgalaxies,galaxygroupsandclusters inreturningahighernumberofpolarizedsourcesduetoourprevi- (Laing et al., 2008; Gaensler et al., 2005). Without an observed ousknowledgeofthepolarizeddetectionsintheregion.However, continuum-emission component of the MB, a single-component ourdataextractionmethodrejectedmultipletargetsinthe‘Wing’ externalFaradaydispersionmodelservesasanappropriateapprox- regionforfallingbelowthesensitivitythreshold.Figure3givestwo imationtothepolarizationsignalassociatedwiththeMB. examplesoftotal((a)and(c))andpolarizedintensity((b)and(d)) Polarization of this form displays a decreasing polarization detectedfromextragalacticradiosources. fractionasafunctionofλ2.Thisdepolarizationcanbedefinedas (cid:13)c 0000RAS,MNRAS000,000–000 DetectionofaCoherentMagneticFieldintheMagellanicBridgethroughFaradayRotation 5 (a) TotalintensityforsourceJoin08 (b) PolarizedintensityforsourceJoin08 (c) TotalintensityforsourceWest02 (d) polarizedintensityforsourceWest02 Figure3.Exampleoftwopolarizedsourcesdetectedinoursurvey:points‘Join08’(a)and(b)and‘West02’(c)and(d).Multi-frequencyimagesfortotal intensity(StokesI)areshownin(a)and(c)andpolarizedintensity(P)in(b)and(d).Bothsourceshavebeenimagedusingthefullbandwidthavailableand therestoringbeamisshowninthebottomleftofeachimage. Table3.Asubsetofmeasuredandcalculatedsourceparameters.Columns(1)and(2)givethesourcelocationinGalacticlongitudeandlatitude,respectively. Column(3)liststheintegratedtotalintensity(I)overthefull2GHzbandwidthwithuncertainties.Integratedpolarizedflux(P)withuncertaintyislisted inColumn(4).Columns(5-8)givethebest-fitparametersreturnedfromqu-fitting:namely,theintrinsicpolarizationfraction(Column(5)),theintrinsic polarizationangle(Column(6)),thetotalFaradaydepthalongtheline-of-sight(Column(7))andtheFaradaydispersion(Column(8)). (1) (2) (3) (4) (5) (6) (7) (8) l b I P p0 Ψ0 φobs σφ (◦) (◦) (mJy) (mJy) (%) (◦) radm−2 radm−2 291.778 -40.785 104.9 ± 0.2 3.2 ± 0.3 5.8+0.7 37+4 +6+3 21+2 −0.6 −4 −4 −2 288.589 -39.501 258.4 ± 0.07 3.9 ± 0.3 1.66+0.09 82+3 −0.2+2 3+2 −0.08 −3 −2 −2 290.958 -45.418 215 ± 3 7.1 ± 0.4 2.8+0.3 49+5 +13+4 23+2 −0.3 −5 −4 −2 285.625 -39.347 123.8 ± 0.2 1.6 ± 0.2 6.38+0.07 143.9+0.5 +26.8+0.3 13.9+0.2 −0.07 −0.5 −0.3 −0.2 296.659 -45.653 73.0 ± 0.2 6.8 ± 0.3 10.1+0.4 71+2 −13.1+0.9 10.7+0.8 −0.4 −2 −1 −0.8 p/p ,wherepistheobservedpolarization.Thiseffectismostev- theform 0 iddeennctetoowfaerxdtserlnoanlgFwaaravdealeyngdtihsps.eDrsuioent,oatnhdeiptusrdeleypeenxdteernncaeldoenpethne- P = p0e2i(Ψ0+φobsλ2)e−2σφ2λ4, (6) sizeoftheobservingbeam,thisdepolarizationmodelisoftenre- whereφ isthetotalobservedFaraday-depthvalue(Equation4) obs ferredtoas‘beamdepolarization’.Inthisscenario,averagingthe and σ2 characterises the variance in Faraday depth on scales φ fluctuationsacrosstheentirebeamarea,theresultispolarizationof smallerthanourbeam. (cid:13)c 0000RAS,MNRAS000,000–000 6 J.F.Kaczmareketal. ofthewalkersisremovedbeforeinitiatinga300-stepexplorationof thenewparametersub-space.Thebestfitmodeliscalculatedasthe meanofthemarginalisedposteriordistributionforeachparameter. Theparameteruncertaintiesaremeasuredfromthe1σdeviationof thewalkersaboveandbelowtheresultantbest-fit. Figure4givesanexamplesolutionfromqu-fitting.Thefrac- tional Stokes spectra (p, q and u) versus λ2 is shown in the top panel(a).Observedvaluesareshownasblack,blueandredpoints forp,qandu,respectively.Thebest-fitsolutionisshowntotrace theobserveddata.ThebestfitsolutiontoΨversusλ2 