Modeling the Magnetic Field in the Galactic Disk using New Rotation Measure Observations from ...

18 Pages·2010·4.98 MB·English

ACCEPTEDFORPUBLICATIONINAPJ;DECEMBER13,2010
PreprinttypesetusingLATEXstyleemulateapjv.11/10/09
MODELINGTHEMAGNETICFIELDINTHEGALACTICDISKUSINGNEWROTATIONMEASUREOBSERVATIONS
FROMTHEVERYLARGEARRAY
C.L.VANECK1,J.C.BROWN1,J.M.STIL1,K.RAE1,S.A.MAO2,3,B.M.GAENSLER4,
A.SHUKUROV5,A.R.TAYLOR1,M.HAVERKORN6,7,P.P.KRONBERG8,9,N.M.MCCLURE-GRIFFITHS3
1.Dept.Physics&Astronomy,UniversityofCalgary,T2N1N4,Canada
2.Harvard-SmithsonianCenterforAstrophysics,Cambridge,MA02138,USA
3.AustraliaTelescopeNationalFacility,CSIROAstronomyandSpaceScience,POBox76,Epping,NSW1710,Australia
4.SydneyInstituteforAstronomy,SchoolofPhysics,TheUniversityofSydney,NSW2006,Australia
5.SchoolofMathematicsandStatistics,UniversityofNewcastle,NewcastleuponTyne,NE17RU,UK
6.ASTRON,OudeHoogeveensedijk4,7991PDDwingeloo,TheNetherlands
0
7.LeidenObservatory,LeidenUniversity,P.O.Box9513,2300RALeiden,TheNetherlands
1 8.DepartmentofPhysics,UniversityofToronto,60St.GeorgeStreet,TorontoM5S1A7,Canadaand
0 9.LosAlamosNationallaboratory,M.S.T006,LosAlamosNM87545USA
2 AcceptedforpublicationinApJ;December13,2010

c
ABSTRACT
e
D We have determined 194 Faraday rotation measures (RMs) of polarized extragalactic radio sources using
new,multi-channelpolarizationobservationsatfrequenciesaround1.4GHzfromtheVeryLargeArray(VLA)

4 intheGalacticplaneat17◦≤l≤63◦and205◦≤l≤253◦.ThiscatalogfillsingapsintheRMcoverageofthe
1 Galactic plane between the Canadian Galactic Plane Survey and Southern Galactic Plane Survey. Using this
catalog we have tested the validity of recently-proposed axisymmetric and bisymmetric models of the large-
]
scale (or regular) Galactic magnetic field, and found that of the existing models we tested, an axisymmetric
A
spiralmodelwithreversalsoccurringinrings(asopposedtoalongspiralarms)bestmatchedourobservations.
G
Buildingonthis,wehaveperformedourownmodeling,usingRMsfrombothextragalacticsourcesandpulsars.
. BydevelopingindependentmodelsforthemagneticfieldintheouterandinnerGalaxy,weconcludethatinthe
h
innerGalaxy,themagneticfieldcloselyfollowsthespiralarms,whileintheouterGalaxy,thefieldisconsistent
p
withbeingpurelyazimuthal. Furthermore, themodelscontainnoreversalsintheouterGalaxy, andtogether
-
o seemtosuggesttheexistenceofasinglereversedregionthatspiralsoutfromtheGalacticcenter.
r Subjectheadings:Galaxy: structure—ISM:magneticfields—polarization
t
s
a
[ 1. INTRODUCTION ship

1 While the importance of the Galactic magnetic field is φ=φ0+λ2RM, (2)
v undisputed–rangingfromstarformationtolarge-scalegalac-
whereRMistheRotationMeasure,definedfromequation1.
8 ticdynamics–muchremainsunknownabouthowthefieldis
Asaresult,measuringthepolarizationangleatseveralwave-
3 generatedorhowitisevolving.Theonlywaytoaddressthese
lengthsforagivensourcecanprovideasimpledetermination
9 questionsistofullyunderstandthepresentoverallstructureof
of the rotation measure for that line of sight, provided that
2 the field, which is an essential constraint to proposed evolu-
thereisnointernalFaradaydispersionbyturbulentmagnetic
2. tionarymodelsofthefield. fields(seee.g.Sokoloffetal.1998).
1 One observation central to the study of the Galactic mag- If there exist multiple polarized emitting regions along a
0 netism is that of the Faraday rotation measure (RM). As a
line of sight, for example, from different regions within the
1 linearlypolarizedelectromagneticwavepropagatesthrougha
primary source, or from different regions within the inter-
: regioncontainingfreethermalelectronsandamagneticfield,
v stellar medium of the Galaxy itself, or turbulent cells with
suchastheinterstellarmedium,theplaneofpolarizationwill
i randomfielddirections,eachemittingregionwillhaveadif-
X rotate through the process known as Faraday rotation. The
ferent RM contributing to the final detected RM, otherwise
amount of rotation, ∆φ [rad], experienced by a wave of a
r knownasRMcomponents. AtechniquedevelopedbyBren-
a givenwavelength,λ[m],isgivenby
tjens&deBruyn(2005),knownasRMSynthesis,isableto
(cid:90) receiver extract the RM components using Fourier transforms. How-
∆φ=0.812λ2 n B·dl, (1) ever,thereremainsthedifficultyofdeterminingwherealong
e
source thelineofsightthecomponentsoriginate,andhowthecom-
ponents‘add’ishighlydependentontheinstrumentationused
wherene[cm−3]istheelectrondensity,B[µG]isthemagnetic todetectthesignals. Therefore,itismorestraightforwardto
field,dl[pc]isthepathlengthelement.Assumingthatthepo- usesinglecomponentRMsourcestoprobethemagneticfield
larization angle at the source, φ◦, is the same for all emitted withintheGalaxy. Thetwosourcesmostoftenusedarepul-
wavelengths,thatFaradayrotationistheonlymechanismact- sars (within the Galaxy) and compact extragalactic sources
ingonthepolarizationangle,andthatthesourceofinterestis (EGS).Wenotethatthehighertheangulardensityoftheob-
theonlysourcecontributingpolarizedemissionalongtheline servedprobes,thegreaterthecapacitytoidentifyandseparate
of sight, then the detected polarization angle, φ, is a linear theorderedandrandomfieldcomponents.
