Magnetic fields in barred galaxies. V. Modelling NGC 1365

1.7 MB·English

by  D. Moss

Astronomy&Astrophysicsmanuscriptno.6222 c ESO2008
(cid:13)
February5,2008
Magnetic fields in barred galaxies
V. Modelling NGC 1365
D.Moss1,A.P.Snodin2,P.Englmaier3,A.Shukurov2,R.Beck4,andD.D.Sokoloff5
1 SchoolofMathematics,UniversityofManchester,OxfordRoad,Manchester,M139PL,UK
2 SchoolofMathematicsandStatistics,UniversityofNewcastle,NewcastleuponTyne,NE17RU,UK
7
3 InstituteofTheoreticalPhysics,UniversityofZu¨rich,Winterthurerstrasse190,8057Zu¨rich,Switzerland
0
4 Max-Planck-Institutfu¨rRadioastronomie,AufdemHu¨gel69,53121Bonn,Germany
0
5 DepartmentofPhysics,MoscowUniversity,119992Moscow,Russia
2
n Received...;accepted...
a
J ABSTRACT

0
Aims. WepresentamodeloftheglobalmagneticfieldinthebarredgalaxyNGC1365basedjointlyonthelarge-scalevelocityfield
1
ofinterstellargasfittedtoHandCO observationsofthisgalaxyandonmean-fielddynamotheory.Theaimofthepaperistopresent

adetailedquantitativecomparisonofagalacticdynamomodelwithindependentradioobservations.
1
Methods. Weconsiderseveralgasdynamicalmodels,basedontworotationcurves.Wetestarangeofnonlineardynamomodelsthat
v
includeplausiblevariationsofthoseparametersthatarepoorlyknownfromobservations.Modelsforthecosmicraydistributionin
7
thegalaxyareintroducedinordertoproducesyntheticradiopolarizationmapsthatallowdirectcomparisonwiththoseobservedat
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λλ3.5and6.2cm.
2
Results. Weshowthatthedynamomodelisrobustinthatthemostimportantmagneticfeaturesarecontrolledbytherelativelywell
1
established properties of thedensity distribution and gasvelocity field. The optimal agreement between thesynthetic polarization
0
mapsandobservationsisobtainedwhenauniformcosmicraydistributionisadopted.Thesemapsaresensitivetothenumberdensity
7
ofthermalionizedgasbecauseofFaradaydepolarizationeffects.Ourresultsarecompatiblewiththeobservedpolarizedradiointensity
0
andFaradayrotationmeasureifthedegreeofionizationisbetween0.01and0.2(withrespecttothetotalgasdensity,ratherthanto
/
h thediffusegasalone).Wefindsomeindirectevidenceforenhancedturbulenceintheregionsofstrongvelocityshear(spiralarmsand
p large-scaleshocksinthebar)andwithin1–2kpcofthegalacticcentre.Weconfirmthatmagneticstressescandriveaninflowofgas
- intotheinner1kpcofthegalaxyatarateofafewM yr−1.
o Conclusions. Thedynamomodelsaresuccessfulto⊙someextentinmodellingthelargescaleregularmagneticfieldinthisgalaxy.
r Ourresultsdemonstratethatdynamomodelsandsyntheticpolarizationmapscanprovideinformationaboutboththegasdynamical
t
s models and conditions in the interstellar medium. In particular, it seems that large-scale deviations from energy equipartition (or
a pressurebalance)betweenlarge-scalemagneticfieldsandcosmicraysareunavoidable.Wedemonstratethatthedynamicaleffectsof
:
v magneticfieldscannotbeeverywhereignoredingalaxymodelling.
i
X Keywords.Galaxies:magneticfields–Galaxies:individual:NGC1365–Galaxies:spiral–ISM:magneticfields
r
a
1. Introduction featuresofthedynamotheorycertainlyarenotunderstoodwell
enough. However, we demonstrate that gross features of the
NGC 1365 is one of the best studied barred galaxies. It has
modelgalacticmagneticfield–atleastinbarredgalaxieswhere
been observed in a broad range of wavelengths, including H
the shear in the large-scale velocity is the dominant induction
(Ondrechen&vanderHulst1989),moleculargas(Curranetal. effect–areratherinsensitivetothepoorlyknowndetailsofthe
2001),Hα(Lindblad1999),andtheradiorange(Sanqvistetal. dynamosystem(mostimportantly,theα-coefficient).Therefore,
1995;Becketal.2005),inadditiontonumerousopticalandin-
wecanplausiblyconstrainthefreedomwithinthedynamomod-
fraredobservations(seeLindblad1999andreferencestherein).
els, and so draw conclusions about the interstellar medium in
DetailedgasdynamicalmodellingbyLindbladetal.(1996)pro-
barredgalaxies.