isgivenin thebottompanel(b).Weattributeanydeviationfromthemodelto Faradaycomplexityofthesourceoraline-of-sightcomponentthat is not accounted for in the simple polarization model we assume (Equation6). (a) FractionalStokesspectra 4 RESULTS In addition to fitting the observed Faraday depth (φ ), our fit- obs tingroutinealsoreturnsbest-fitvaluesforallpolarizationparam- etersdefinedinEquation6,namelyp ,Ψ andσ .Asubsample 0 0 φ ofsourceswiththeresultantbest-fitparametersisgiveninTable3, withthefulldatasetavailableinAppendixB. Figure5 shows the best-fit φ of every polarized radio obs source plotted over the HI emission of the region from GASS (McClure-Griffithsetal.,2009;Kalberlaetal.,2010).Redcircles indicateapositiveφ andafieldthatisorientedtowardstheob- obs server;bluecircles,theopposite.Blackcrossessignifyaφ that obs is consistent with zero to 2×dφ where dφ is the returned uncer- taintyinFaradaydepthfromqu-fitting. We divide the observed polarized sources into two popula- (b) Ψvs.λ2 tions – those where the MB intersects the sightline to the polar- ized source and those with sightlines that are unaffected by the Figure4. (a)Observeddataandbest-fitsolutionforqu-fittingtoapoint MB.Wedefinean‘on-Bridge’regiontobetheareadefinedbya inthe‘West’region.ObservedfractionalStokesqanduareshownasblue non-extinctioncorrectedHαintensityofI =0.06R,shownasthe andredpoints,respectively,whereasthemodelsolutionisshownasblue Hα lowestcontourinFigure8.TheHαdatasetandsubsequentanalysis andredlines.Theobservedandmodelpolarizedfractionisshownasblack pointsandablacklineforreference.(b)Correspondingfittopolarization isdiscussedinmoredetailinSection§5.1.Allsourcesassociated angle(Ψ)versusλ2fortheaforementionedsolutionfromqu-fitting. withthe‘Wing,’‘West’and‘Join’regionsmeetthiscriterion.The ‘North’and‘South’regionsareconsideredtobe‘off-Bridge’and serveasaprobeoftheMW’sFaradaydepthstructureintheregion. Wecalculatethebest-fitφ ,σ andΨ foreachpointsource Of all the φobs-values in the imaged region, 84% are posi- obs φ 0 tive (red), and all of the negative (blue) and null (cross) Faraday byfittinganexternalFaradaydispersionmodel(Equation6)simul- taneouslytotheextractedq(λ2)andu(λ2)data.Thistechniqueis depths are associated with the on-Bridge region (Figure5). Fig- calledqu-fittingandSunetal.(2015)showittobethebestalgo- ure6showstheφobs populationofallon-andoff-Bridgesources asacumulativehistogramandhighlightsthecleardiscrepancyin rithmcurrentlyavailableforminimisingscatterinderivedpolariza- Faraday depths for each population. We test the statistical likeli- tion parameters. We take a Monte Carlo Markov chain (MCMC) hoodthattheFaradaydepthsassociatedwithpointsonandoffthe approach to fitting our complex polarization parameters by em- ployingthe‘emcee’Pythonmodule(Foreman-Mackeyetal.,2013). BridgecomefromasinglepopulationbyperformingaK-sample Anderson-Darling test on the best-fit φ -values for all sources ComparedtoLevenburg-Marquardtfitting,MCMCbetterexplores obs thathavebeendetectedto8σ orhigherinpolarizedintensity.The the parameter space, and returns numerically-determined uncer- P returned normalised test statistic allows us to reject the null hy- taintiesforthemodelparameters.Thelog-likelihoodofthecom- plex polarization model of the joint qu chi-squared (χ2) is min- pothesiswitha99.992%confidencelevel.ThedifferenceinFara- day depths between the populations of φ -values indicate that imised to find the best-fitting