functionofthesquareofthewavelengththroughtherelation- Forthepurposesofmodeling,theGalacticmagneticfieldis
often,andsomewhatarbitrarily,dividedintotwocomponents:
[email protected];[email protected] alarge-scaleorregularcomponent,B ,withspatialscaleson
u
2 VANECKETAL.
theorderofafewkpc,andaturbulentorrandomcomponent
Br, withspatialscalesontheorderoftensofpc(Ruzmaikin Q3 Q2
etal. 1988),withsignificantdifferentspatialscalesobserved VLA CGPS
between and within the spiral arms (Haverkorn et al. 2006,
Perseus
2008). Furthermore, the regular component is observed to local
beconcentratedinthedisk(Simard-Normandin&Kronberg
1980), with a dominant azimuthal component, some radial
component(thusindicatingaspiralfield),andaweakvertical
orzcomponent(Maoetal.2010).
Sagittarius-
Additionally, recent work has focused on developing and
Carina
testing competing models, and determining the existence of
largescalereversalsinthemagneticfield. Magneticfieldre-
Norma
versals occur where the magnetic field direction completely
reversesover ashort changein radiusand/orazimuth within Scutum- VLA
the disk of the Galaxy. The number of reversals depends on Crux
the interpretation of the existing RM data and is presently a
verycontroversialsubject(e.g.Brown&Taylor 2001;Weis- Q4 SGPS Q1
berg et al. 2004; Vallée 2005; Han et al. 2006; Brown et al.
2007; Sun et al. 2008; Vallée 2008; Men et al. 2008; Jans-
sonetal. 2009;Kronberg&Newton-McGee2009;Nota& FIG.1.—ViewoftheMilkyWayfromabovethenorthGalacticpoleillus-
Katgert2010). ModelsoftheGalacticmagneticfieldaregen- tratingthemainsurveyregionsofextragalacticrotationmeasuresusedinthis
paper. Thegreyscalebackgroundistheelectrondensitydistributionmodel
erallyclassifiedasaxisymmetricspiral(ASS),whichrequires
ofCordesandLazio(2002).Thedarklinesaretheboundariesoftheregions
symmetry under the same rotation of the disk by π around observedbytheCGPSandSGPS,whilethewhitelinesdenotethe2areas
theGalacticcenter,bisymmetricspiral(BSS),whichrequires targetedbytheVLAdatausedforthisproject. Thedashedlinesshowthe
anti-symmetryunderrotationbyπ, ormixedspiralstructure delineationsbetweentheGalacticquadrants(Q1-Q4).
(MSS),whichcontainbothASSandBSScomponents(Beck
et al. 1996). Most models are made to follow the spiral arm −3◦≤b≤3◦and43◦<l≤63◦,−4◦≤b≤4◦andinQ3with
structureoftheGalaxysinceanapproximatealignmentofthe 205◦ ≤l ≤253◦, −5◦ ≤b≤5◦. We increased the latitude
regularmagneticfieldsandspiralarmsiscommonlyobserved coverage for higher longitudes to maximize the number of
inexternalgalaxies(e.g.Beck2007). sourceswehad, whilestillmaintaininglines-of-sightlargely
Forallofthesemodels,sufficientnumbersoflow-latitude, confinedwithintheGalacticdiskundertheassumptionsofa
highqualityRMdatainkeyregionshavebeenlacking.While Galactic radius of 20 kpc and a warm ionized medium scale
the recent catalog of Taylor et al. (2009) significantly in- heightof1.8kpc(Gaensleretal.2008).
creasesthenumberofpublishedEGSRMsourcesacrossthe ThesourcesobservedwereselectedfromtheNRAO-VLA
entiresky,thoseintheplanelackadequatereliabilityformod- Sky Survey (NVSS; Condon et al. 1998) with the following
elingthemagneticfieldinthedisk(seesection2). criteria: 1)theywereunresolved,havinganNVSSfittedma-
In this paper, we present our new low-latitude EGS RM joraxisoflessthan60arcseconds;2)theirlinearlypolarized
catalog derived from new observations from the Very Large flux as given in the published NVSS catalogue was greater
Array (VLA), filling in gaps in Galactic plane coverage in than2mJy(biascorrected);3)theyhadaminimumfractional
quadrant1(Q1;0◦<l<90◦)andquadrant3(Q3;180◦<l< polarization of 2% in Q3 or 1% in Q1. We used a different
270◦).Weusethesedatatofurtherdiscriminatebetweenthree minimum fractional polarization in Q1 than in Q3 to mini-
popular models investigated by Sun et al. (2008). We then mizeselectionagainsthighRMsasaresultofbandwidthde-
combine these data with previous observations to develop polarizationintheNVSS.Usingthesecriteria,weobserveda
magneticfieldmodelsforthreeseparatesectorsoftheGalac- totalof486sources.
tic disk and find some remarkable consistencies between the We observed each source in spectral-line mode, using an
sectors,suggestingglobalfeaturesofthefield. integration time of at least 2 minutes in two separate 25
MHzbands,eachwith7channels,giving14wavelengthsand
2. OBSERVATIONS 14 corresponding polarization angles. For our first observa-
Two recent projects have produced catalogues for several tions of 76 sources (June 8), we centered the two bands at
hundredEGSRMsintheplaneoftheGalaxy: theCanadian 1365 MHz and 1515 MHz. The 1515 MHz band was unus-
Galactic Plane Survey (CGPS; Taylor et al. 2003; Brown et ableduetoradiofrequencyinterference(RFI),sothesources
al. 2003a) and the Southern Galactic Plane Survey (SGPS; from these observations were discarded. For all subsequent
Haverkornetal.2006;Brownetal.2007). Whilecoveringa sources,weusedbandscenteredat1365MHzand1485MHz.