videdquantitativemodelsforthegravityandgasvelocityfields
We findfairagreementbetweenradiopolarizationobserva-
inthisgalaxythatfittheHand,tosomeextent,theCOobser-
tionsandthemagneticfieldobtainedasasolutionofthemean-
vations.
field dynamo equations, using velocity and density fields ob-
Theaimofthispaperistoaddtotheseeffortsbytheinclu- tained from gas dynamical simulations, although the distribu-
sionofmagneticfields.Thegasdynamicalmodelofthegalaxy tion of polarized intensity is reproducedbetter than that of po-
then can be tested against independentradio data, which were larization angles. Our models also support the idea that inter-
notincludedintheconstructionofthemodel.Ofcourse,thisin- stellar turbulenceis enhancedin the vicinity of dust lanes near
volves an additionalpiece of theory and some further assump- the bar major axis, and that the energy density of cosmic rays
tions (concerning, e.g., the applicability of dynamo theory to can depend only weakly on position in the galaxy, thus devi-
galaxies and uncertainties in some dynamo parameters). Some ating significantlyfromequipartitionwith interstellar magnetic
field. As a result, radio polarizationobservationand modelling
Sendoffprintrequeststo:D.Moss of magnetic fields are important ingredientsof both the theory
2 Mossetal.:ModellingNGC1365
andobservationsofbarredgalaxies.Thisworkresemblesquite kindlyprovidedtousbyP.O.Lindblad.Thispotential(the‘LLA
strongly an earlier study of another barred galaxy, NGC 1097 model’inthefollowing)includesthegravitationalpotentialsof
(Mosset al. 2001), butrepresentsa significantimprovementin the disc and spiral arms and was derived from the nonaxisym-
that we now use a dynamical model that specifically models metric part of the deprojected J-band image. Their best fit pa-
NGC1365,ratherthanthegenericdynamicalmodeladoptedfor rametersare A = 1.2and A = 0.3forthe relativecontri-
bar spiral
NGC 1097.Also, thedynamomodelwe use here isfullythree butionsofthebarandspiralarms.Themodelrotationcurvefits
dimensional,whereasthatofMossetal.(2001)usedthe‘no-z’ theHrotationcurveforgalactocentricdistancesr > 120 and
′′
approximationtoremoveexplicitdependenceontheverticalco- givesreasonableresonancelocationsinsidethisradius.Various
ordinate.Broadlycomparablestudieshavealso beenpublished versions of the LLA model used the bar angular velocity of
by Otmianowska-Mazur et al. (2002), Soida et al. (2006) and Ω =18kms 1kpc 1(modelBSM)and17kms 1kpc 1(model
p − − − −
Vollmeretal.(2006). BSM2),withthecorotationradiuscloseto14kpcinbothcases.
ThefullgravitationalpotentialoftheLLAmodelisobtained
from two independent observations: (i) the H rotation curve,
2. Theobservedmagneticstructure
usedtofixthetotalradialmassdistributionofthegalaxyinclud-
NGC1365wasobservedintotalandpolarizedradiocontinuum ingdarkmatter,and(ii)theJ-banddata,tracingthestellarmass
with theVLA DnCarrayatλ3.5cmandλ6.2cm. Thefullde- distribution,whichisonlyusedtoderive(afterdeprojection)the
tails and the mapsat 15 and 25 angularresolutionare given amplitude of nonaxisymmetric perturbations in the disc plane.
′′ ′′
inBecketal.(2005).Thetotalradiointensity(ameasureofto- The latter cannot be used to derive the rotation curve reliably
tal magnetic field strength and thermal emission) follows well becauseofthepresenceofdarkmatter,andtheformeralsocan
the optical bar and the spiral arms. According to the observed bemisleadingwhenthegasflowissignificantlynonaxisymmet-
spectralindices,thethermalfractionisabout20%atλ6.2cm. ric.
Thepolarizedemission(Fig.1)isstrongestinthecentralre- Lindbladetal.(1996)adopted20Mpc(1 = 97pc)forthe
′′
gionandinnerbar,butdecreasesrapidlytowardsthe outerbar.
distanceofNGC1365,butweadjustedthemodeltoadistance
Thereisalsosignificantpolarizedemissionbetweenthebarand of18.6Mpc(1 =90pc)(Lindblad1999).