parameters. For each pointing, we obs thepolarizedradiationonandofftheMBprobedistinctlydifferent initialise a set of 200 parallel samplers that individually and ran- domlyexplorethen-dimensionalparameterspace(wherenisthe magneticenvironments. degreesoffreedom).Eachofthesesamplers–called‘walkers’– iterativelycalculatethelikelihoodofagivenlocationinparameter 4.1 CorrectingforFaradayRotationduetotheMW spaceandindoingsomapoutaprobabilitydistributionforasetof Foreground parameters. Weinitialisethewalkerstorandomvaluesofthefreeparame- TheamountofFaradayrotationobservedtowardsanextragalactic tersandrunthree300iteration‘burn-in’phaseswherethesamples pointsource(φ )willalwaysincludesomecontributionfromthe obs settleonaparametersetofhighestlikelihood.Thepositionhistory MW.Therefore,beforetheline-of-sightmagnetic-fieldstrengthcan (cid:13)c 0000RAS,MNRAS000,000–000 DetectionofaCoherentMagneticFieldintheMagellanicBridgethroughFaradayRotation 7 ) 2 -m c 8 1 0 1 ( I Figure5.φobsvaluesfittoanexternalFaradaydispersionmodeloverlaidonamapofHIintensityfromGASS(Kalberlaetal.,2010)inthevelocityrange of+100 ≤ vLSR ≤ +300kms−1.BlackcontoursrepresentHIemissivityof1.2and5.0×1020cm−2.Thesizeofeachcircleisrepresentativeofthe magnitudeofφ,withscale-circlesshowninthebottomleftcorner.Redcirclesrepresentaline-of-sightmagneticfieldpointingtowardstheobserver(positive φ),andbluecirclesshowafieldthatispointingaway(negativeφ).Blackcrossesshowφvaluesconsistentwithzeroto2×dφ. be estimated, the Galaxy’s contribution to the observed Faraday modelwerevalid,thedistributionofFaradaydepthsshouldbecome depth must be fit and corrected for. The 43 off-Bridge φ can moresimilaraftertheforegroundcorrectionhasbeenapplied.We obs bedescribedbyatilted-planeφ -model,whoseparametersare testthistheorybyconductingtwoseparateAnderson-Darlingtests MW obtainedusinganon-linearleast-squaresfittothedata.Thebest-fit ontheφ andφ distributionsforthetwooff-Bridgeregions. obs corr solutionwasfoundtobeoftheform We find that before the foreground correction is applied there is ∼ 98% confidence that the two background samples are drawn φ = −0.511(cid:96) + 1.28b + 225, (7) MW fromdifferentpopulations.Onceourmodelissubtractedfromthe wherelandbarethecoordinatesinGalacticlongitudeandlatitude, raw,observedFaradaydepths,thelikelihoodthatthetwopopula- respectively. The plane is shown in Figure7. By subtracting the tionsareuniquedropsto67%.Atthislevelthereisnolongersuf- resultantFaradaydepthsurfacefromallφ ,theresidualFaraday ficientconfidencetosaytheyarenotdrawnfromthesameparent obs depths(φ areconsideredtobeforeground-corrected). distribution. We therefore consider our simplified tilted-plane as- corr sumptionoftheFaradaydepthdistributionoftheMW-foreground WecompareourMWFaradaydepthmodelwithsimilarmod- tobejustifiable. elsfromMaoetal.(2008)andOppermannetal.(2015).Testinga pointinthecentreofthe‘Join’region((cid:96) = 290◦,b = −38◦), Figure8 shows the foreground-subtracted Faraday depths ourfitreturnsaφ -valueof+28radm−2.Atthesameposition, MB acrosstheimagedregion.Weexpectthatafterourforegroundcor- MWmodelsfromMaoetal.(2008)andOppermannetal.