significantfractionoftheGalacticdisk,thesesurveyslefttwo When possible, we observed a primary flux calibrator
gapsintheEGSRMcoverageoftheGalacticplaneasshown (3C286 or 3C138) in both observing bands at the beginning
inFigure1. and the end of an observation run. For the duration of a
In June and July of 2008, we carried out 48 hours of ob- given run, we observed sources in groups of 15-18 sources
servingwiththeVLAundertheprogramAM959tofillinthe inonebandwithina1hourwindow. Everyhour, wevisited
gaps in EGS RMs between the CGPS and SGPS. Observa- a phase calibrator that was usually within 10 degrees of the
tionsdoneonJune8andJune20werecarriedoutinDnCcon- targetgroup. Wethenrepeatedtheobservationsofthetarget
figurationwherewegaveprioritytolow-declinationsources, group in the second band (i.e. band A: phase calibrator →
while the remaining observations (carried out on June 29, band A: target group: → band A: phase calibrator → band
July 4, July 5, July 10, and July 12) were in D configura- B:phasecalibrator→bandB:targetgroup→bandB:phase
tion. OurobservationsinQ1wereconfinedto17◦≤l≤43◦, calibrator→repeat).
MODELINGTHEMAGNETICFIELDINTHEGALACTICDISK 3
Data reduction was carried out using AIPS software. The
AIPS task IMAGR was used to do imaging and cleaning,
whichwasperformeddowntothenoiselevelforeachsource
(between0.6mJyand1.1mJy). CLEANboxesweredefined
tightly around the target source to prevent cleaning of side-
lobes of the dirty beam. Baselines shorter than 1 kλ were
excluded to reduce extended emission (equalling about 30%
ofallbaselines). NoadditionalweightingwasusedintheUV
plane. Polarization calibration was done using the standard
calibration method as described in the AIPS manual, using
3C286asapolarizationcalibrator. Wenotethatpolarization
calibrationinAIPScanonlybedoneononechannelatatime.
Thus,eachofthe14channelswascalibratedandimagedsep-
arately, using 10(cid:48)(cid:48) pixels and a 50(cid:48)(cid:48) clean beam. The polar-
izationangleandpolarizedintensityforeachchannel(i.e. at
each wavelength) were then extracted from the source pixel
withthegreatestchannel-averagedpolarizedintensity(deter-
minedbyaveragingthepolarizedintensityfromtheindividual
channels).
Fromthesepolarizationangles,theRMiscalculatedusing
aleast-squaresfittothepolarizationangleversuswavelength- FIG.2.—DeterminingrotationmeasuresfortheVLAobservations.Top:A
demonstrationofthepolarisationanglenπdeterminationmethodforrotation
squaredplot,asreflectedbyequation(2). Sincepolarization
measurecalculationsasdescribedinthetext. Thetrianglesaretheobserved
anglesareonlydefinedbetween0andπ,allpolarizationan- angles,circlesaretheadjustedangles. Thedashed(dotted)linesaretheex-
gle measurements are subject to an issue of ‘nπ ambiguity’. trapolationsoftheright(left)band,andareusedtodeterminetheinter-band
Toaddressthisissuewithinourdata,wehaveusedthealgo- nπadjustmentneededtoproducethebestfit. Thesolidlineistherotation
measuredeterminedusingbothbandsafterapplyingthealgorithm. Bottom
rithm used by Brown et al. (2003a) to determine the relative
left:TherotationmeasuretransferfunctionforRMsynthesisresultingfrom
anglesbetweenchannelswithineachbandseparately. Tode- the 14-channel sampling. Bottom right: The RM Synthesis result for the
terminethenπbetweenthetwo25MHzbandsobserved,best samesource. Thelightdottedlineistherawspectrum,thegreysolidline
istheRMCLEANcomponentspectrum,andthesolidblacklineisthefinal
fitlinesweredeterminedseparatelyforeachbandandextrap-
CLEANedspectrum.
olated out to the other band. If the determined value for n
asdeterminedbytheseparatebandswasdifferent,thesource
wasdiscarded.Thebandswerethenadjustedbytheappropri- sourcesasdocumentedinTable1,andillustratedinFigure3.
atenπ,andtheRMwasdeterminedfromtheslopeofthebest Asaconsistencycheckofthiscatalog,wehavecomparedour
fitlineusingbothbandstogether(seeFigure2). Theerrorin RMstothefollowingtwodeterminationsofRMsforthesame
RMwasdeterminedastheerrorinslopeofthe2-bandbestfit sources. In addition to the linear fitting method described
line. above,wealsocalculatedRMsfromthesamedatausingRM
In order to be considered a reliable RM value, the source synthesis,asoutlinedbyBrentjens&deBruyn(2005),which
hadtohavea‘probability-of-fit’fortheleast-squaresfitofpo- employsFouriertransformstodeterminetheRM.Theresult-
larizationangleversusλ2begreaterthanthestandardvalueof ing RM spectra were processed with the RM CLEAN algo-
rithm, as outlined in Heald et al. (2009). The values found
10%. Inaddition, thesourcealsohadtopasstwomoretests
that were designed to confirm that the nπ algorithm worked withthesynthesisandlinearfittingmethodsareincomplete
consistently and that the source has a single RM value (or, agreement,withthevariationbetweenthetwomethodsmuch
lessthanthestatederrorinRM.TheRMsynthesisresultsare
alternatively, a consistent, dominant RM component). First,
includedinTable1.