′′
the spiral arms. No concentrationin the spiral arms can be de-
Isothermalgasdynamicalmodelswerecalculatedusingthe
tected. At λ6.2cm, where the sensitivity is highest, the polar-
codeZEUS2D,publishedbyStone& Norman(1992),andwe
ized emission forms a smooth halo aroundthe bar. The degree
found a close match to the model of Lindblad et al. (1996).
ofpolarizationislowinthebarandspiralarms,indicatingthat
However we did not attempt to take into account the warp in
the turbulent magnetic field dominates in the regions of high
the outer disc, as we are mostly interested in the inner region.
gasdensityandstrongstar formation,while theregularfield is
Our basic models, illustrated in Fig. 2b,c have the bar angu-
strong between the bar and the spiral arms. At λ3.5cm, most
lar velocity Ω = 16.16kms 1kpc 1 and the corotationradius
oftheextendedpolarizedemissionoutsidethebarislostinthe p − −
at R = 15.5kpc; we also considered a model (Fig. 2a) with
noise because of the steep synchrotronspectrum. Furthermore, c
Ω = 17kms 1kpc 1 and R = 16.3kpc. The angularvelocity
thesensitivityoftheVLAtoextendedstructuresisreducedfor p − − c
of the spiral pattern is taken to be equal to that of the bar. For
scalesbeyond3arcminutesatλ3.5cm,whichaffectsthevisibil-
reasonsexplainedbelowin Section 4, the resultinggas density
ityofthelarge-scalepolarizedemissioninNGC1365,whileat
in the bar region was too low to reproduce the observed mag-
λ6.2cmthecriticallimitis5 arcminutesandso doesnotaffect
neticfieldwithinthedynamomodel.ThegasdensityintheLLA
ourobservations.
modelcanbearguedtobeunderestimatedinsidethecorotation
Thepeakpolarizedintensityis368mJyperbeamatλ3.5cm
radiusbecausetherotationcurveusedhadpoorresolution,and
inthemassivedustlanenortheastofthecentre(seeBecketal.
underestimates the depth of the potential well. We derived our
2005). The fractional polarization is 0.8. At the same position
basicmodelfromtheLLAmodel,byreplacingtherotationcurve
the λ6.2cmmaprevealsa localminimumwith polarizedinten-
usedbyLindbladetal.(1996)withthemorerecentCOrotation
sityof150mJy/beam,correspondingtoafractionalpolarization
curveofSofueetal.(1999).Thismodifiedmodelwasmuchbet-
ofonly0.2,whichisneartheexpectedcontributionfrominstru-
terabletoreproducetheobservedmagneticfield,whileremain-
mentalpolarizationbythe brightnuclearregion.Thisindicates
inginagreementwiththeoverallmorphologyofthemolecular
thatstrongdepolarizationoccursatλ6.2cminthecentralregion,
gasdistribution.Asignificantdifferenceisthatthereismorema-
bya factorofatleast4.Inthe barandspiralarmsthedepolar-
terialinthecentralregionswhenSofue’srotationcurveisused.
izationfactoris2–3(Becketal.2005).
TherotationcurveusedhereisshowninFig.3a,withtheposi-
Polarizedemissioncanemergefromcoherent,regularmag-
tionsofresonancesillustratedinFig.3b.
netic fields or from anisotropic random magnetic fields; these
possibilitiescanbedistinguishedwiththehelpofFaradayrota- We also studied the dependence of the gas dynamics and
tionmeasures.InNGC1097,anisotropicfieldsdominateinthe magneticfieldonthesoundspeedadoptedintheisothermalgas
barregion(Becket al. 2005).However,dueto the weak polar- model.Thisparameterisuncertaininourmodelsforseveralrea-
ized intensity in NGC 1365, the observations available cannot sons. Englmaier & Gerhard (1997) showed that the large-scale
providea large-scalemap of Faraday rotation,so that the rela- gasdistributionin isothermalgasflow modelsof barredgalax-
tivecontributionsofcoherentandanisotropicrandommagnetic ies can depend on the sound speed, even if the pressure forces
fieldsremainsunclear. arenegligible.Sincetheposition,andevenexistence,ofshocks
dependsonMachnumber,theglobalgasflowconfigurationcan
change as a result of a relatively small change in the speed of
3. Themodel sound. Different parts of the multi-phase interstellar medium
(ISM) may not follow the same global gas flow. Different nu-
3.1.GasdynamicalmodelsofNGC1365
mericalmethodshavebeenshowntorepresentdifferentaspects
WereproducedthegasdynamicalmodelofLindblad,Lindblad of the ISM with varying success. Sticky particle methods, for
&Athanassoula(1996)usingtheirgravitationalpotential‘BSM’ example,modelbettertheclumpyISM,whilegrid-basedmeth-
Mossetal.:ModellingNGC1365 3
Fig.1. The polarized intensity contours and magnetic vectors of the polarized radio emission at the wavelengths λ3.5cm (left
hand panel) and λ6.2cm (right hand panel) (both smoothed to a resolution 25 ; the beam size is shown in the lower right of
′′
each panel), superimposedonto an ESO optical image of NGC 1365, kindly providedby P. O. Lindblad. The contour levels are
1,2,3,4,6,8,12,...times 30µJy/beam at λ3.5cm and 40µJy/beam at λ6.2cm; the r.m.s. noise is 15µJy/beam at λ3.5cm and
14µJy/beamatλ6.2cm.