(2015) rection,themajorityofoff-Bridgesourceswouldhavevaluesnear returnvaluesof+28radm−2 and+25radm−2,respectively.The zero,butthisisnotobserved.Weassumethatthemajorcausefor closeagreementamongstallthreeMWmodelsaddsconfidenceto this discrepancy is that our foreground model is an oversimplifi- ourMWcorrection. cation of the likely complex Faraday structure of the MW (Op- Wefurthertestthevalidityoftheforegroundφ -modelby permann et al., 2015). We test the merit of a higher-order fore- MW comparing the distributions of the uncorrected and corrected φ- groundFaradaydepthmodel,butitproducesminimalimprovement values(φ andφ ,respectively)forpointsinthe‘North’and whileincreasingthedegreesoffreedom.Ifourforegroundfitwas obs MB ‘South’regions.Iftheassumptionsmadetocreatetheforeground wellfounded,wewouldexpecttohaveameanφ -valueofoff- corr (cid:13)c 0000RAS,MNRAS000,000–000 8 J.F.Kaczmareketal. Figure6.CumulativehistogramofRMvaluesforon-Bridge(red)andoff- Bridge(black)sources.Thefigureistruncatedatφ = ±45radm−2for Figure7.Anestimationoftheforeground-andbackground-φcoveringour clarity. fieldofview,assumingtheFaradaydepthvariesasatiltedplaneacross ourimagedregion.Thefitusedthe43off-Bridgesourceswhichareshown aswhitedots.Thelocationoftheon-Bridgesourcesareshownaswhite Bridgepointsnearzero:oursamplereturnsφ = 0.3radm−2 off,corr crosses. withastandarddeviationof12.0radm−2,comparedtoφ = off,obs 25radm−2 before subtracting the foreground. We note that the foregroundφMW fitdoesnotattempttofitandsubtracttheFara- anyofthebackgroundsourcesatourphysical-scalesensitivityof dayrotationthatisintrinsictothebackgroundsource.Schnitzeler 8arcseconds. (2010) estimates the spread in intrinsic Faraday depths of extra- galacticsourcestobe(cid:39) 6radm−2,whichcanaccountformuchof thelargestandarddeviationoftheoff-Bridge,foreground-corrected Faradaydepths. 5 THELINE-OF-SIGHTMAGNETIC-FIELDSTRENGTH The uncertainty in the foreground Faraday depth subtrac- 5.1 EmissionMeasures tion must be included the error in the Faraday depth of the on- Bridge sources. The magnitude of the increased error was deter- Ourobjectiveistocalculatetheline-of-sightmagneticfield(B ) (cid:107) minedthroughbootstrappingtheforegroundφ surface10,000 associatedwiththeMB;however,B isdegeneratewithestimates MW (cid:107) times with the standard deviation of the correction at each loca- ofelectrondensity(n ).Thereforeanindependentestimateofn e e tion(σ ).ThemeanuncertaintyinFaradaydepthsthroughthis is required. By making some assumptions about the line-of-sight φMW methodisσ = 0.21radm−2.Theexpressionforthetotalun- depth of the ionized medium, it is possible to use observed Hα φMW certaintyintheFaradaydepthofabackgroundradiosourcethere- intensitiesasameanstoindependentlyestimaten2 bytakingad- e forebecomes vantageoftheimpliedemissionmeasure(EM).TheEMisdefined astheintegralofthesquareoftheelectrondensityalongthepath- dφ(l,b)2 = dφ2 + σ2 (l,b), (8) MCMC φMW lengthofionizedgas(LHII)andcanbederivedfromthemeasured where(l,b)arethecoordinatesofthepointsource. Hαintensity(IHα)inrayleighs(R)1 WeinferthattheMBFaradayrotation,φMB,accountsforthe (cid:90) L majorityoftheresidualrotationseeninpointsassociatedwiththe EM= ne(l)2dl=2.75T40.92IHα pccm−6. (9) MBandassumeforallfurtheranalysisthat(φ −φ ) = φ , 0 obs MW corr whereφ ≈ φ .Amapofforeground-correctedφ isgiven WeutilisetheworkcarriedoutbyBargeretal.(2013),which corr MB MB inFigure8,whichshowsnegativeFaradaydepthsspanningtheen- offerskinematicallyresolvedintensitiesoftheHαemissionacross tiretyoftheMB.Analysisofthistrendshowsthat68%ofthepolar- ourentireMB.TheobservationsusedinBargeretal.