we confirmed that the 4 pixels adjacent to the central pixel
ThesecondcomparisonwaswiththeRMcatalogproduced
(above, below, and to the sides) had similar RMs. Sources
with the mean RM of the 4 adjacent pixels greater than 2σ directly from the original NVSS observations by Taylor et
al. (2009), where RMs are calculated using observations at
differentthanthecentralpixelRMvaluewererejected. Sec-
1364.9 and 1435.1 MHz. Their method used two polariza-
ond, we confirmed that the fractional polarization (linearly
tion angle measurements, combined with depolarization in-
polarized intensity divided by Stokes I) was constant with
λ2. WhilethepresenceofmultipleRMcomponentsmaystill formation to solve the half-rotation ambiguity. Figure 4 is
a comparison of RMs of sources for which there are values
combinetoproducelinearbehaviorinpolarizationanglever-
from both surveys. It is clear that some of the sources have
susλ2oversmallwavelengthranges(therebyleadingtoincor-
RMs determined by the two techniques that differ by ∼650
rectcalculatedRMs),multiplecomponentsarealsoexpected
radm−2. A1πambiguityintroducesa∼650radm−2offsetin
toproducenonlinearbehaviorinpolarizedintensityversusλ2
aRMdeterminedbyTayloretal.(2009). Forourdata,how-
(Goldstein & Reed 1984; Farnsworth, Rudnick, & Brown
ever, a 1π ambiguity would require an actual RM of greater
2011). Bycontrast,asingle(oratleast,dominant)RMcom-
than10,000radm−2. Consequently,itiscertainthattheoffset
ponent is expected to have polarized intensity versus λ2 be
sources in Figure 4 reflect the 1π ambiguity of the Taylor et
roughly constant. Therefore, we used a second ‘probability-
al.(2009)algorithm. Thelinearcorrelationcoefficientforall
of-fit’ test (also at the 10% level) of the fractional polariza-
146 matched sources is 0.20, but this rises to 0.96 when the
tionvaluesversusλ2 againstalinewithzeroslopeandoffset
13offsetsourcesareremovedfromthecalculation. Thiscor-
equaltothemeanfractionalpolarization. Sourcesfailingthis
relationismuchhigherthanthatfoundbyMaoetal. (2010;
testwerealsodiscarded.
0.39intheNorth, and0.36intheSouth), likelybecauseour
Using this method, we determined reliable RMs for 194
dataincludesamuchlargerrangeofRMswhichreducesthe
4 VANECKETAL.
FIG.3.—RotationmeasuresourcesfromTable1. Greyfilledsourcesindicatepositiverotationmeasureandblackopensymbolsindicatenegativerotation
measures;diametersofsymbolsarelinearlyproportionaltothemagnitudeofRMtruncatedbetween100and600radm−2sothatsourceswith|RM|<100rad
m−2aresetto100radm−2,andthosewith|RM|>600radm−2aresetto600radm−2. ThetoppanelrepresentssourcesfromGalacticquadrant1(Q1),while
thebottompanelrepresentssourcesfromGalacticquadrant3(Q3).
Canadian Galactic Plane Survey (Brown et al. 2003a), the
effect of random errors. As well as the ∼650 rad m−2 offset
Southern Galactic Plane Survey (Brown et al. 2007), and a
forafewsources,thereareadditionaldifferencesbetweenour
sample of RMs along sight lines close to the Galactic centre
RMvaluesandthoseofTayloretal.(2009). Asdemonstrated
(Royetal.2005). Usinghigh-latitudeCGPSdata(seeRae&
in Figure 4, their values are systematically lower than ours,
Brown 2011), Sun et al. (2008) show an RM latitude pro-
withameanshiftof10radm−2. Further,thestandarddevia- filebetween100◦<(cid:96)<120◦ (theirFigure12)whichclearly
tionofthedifferencesbetweentheirvaluesandours(neglect- suggeststhatonlytheASS+RINGorASS+ARMmodelsare
ing the 1π shifts and differences between sources with large good contenders, particularly in this longitude range. How-
RMs) is 23 rad m−2. Given that we are working in the part ever, as stated by Jansson et al. (2009), filling in the gaps
of the sky, namely the Galactic disk, where RMs vary sig- of the EGS RM data in the disk is essential to properly dis-
nificantlyoverrelativelyshortangulardistances,andthefact cernbetweenthemodels. Withournewdata,wearenowina
that we systematically resolve nπ ambiguities more reliably positiontocontributetotheassessmentofthesethreemodels.
thantheirtechniquedoesinthesamepartofthesky,thereisa
significantadvantagetousingourRMvaluesinoureffortto
infermagneticfieldstructureintheplaneoftheGalaxy. The
systematicshiftoftheRMsinferredfromthetwotechniques,
andthevariancebetweenthetwo,undoubtedlyindicateerrors
inoneorbothofthemethods. Theseerrorsareworthinves-
tigating further, but because they are almost certainly small
relative to the real large scale trends in RM in the Galactic
plane (the RMs vary systematically by hundreds of rad m−2
buttheshiftandvariancearebothontheorderof10radm−2)
theyarenotimportantforthisstudy.
