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

3.1 MB·

by  J. F. Kaczmarek

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
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0
1
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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