(2013)were izedsourcesfollowthistrendto2×dφ,wheredφisthecalculated madewiththeWisconsinHαMapper(WHAM)telescope,which errorinourFaradaydepthmeasurement. has sensitivities of a few hundredths of a rayleigh (see Haffner φ maycontaincontributionsfromlocalisedenhancements et al. 2003 for a complete summary of the telescope and survey MB – such as HII and star formation regions – that may influence technique). WHAM has a 1◦ beam, which is equivalent to a di- the observed magnetic field on scales to which we are sensitive ameterofnearly1kpcattheassumedaveragedistancetotheMB (∼ 2pc).Inordertoidentifyanyphenomenathatcouldinfluence of55kpc.WhiletheWHAMbeamisconsiderablylargerthanthe the small-scale magnetic field fluctuations in the MB, we cross- finalresolutionofourradiodata,atthissizeitislesssensitiveto reference our region of sky with Simbad (Wenger et al., 2000) small-scaleHαemissionstemmingfromindividualHIIregionsand andfind7molecularclouds(Chenetal.,2014)and4HIIregions isoptimisedtodetectfaintemissionfromdiffuseionizedgas.For (Meaburn,1986;Bicaetal.,2008)thatarelocatedinthe‘Wing’ region. Three of the molecular clouds and three HII regions are near the small patch of positive φ-values near l = 295◦,b = 1 1R = (106/4π)photonscm−2s−1sr−1whichisequivalentto5.7× −42◦.Theseindividualmolecularcloudsdonotdirectlyalignwith 10−18ergcm−2s−1arcsec−2forHα. (cid:13)c 0000RAS,MNRAS000,000–000 DetectionofaCoherentMagneticFieldintheMagellanicBridgethroughFaradayRotation 9 simplicity,weassumeanelectrontemperatureofTe =104K(de- rameterswillbedenotedwithsubscriptHIIandallneutralgaspa- notedT4),asassumedinBargeretal.(2013).Figure8showsthe rameterswillbedenotedwithsubscriptHI,unlessotherwisenoted. MBregionwithwhitecontoursindicatinglevelsofuncorrectedHα emissionfromBargeretal.(2013),tracingthe0.06,0.15and1.0R intensitylevels. 5.2.1 Case1:ConstantDispersionMeasure ObservedHαintensitiesarereducedfromtheirintrinsicval- Whenestimatingtheline-of-sightmagneticfieldstrength,thesim- ues due to dust contained within the MB itself and in the MW. plestmodelofthedistributionofmaterialintheMBisoneinwhich These are known as internal and foreground extinction, respec- theneutralandionizedgasarewell-mixed.Insuchascenario,the tively.Wehavecorrectedforbothsourcesofextinctionaccording bulkoftheneutralgaswouldbedistributedacrosstheMBinsmall to Table 2 from Barger et al. (2013). We assume that the ‘Join’ clumps, with the ionized medium distributed uniformly amongst and‘West’regionshavesimilarinterstellar-andlocaldustcontent the neutral clouds. Therefore, the effective depth of the ionized –andthereforeanidenticaltotal-extinctioncorrectionof28%has mediumcanbeexpressedasafractionofthedepthoftheneutral beenapplied.Hα-intensitycorrectionof22%hasbeenappliedto material,L = fL ,whereL isthedepthoftheneutralgas all‘Wing’points.Forallfutureanalysisanddiscussion,Hαinten- HII HI HI andf isthefillingfactorofionizedgasalongthetotalline-of-sight sitieshavebeenextinctioncorrected,unlessstatedotherwise. (Reynolds,1991). We cross-reference the position of each background polar- Little is known of the effective filling factor of ionized gas izedsourcewiththeWHAMdataandacceptthepointingwiththe alongtheline-of-sight,butafillingfactoroff = 1ishighlyun- smallestangularseparationfromourtargetastherepresentativeHα likely.Previousworkonnearbyhigh-velocitycloudsintheLeading brightnessforthatparticularsightline.BecausetheWHAMsurvey Arm(McClure-Griffithsetal.,2010)hasassumedafillingfactorof oftheMBisNyquistsampled,themaximumangularseparational- f ∼ 0.5 to describe the distribution of the ionized gas and we lowedislessthan30arcminutes,whichcorrespondsto≤ 