FIG.4.—ComparisonofNVSSRMscalculatedbyTayloretal.(2009)to
3. OBSERVATIONALDISCRIMINATIONOFPOPULARGMF ournewVLARMspresentedhere.Thesolidlineisthe1:1linecorrespond-
MODELS ingtocompleteagreement. Intheleftpanel, thedashedlinesareparallel
Sun et al. (2008) presented a thorough investigation of tothe1:1linewiththe±650radm−2offsetthata±πRMambiguityerror
wouldaddtoanRMdeterminedbytheTayloretal.(2009)algorithm(as
three models for the Galactic magnetic field which repre-
theydiscuss,thevalueoftheshiftfroma1πambiguityerrorisdetermined
sented a culmination of a variety of inputs from earlier pop- bythetwowavelengthsforwhichpolarizationinformationisavailableforthe
ularmodels. ThethreemodelstheypresentareaBSSmodel NVSScatalog). Roughly5%ofthecorrespondingsourceshavea±650rad
and two ASS models: one with magnetic field reversals fol- m−2offset.Giventhata1πRMambiguityerrorinasourcedeterminedfrom
ouralgorithmwouldgiveasignificantlylargeroffset,weattributetheoffsets
lowing the spiral arms of the Galaxy (ASS+ARM), and the
ofthislimitednumberofsourcestounresolvedambiguitiesinthosespecific
otherwithreversalsinringsofconstantradius(ASS+RING). Tayloretal.(2009)sources.Therightpanelisanenlargementofpartofthe
PartoftheeffortsbySunetal. (2008)includedanexploration leftpanel,showingthescatterofthepointsaboutthe1:1curve. Thereisa
ofhowwellthesemodelsfitpulsarRMs(Hanetal.1999)and slightsystematicshiftoftheTayloretal.(2009)RMstowardsmorenegative
values,witha23radm−2 standarddeviationofthedifferencebetweenthe
previouslypublishedextragalacticRMsfromthe
two.
MODELINGTHEMAGNETICFIELDINTHEGALACTICDISK 5
Figure 5 shows our RMs in the Q1 and Q3 regions seper- versely,themodelofBrownetal.(2007)doesnotdowellin
ately, with the predictions of the models from Sun et al. Q1,asdemonstratedbyJanssonetal. (2009). Furthermore,
(2008) overlaid. As shown, the three models have very dif- astheCGPSobservationshaveprogressed,ithasbecomeev-
ferent predictions in EGS RMs in Q1 where the reversal’s ident that a simple spiral model in the outer Galaxy is not
tangent point occurs, but, as could be expected, the three consistentwiththedata(Rae&Brown 2011). Wealsonote
models are very similar in Q3. Our data from Q1 is most thatShukurov (2005)suggestedthatthereversalintheMilky
consistent with the ASS+RING model, particularly between Way may be localized in a region within several kiloparsecs
40◦ <(cid:96)<60◦, where the RMs being generally positive and near the Sun. If this is the case, an entirely different type of
decreasing with increasing longitude. The other two models analysisisrequired,suchaswhatweproposebelow.
predictnegativeRMsinthisregion. While many other recent works have focused on building
an empirical model of the large-scale magnetic field for the
entireGalacticdisk(e.g.Weisbergetal.2004;Hanetal.2006;
Vallée2008)orhavelookedatonlyspecificregionsofthedisk
(e.g. Brown et al. 2007; Nota & Katgert 2010), we chose to
take a ‘hybrid’ approach. Our modeling work examines the
entireGalacticdisk,butin3separatesectorstoseeifwecan
determine any common features or structure. We purposely
donotapplyany‘boundarymatching’conditionsbetweenthe
sectors in order to facilitate independent results for each of
thethreesectorsexamined. Itwasourintentiontoseeifthere
wasanycommonalityamongstthedifferentsectorsthatcould
bearrivedatindependently. Withthisinmind, wechosethe
following three sectors, as illustrated in Figure 6: Sector A
isolatestheouterGalaxy(excludingthelocalarm)andspans
mostofquadrants2and3(Q2andQ3);SectorBspansallof
quadrant 4 (Q4) which includes the half of the inner Galaxy
withsignificantlinesofsightalongthespiralarms;SectorC
spans all of quadrant 1 (Q1) which includes the half of the
inner Galaxy that has lines-of-sight primarily perpendicular
tothespiralarms.
ThemethodweuseisdescribedbyBrownetal.(2007)and
in greater detail in Brown (2002). In summary, we attempt
to empirically reproduce the observed RMs of both pulsars
andEGSusingtheelectrondensityofCordes&Lazio(2002,
hereafter NE2001), and various magnetic field models. We
FIG.5.—RotationmeasureversusGalacticlongitudeforsourcesinquad-
rant 1 (upper panel) and quadrant 3 (lower panel). The diamonds are 3 acknowledge that this modeling technique is limited in the
degree-averagedindependentbins(errorbarsarethebinwidthandstandard sensethatitreliesheavilyonthevalidityoftheassumedelec-
deviationofthemean)oftheindividualsources(shownasblackasterisks). trondensityandmagneticfieldmodels.However,theNE2001
Binsshowninblackcontainatleast5sources;binsshowningreycontain
modelreproduceswellthedispersionmeasuresofpulsarsand
between2and4sources. Thethreelinesshowthepredictionsofthemod-
elsinvestigatedbySunetal. (2008)takendirectlyfromtheirFigure10,as observedspiralstructureatlowlatitudes,thoughitdoeshave
specifiedintheupperrightcornerofeachpanel. limited value at mid to high latitudes (Gaensler et al. 2008).
In our case, we are only interested in low latitudes, so with
The ASS+RING model is also more consistent with dy- all other caveats, we have chosen to use this electron den-
namomodelswheretheaxisymmetricsolutionsofthemean- sity model. While it is possible to construct magnetic field
field dynamo equations in a thin disk are of the form B = modelsusingaconstantelectrondensity(e.g.Nota&Katgert
u
Q(R)b(z,R),whereQ(R)describesthefieldstrengthalongthe 2010), such models put all of the structure of the RMs into
radius,R,andbdescribesthefielddistributionperpendicular themagneticfield. Instead,wewereinterestedinattempting
to the disk (with R and z the cylindrical coordinates; Ruz- to explore the relationship between the spiral arms and the
maikin et al. 1985; Poezd et al. 1993). A reversal of an magneticfield.