500pcat assumethesamevalueforouranalysis.InSection5.3,webriefly ourassumeddistancetotheMBof55kpc.EMsarethenderivedto- exploretheimplicationsofarangeoffillingfactors.Combiningthe wardseachmatchedsightline.MeanEMsforeachregionarelisted derivedEMwithourline-of-sightestimates,theDMbecomes inTable4. DM = (EMfL )1/2. (11) HI IncorporatingtheaboveexpressionforDMwithEquation10, 5.2 DistributionofIonizedMedium estimatesofthemagneticfieldalongtheline-of-sightcanbeeval- uatedas Inordertoestimatethemagnetic-fieldstrengthalongtheline-of- φ sight through the MB, we assume that there is no correlation be- B = MB . (12) (cid:107) 0.812(EMfL )1/2 tweenelectrondensityandmagnetic-fieldstrength.Thishasbeen HI showntobeareasonableapproximationfortypicalgasdensitiesas- ThisassumptionofthegeometryoftheionizedmaterialintheMB sociatedwiththediffuseinterstellarmedium(Crutcheretal.,2003). is likely an oversimplification of the actual distribution, which is RearrangingEquation3,itcanbeshownthattheequationformag- expectedtovaryasafunctionofpositionalongtheMB. neticfieldalongtheline-of-sightbecomes φ B = MB , (10) (cid:107) 0.812n L 5.2.2 Case2:ConstantRegionalIonizationFraction e HII whereφMBistheMW-foregroundcorrectedFaradaydepthandne IncontrasttoCase1,whereweestimatedtheeffectivepathlength isthemeanelectrondensityalongthetotalpathlengthofionized oftheionizedmaterial,hereweestimatethefree-electroncontent material(LHII). ofasightlineusingtheionizationfractions(X)acrosstheMB.In Often, pulsar dispersion measures (DM= n L ) can be ordertomotivatethisapproach,afewassumptionsmustbemade. e HII usedtoconstructwell-formedestimatesofthepathlengthandelec- Firstly,weassumethatthebulkoftheMBmaterialisinthevelocity trondensitythroughthedifferentregions.Unfortunately,thereare range +100 ≤ v ≤ +300kms−1 relative to the Galactic LSR noknownpulsarsintheMBandverylittleisknownaboutthemor- centre(Putmanetal.,2003;Mulleretal.,2003). phologyandline-of-sightdepthoftheMB. Followingfromthepreviousassumption,wealsoassumethat Subramanian & Subramaniam (2009) argue that the SMC the observed HI depth from GASS (Kalberla et al., 2010) in our is nearly edge-on, indicating a pathlength through the galaxy of selectedvelocityrangeprobestheentireline-of-sightdepthofthe ≥ 5kpc. If the bulk of the material in the MB had its origins in MBsuchthattheionizationfractionofaregionrepresentsthesum the SMC, one might expect the depth of the MB to be equally ofionizedmaterialintheMBalongagivensightline.Previousin- large. Muller et al. (2004) argue that there are numerous obser- vestigations into the MB have shown this assumption to be rea- vationsthroughouttheMBthathintatalargeline-of-sightdepth sonableinthediffuseregionsoftheMB,whereobservationhave andGardineretal.(1994)estimatethepathlengththroughregions showntheretobelittledustcontent(Smokeretal.,2000;Lehner of the MB 5kpc(cid:46) L (cid:46)10kpc. For simplicity, we parameterise etal.,2008).Howevertherehavebeenobservationsofmoleculesin andevaluatethedepthoftheMBasL = 5kpcandconsiderthe the‘Wing’region(Mulleretal.,2004;Mizunoetal.,2006;Lehner 5 implicationsofdifferentpathlengthsthroughthisparameter,with etal.,2008)andthisassumptionwillserveasalowerlimittoour 1(cid:46)L (cid:46)2. estimatesofneutral-andionized-gasdensitiesinthisregion.This 5 Severalindependentassumptionscorrespondingtothedistri- secondassumptionindirectlyimpliesthattheneutralandionized butionandgeometryofionized-andneutral-gascanbemadeinor- gas