axisymmetricfieldoccursatR=R whereQ(R )=0(i.e. ona Themagneticfieldmodelsinvestigatedherearedefinedin
0 0
circle). Wenote,however,thatnoneofthemodelsdiscussed termsofseveralregionswithdistinctmagneticfieldconfigu-
herefittheobservationsaswellaswouldbedesired.Theidea rations (direction and magnetic pitch angle), as illustrated in
thatthefieldisnotassimpleasanaxisymmetricorbisymmet- Figure6,butthestrengthanddirectionofthefieldareoutputs
ricspiralhasbeendiscussedextensivelybyMenetal.(2008). obtainedminimizingthedifferencebetweenthedataandthe
modelthroughlinearinversiontheory(Menke 1984).Bydef-
4. MULTI-SECTORMODELOFTHEMAGNETICFIELDINTHE inition within the model, positive fitted field strengths corre-
GALACTICDISK spondtoacounter-clockwisefield(asviewedfromtheNorth
AsdiscussedbyJanssonetal. (2009), noneoftheglobal Galactic pole) within that region, while negative fitted field
models of the large-scale magnetic field studied to date ade- valuescorrespondtoaclockwisedirection. Inaddition,since
quatelyreproducethedataacrosstheentiredisk. Inthepre- thegoalofourmodelingistoexplorethelarge-scalefield,we
vious section, we determined that the ASS+RING described ignorethesmall-scaleclumpsandvoidsofNE2001,anduse
by Sun et al. (2008) fit best for our Q1 data. This model, onlythethin,thick,andspiralarmcomponents.
however, is quite different than that of Brown et al. (2007) In addition, we placed the following restrictions on all of
thatwasquitesuccessfulinreproducingthedatainQ4. Con- the models we investigated. First, the magnetic field for
6 VANECKETAL.
ing. DuetotheintrinsicscatteroftheEGSRMsandthehigh
angulardensityofEGSavailabletous,wesmoothedtheob-
served and modeled EGS RMs, as described below, before
calculatingthe(cid:104)(∆RM)2(cid:105)1/2value.
WeusedEGSRMsfromthedatapresentedhere,aswellas
theSGPSandCGPSdatasets. WetreatedtheEGSsasbeing
located at the edge of the model (R=20 kpc). Since we did
not wish to investigate the complex nature of the field likely
tobefoundneartheGalacticcenter,wedidnotuseanyEGS
RM sources within ±10◦ Galactic center and consequently
didnotuseanyoftheRMsdeterminedbyRoyetal.(2005).
Wealsodidnotconsideranyverticalstructureinourmodel.
Therefore, we removed any sources with a calculated height
|z|>1.5kpc. Withthesecriteria,wewereleftwith184ofthe
194RMsdescribedinsection2,142ofthe148RMsfromthe
SGPS(Brownetal.2007)and1020sourcesfromtheCGPS,
atotalof1346EGSsources.
Weused557pulsarRMsfromthefollowingsources:Nout-
sos et al. (2008), Han et al. (2006), Weisberg et al. (2004),
Mitraetal.(2003),Hanetal.(1999)andTayloretal. (1993)
where pulsars were selected with |z| < 1.5 kpc. For self-
consistency,weuseddistancestothepulsarspredictedbythe
NE2001model.
The EGS and pulsar RMs were then split by sector as de-
scribed in the following sections. The primary objective of
our modeling is to produce the best-fitting empirical model
with the fewest parameters. To that end, we decided to ex-
ploretheouterGalaxyfirst,sinceitcanbeexpectedtobethe
simplestinnature.
4.1. ModelSectorA:TheOuterGalaxy(Q2andQ3)
WedefineSectorAtobe100◦<(cid:96)<260◦. Inthisregion,
we have RMs for 88 pulsars, and 847 EGS (21 from SGPS,
108fromthecataloginthispaper,718fromCGPS).
As demonstrated by earlier CGPS work, RM data in the
outerGalaxyholdsnostrongevidenceforalarge-scalerever-
sal(Brown&Taylor 2001;Brown2002;Brownetal.2003b).
There is some evidence that suggests that the field decays
as R−1, consistent with the decay in electron density (Brown
et al. 2003b). Since the relationship between the large-scale
magneticfieldandtheelectrondensityhasnotbeenformally
identified,weinvestigatedseveraldifferentradialprofilesfor
FIG.6.—Comparisonofmagneticfieldregionsanddelineationforthe3
sectorsinvestigatedinthispaper.Toppanelshowsthe3sectorswithprevious thelarge-scalefieldincludingR−1,R−1/2,exp(−R/5kpc),and
orcomparativemodeldelineations:RegionA:Logarithmicspiralwith11.5◦ exp(−R/10kpc)andconstantfieldstrength. Allprofilespro-
magneticpitchangle; RegionB:ModelfromBrownetal.(2007); Region
ducesimilarresultsinthemodeling, astherearenotenough
C:ASS+RINGmodelfromSunetal. (2008). Thebottompanelshowsthe
regiondelineationsandmagneticfielddirectionsforourproposedmodelsin pulsar data to effectively constrain the radial profile of the
thethreesectors. ThenumberscorrespondtotheregionslistedinTable2. large-scale magnetic field in the outer Galaxy. Therefore,
Wenotethatthefielddirectionsindicatedonthelowerpanelareanoutputof we modeled this region as a single magnetic entity with an
themodel,andwerenotassignedapriori.
R−1 decay profile, consistent with earlier observational sug-
GalactocentricradiiR>20kpcorR<3kpcwassettozero. gestions. Thequestionwewereinterestedinaddressingwas
Similarly,thefieldwasassumedtobezerofor|z|>1.5kpc. whetheraspiralfieldwasmoreorlessappropriatethanapre-
In addition, all models have a circular region containing the dominantly azimuthal field. Recent work by Rae & Brown
molecularringoftheNE2001electronmodel(3kpc≤R≤5 (2011) provides evidence for a very small pitch angle in the
kpc)withacircularmagneticfieldregardlessofthegeometry outerGalaxy,bydeterminingthevalueforthe‘RMnullpoint’
beingtestedintherestoftheGalaxy. in the outer Galaxy (the longitude where the RMs transition
Using the best-fit values for the magnetic field regions in from positive to negative, corresponding to where the mag-
eachmodel(giveninTable2),wearethenabletodetermine netic field is, on average, perpendicular to the line of sight)
themodelRMsforeachoftheobservedsourcelocations. To as(cid:96)=179◦±1◦. Weinvestigatedarangeofpitchanglesand
assessthequalityoffitofeachmodel,wecalculatedtheroot foundthatthoseclosetozerowereclearlypreferredasindi-
meansquareoftheresidualsinRMs, cated by a minimum in (cid:104)(∆RM)2(cid:105)1/2 at a pitch angle of 0◦
(cid:104)(∆RM)2(cid:105)1/2=(cid:104)(RM −RM )2(cid:105)1/2, (3) anda10%changein(cid:104)(∆RM)2(cid:105)1/2 occurringatapitchangle
observed model of4◦.
where the goal was to minimize this value with the model- In Figure 7, we present the results for a spiral model in-
MODELINGTHEMAGNETICFIELDINTHEGALACTICDISK 7
clined at 11.5◦, consistent with the spiral arms of NE2001, InthissegmentoftheGalaxy,weusedasourstartingposi-
andcomparetheresultswiththebestfitforapurelyazimuthal tiontheASS+RINGmodeldescribedbySunetal. (2008). In
model (magnetic pitch angle of 0◦). Both models reproduce particular,webeganbyassumingthatintheinnerGalaxy,the
thegentletrendofthedatatochangefrompositiveRMinQ3 magneticregiondelineationsarecircular,butthefieldswithin
tonegativeRMinQ2. However,thepurelyazimuthalmodel the regions are spiral. We note a few critical differences be-
minimizesthe(cid:104)(∆RM)2(cid:105)1/2 by30%betterthanthelogarith- tweenourmodelandtheirs: 1)weuseonlythesmoothcom-
mic spiral model. Figure 7 also serves to illustrate that the ponentsofNE2001asnotedabove(Sunetal. usedallcom-
observed ‘null point’ of the CGPS data clearly occurs close ponents); 2) we use a maximum scale height of the field as
to 180◦ longitude as predicted by the circular model, imply- 1.5kpc(Sunetal. use1.0kpc); 3)wehavefiveseparatere-
ing a field with a very small or even zero pitch angle com- gions(Sunetal. havefour);4)weuseamagneticpitchangle
paredtothespiralarms. Thisisincontrastwiththepredicted within the individual regions of 11.5◦, except for the inner-
nullof(cid:96)=166◦ predictedbythespiralmodelwiththesame most region (1C as labeled on Figure 6) and the outermost
pitchasthespiralarms(asdefinedbyCordes&Lazio2002). region(5C),whichwedefinetobeazimuthaltobeconsistent
The slight shift of the null-point in the data to (cid:96)>180◦ is withourworkinsectorsAandB(Sunetal. used12◦ inall
more likely due to small-scale structures such as supernova regions).
remnantsdominatingthelineofsightmagneticfieldatthese The first region boundary of our model is located at R=
longitudes (e.g. Kothes & Brown 2009), rather than a spiral 5.0kpctocorrespondtothemolecularringofNE2001. The
fieldwiththeopposite‘handedness’tothatoftheopticalspi- remainingboundarieswereoptimizedusingthe(cid:104)(∆RM)2(cid:105)1/2
ralarms. value as the quality-of-fit measure. The optimized boundary
locationswerefoundtobeR=5.8kpc,R=7.2kpc,andR=
4.2. ModelSectorB:SGPSregion(Q4) 8.4kpc.
WedefineSectorBtobe260◦<(cid:96)<360◦,whichisslightly For this model, our best fit magnetic field model is pre-
smaller than the area modeled by Brown et al. (2007). This dominantly clockwise with a reversed (clockwise) region in
regioncontains292pulsarsand121EGS(allfromtheSGPS). the inner Galaxy, as shown in Figure 6. Figure 9 shows
For their model, Brown et al. (2007) used the available a direct comparison to the data and values predicted by
pulsar RMs combined with new EGS RMs from the SGPS the ASS+RING model and our model. When the data are
to model the magnetic field within the SGPS region. The smoothed,ourmodelshowsafactorof4improvementinthe
modelhadmagneticregionsdelineatedbythespiralarmsof (cid:104)(∆RM)2(cid:105)1/2overtheASS+RINGmodel.
NE2001,withamagneticpitchangleof11.5◦ inallregions,
exceptthe‘molecularring’whichismodeledasanazimuthal
field. ForR<3kpcorR>20kpcthefieldwasassumedto 4.4. CombiningtheSectors
bezero,andtherewasnoverticalcomponentassumedforthe
When we consider our three sectors together, as shown in
field. TheirfieldstrengthwasassumedtohaveaR−1 depen-
Figure 10, a picture emerges of a predominantly clockwise
dence, which facilitated a model with significant difference
Galacticmagneticfieldwithwhatcouldbeinterpretedassin-
in strength between the inner and outer Galaxy. This was
glereversed(counter-clockwise)regionspiralingoutfromthe
needed since some of the regions appeared in the modeling
Galacticcenter,asillustratedinFigure11. Accordingtoour
regiontwice–onceintheinnerGalaxy,andonceintheouter
analysis,thefieldintheinnerGalaxyhasaspiralshape(with
Galaxy – as a consequence of the spiral geometry (e.g. the
apitchangleestimatedhereas11.5◦)andisgenerallyaligned
NormaarmintheirFigure4).
withthespiralarmswhileintheouterGalaxyitis(almost)az-
Given how well the model of Brown et al. (2007) agreed
imuthal. ThisisconsistentwiththeobservationsofKronberg
with the data, we decided to keep much of this model the
& Newton-McGee (2009) who suggested explicitly that the
same. Tothatend,wemergedallseparateregionsbeyondthe
GalaxyisamixofanaxisymmetricfieldintheouterGalaxy
Sagittarius-Carinaarmintoonemagneticfieldregion,andre-
and a bisymmetric field in the inner Galaxy. The opposite
definedthefieldinthisnewouter-Galaxyregiontobepurely
signs of the two molecular rings may be suggestive of a bi-
azimuthal, and still retained the R−1 dependence in this re-
symmetricfieldoriginatingfromtheGalacticbar. Moredata
gion,consistentwithBrownetal.(2003b). However,forthe
andperhapsanewelectrondensitymodelcontainingthebar
remainingregionsintheinnerGalaxy, werevertedtoacon-
would be necessary in order to properly investigate this re-
stantfieldstrength,assuggestedbyNota&Katgert(2010).
gion.