are well mixed (i.e. f ∼ 1;L (cid:39) L ) since any reported HI HII dertovalidateourB measurements.Below,wedescribethreesep- ionizationfractionisreflectiveofthepathlengthofneutralgas. (cid:107) arate ionized gas distributions and discuss how each might affect Followingfromtheseassumptions,theelectrondensityiscal- derivedmagnetic-fieldstrengths.Inourdiscussion,allionizedpa- culatedsimplyastheionizationfractionmultipliedbytheneutral- (cid:13)c 0000RAS,MNRAS000,000–000 10 J.F.Kaczmareketal. ) 2 -m c 8 1 0 1 ( I Figure8.NeutralHydrogenintensityfromGASS(Kalberlaetal.,2010)inthevelocityrangeof+100 ≤ vLSR ≤ +300kms−1 overlaidwithwhite contoursrepresentingnon-extinctioncorrectedHαintensitiesof0.06,0.15and1.0RasmeasuredfromWHAM(Bargeretal.,2013).Circlesrepresentthe foreground-correctedFaradaydepth(φMB)valuestowardseachpolarizedbackgroundsource.Redandbluecirclesrepresentaline-of-sightmagneticfield orientedtowardsandawayfromtheobserver,respectively.Blackcrossesmarktheexistenceofφvaluesthatareconsistentwithzeroto2×dφ. gasdensity valuesdonotrepresentsmall-scalevariationsinthedistributionof material.Incontrast,thespectroscopicworkofLehneretal.(2008) X(cid:104)N (cid:105) ne = fLHI . (13) foundionizationfractionsashighasX (cid:39) 90%alongthreesight- HI linescorrespondingtothe‘Join’and‘West’regions.Astheirsight- AswithCase1,theaboveexpressionhastheunderlyingpremise linesprobedlocalizeddistributions,thisapproachwouldhavebeen ofLHII = fLHI.ItfollowsthenthattheDMcanbewrittenas susceptibletosmall-scaleenhancements. DM = X(cid:104)NHI(cid:105)L = 3.09×1018X(cid:104)N (cid:105), (14) Motivatedbythewidevariabilityinionizationfractions,we fL HII HI choosetoevaluatetheionizationlevelofthevariousregionsindi- HI wheretheconstant3.09×1018istheconversionfactorofpctocm. vidually. In the region of the Wing, we compare the HI and Hα columndensitiesfromTable3inBargeretal.(2013),tocalculate With an expression for the DM, it is now possible to esti- amultiphaseionizationfractionofX (cid:39) 29%inthe‘Wing’.We matethemagneticfieldalongtheline-of-sightbycombiningEqua- evaluatethe‘Join’and‘West’regionsatanionizationfractionof tions10and14, X (cid:39)46%,assumingthatthe‘Join’and‘West’regionshostsimilar (cid:18) (cid:19) B = 3.80×1018 φMB . (15) distributionsofmaterial.Evaluationofthisionizationlevelmakes (cid:107) X(cid:104)NHI(cid:105) itsimpletoexploretherangeofpossiblemagneticfieldstrengths. The MB is highly ionized with ionization fractions depen- In the region of the SMC-Wing, there is a clear variation of dent upon location within the MB (Lehner et al., 2008; Barger HI columndensitiesaswellasHαintensities(Figure8).Follow- et al., 2013). Barger et al. (2013) determined the minimum mul- ingBargeretal.(2013),wechoosetobreakuptheWingintotwo tiphase ionization fraction across the MB and argued that in the regionscorrespondingtotherelativeHαbrightness.Ifasightline casewheretheneutralandionizedgasiswell-mixed,theaverage isassociatedwithanuncorrectedHαbrightnesslargerthan0.15R, ionizationfractionintheregionofthediffuseMBisX (cid:39) 46%, this region is classified as the ‘Hα-Wing’ and assigned a HI col- andX (cid:39) 29%inthe‘Wing’region.Astheseionizationfractions umn density of 6.8×1020cm−2, else we consider the region to representtheaveragevaluescalculatedovertheentireregion,the bethe‘HI-Wing’andevaluateitashavingaHIcolumndensityof (cid:13)c 0000RAS,MNRAS000,000–000

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