The best-fit magnetic field results for our variation on the
Wealsonotethatthis‘spiraling-out’reversedregioncould
Brownetal.(2007)modelarevirtuallyindistinguishablefrom
extend into Q1 at larger Galactic radii, but without any data
theoriginal. AsshowninFigure8,the(cid:104)(∆RM)2(cid:105)1/2 forour
from pulsars located on the far side of the Galaxy in this re-
newmodelisnotstatisticallysignificantlydifferentfromthat
gion,determiningtheexistenceofsucharegionisnotpossi-
forthemodelofBrownetal.(2007). However,themodelis
ble. Ourmodelmaybeconsideredassomethingofazeroth-
less complicated as illustrated in Figure 6. It has 8 regions
orderapproximation;itwasconstructedinapiece-wiseman-
comparedto9regionsintheoriginalmodel,andhasremoved
ner, yet there is some consistency across the whole Galactic
the complexity of the R−1 dependence in the inner Galaxy. disk. The discontinuities that occur at the boundaries are a
Thereductioninthenumberofparameterswhilemaintaining consequence of this and indicate that the actual field config-
agoodqualityoffit,makesthisnewmodelmoreattractive. urationcannotbefullymodeledusingthesimplegeometries
thatwehavetested. Explorationofmorecomplexgeometries
4.3. ModelSectorC:VLAregion(Q1)
will be necessary to improve the boundary matching. How-
WedefineSectorCtobe0◦<(cid:96)<100◦. Inthisregion,we ever, if such a model significantly increases the number of
have177pulsarRMsand378EGSRMs(302fromCGPS,76 parameterswithinthemodel,additionaldatawillcertainlybe
fromourVLAobservations). neededtoproperlyconstrainthemodel.
8 VANECKETAL.
400
EGS Data
5o independent bins
200 Circular field
Spiral field
0
-200
-400
)
-2m 400 EGS (smoothed)
d Data
a Circular field
(r 200 Spiral field
e
r
u
s 0
a
e
M
n -200
o < RM2>1/2 for blue = 49.21
ati < RM2>1/2 for red = 66.09
ot -400
R
400
Pulsars
Data
Circular field
200
Spiral field
0
-200
-400
250 200 180 166 150 100
Galactic Longitude
FIG.7.—ComparisonRMversuslongitudegraphsforobservationsandmodelsinSectorA.ThetoppanelshowstheindividualEGSRMsfromobservations
(filledblackcircles)andthosedataaveragedinto5degreeindependentbins(greendiamonds).ThemodeledEGSRMsforthebest-fitmodelbasedonourcircular
fieldareshownasopenbluecircles,andthoseforalogarithmicspiralwithapitchangleof11.5◦areshownasopenredcircles. Themiddlepanelshowsthe
samedataasintoppanel,exceptthatthecorrespondingdatahavebeenbox-caraveragedover9◦inlongitudewithastepsizeof3◦.Binsymbolsinthemiddle
panelshadedgreyindicatebinswithfewerthan5sources.Themean[median]numberofsourcesperbinis47[56].Thegreenandblueverticallinesshowthe
correspondingRMnullpointsforthetwodifferentmodeledRMdatasets.ThebottompanelshowstheRMsofpulsarsforobservationsandthesamemodels.
MODELINGTHEMAGNETICFIELDINTHEGALACTICDISK 9
1200
600
0
EGS Data
-600 5o independent bins
Our model
Brown07 model
-1200
)
-2m 1200
< RM2>1/2 for blue = 127.56
d
a < RM2>1/2 for red = 129.08
r 600
(
e
r
u
s 0
a
e
M
n -600 EGS (smoothed)
o Data
ati BrownO0u7r mmooddeell
ot -1200
R
1200
600
0
Pulsars
-600
Data
Our model
Brown07 model
-1200
360 340 320 300 280 260
Galactic Longitude
FIG.8.—ComparisonRMversuslongitudegraphsforobservationsandmodelsinSectorB.ThepanelsarethesameasinFigure7withthecomparativemodel
(inred)beingthatfromBrownetal.(2007)andourmodel(inblue)asdescribedinthetext.Themean[median]numberofsourcesperbininthemiddlepanel
is12[12].
10 VANECKETAL.
600
300
0
EGS Data
-300 5o independent bins
Our Model
Sun08 ASS+RING
-600
)
-2m 600
< RM2>1/2 for blue = 108.20
d
a < RM2>1/2 for red = 273.40
r 300
(
e
r
u
s 0
a
e
M
n -300 EGS (smoothed)
o Data
ati Sun08 AOSuSr+ MRoINdGel
ot -600
R
600
300
0
Pulsars
-300
Data
Our Model
Sun08 ASS+RING
-600
100 80 60 40 20 0
Galactic Longitude
FIG.9.—ComparisonRMversuslongitudegraphsforobservationsandmodelsinSectorC.ThepanelsarethesameasinFigure7withthecomparativemodel
(inred)beingthatfromSunetal. (2008)andourmodel(inblue)asdescribedinthetext.Themean[median]numberofsourcesperbininthemiddlepanelis
44[49].