Fig.2. Themodelgasdensitywithsuperimposedvelocityvectorsinthereferenceframecorotatingwiththebar,ingasdynamical
modelsbasedon(a)therotationcurveoftheLLAmodelwithc = 10kms 1 (lefthandpanel),andtherotationcurveofSofueet
s −
al.(1999)with(b)c =10kms 1(middlepanel)and(c)c =30kms 1(righthandpanel),withc thesoundspeed.Shadesofgrey
s − s − s
representthelogarithmofgasdensity(darkershadescorrespondingtolargervalues),witheachshadecorrespondingtothe same
densityineachpanel.Notethesmallerdensitycontrastinthebarregioninthemodelwithhigherspeedofsound(panelc).
ods give a better description of the shocks and the smooth gas Ourmagneticfield modelalso reliesonthegasdensityob-
component. tainedfromgasdynamicalsimulationstogetherwiththevelocity
field;thisisdiscussedinSect.3.2–seeEq.(4).
TheglobalmagneticfielddependsonthegasflowviaEqs(1)
and (2); however, it is not a priori clear which component of
the ISM carries the magnetic field and, therefore, what is the
appropriatesoundspeedofthegas.Wehaveconsideredmodels
withthespeedofsoundequalto10and30kms 1(seeSect.5.4).
−
4 Mossetal.:ModellingNGC1365
Table 1. Parameters of models discussed in the text, as defined in Sect. 3.2. In all the models, the angular speed of the bar is
Ω =16.16kms 1kpc 1withthecorotationradiusat15.5kpc.
p − −
Model R η q r f c
α 0 η η η s
[1026cm2s 1] [kpc] [kms 1]
− −
1 3.0 1.0 3 3.0 0 10
2 3.0 1.0 3 1.5 2 10
3 0.0 1.0 3 1.5 2 10
4 2.7 2.5 3 1.5 2 10
5 3.0 2.0 3 1.5 2 10
6 3.0 1.0 3 1.5 2 30
3.2.Thedynamomodel dimensionalgalacticdynamomodelsdescribedinMoss(1997),
exceptthatcylindricalpolarcoordinateswereusedthere.
Dynamo models, specifically simple mean-field turbulent dy-
In Eq. (1), α parameterizesthe dynamoaction of the inter-
namos, are remarkably successful in explaining the observed stellarturbulence,andηistheturbulentmagneticdiffusivity.We
features of galactic magnetic fields (see, e.g., Ruzmaikin et al.
assumebothofthesequantitiestobescalars(ratherthantensors)
1988; Beck et al. 1996; Widrow 2002 for reviews). Despite
and,inordertoobtainasteadystatewithsaturateddynamoac-
the fact that the nonlinear behaviour of turbulent dynamos is
tion,introduceasimpleα-quenchingnonlinearityintotheprob-
stillcontroversial,mean-fieldmodelsprovidearemarkablyreli-
lem,writing
ableempiricaldescriptionoflarge-scale(regular)galacticmag-
neticfields(Shukurov2004).Fortunately,dynamosolutionsfor α= α0 , B2 =4πρ(r)v2 , (2)
galaxiesarequiteinsensitivetothoseparametersthatarepoorly 1+ξB2/B2 eq t
eq
known, such as the form of the α-effect and even, to a lesser
extent,theturbulentmagneticdiffusivity.Thisisespeciallytrue Ω(r)
α =α f(z), (3)
of models for barred galaxies where large-scale velocity shear 0 ∗ Ω0
plays a dominant role in determining magnetic field structure
(Mossetal.1998a,2001);thentheprimaryroleoftheα-effect with
istomaintainthefieldagainstdecay.
sin(πz/h), z h/2,
Ourmodelcanberegardedasadevelopmentofthedynamo | |≤
mneotidcelfioefldMionssaegteanl.e(r2ic00b1a)r,reudsegdatloaxmy.odWeelthneowlarignet-rsocdaulceemfaugr-- f(z)= cosh(2|z|/h−1)2 −1sgnz, |z|>h/2.
therelaborationsrequiredtoreproducethebasicfeaturesofthe HereΩihsatypicalvalueoifΩ,B isthemagneticfieldstrength
global magnetic pattern in NGC 1365. We solve the standard 0 eq
correspondingto equipartitionbetween magnetic and turbulent
mean field dynamo equation for the large-scale, regular mag-
kineticenergies,andα isaconstant,whichwecanadjust.Quite
neticfieldB
arbitrarily,weadoptΩ∗ =Ωatr =3kpc,andEq.(3)showsthat
0
α is the maximum value of α at this radius. Thus we are as-
∂B
= u B+αB 1 η B η B , (1) su∗mingthatthe large-scalemagneticfield significantlyreduces
∂t ∇×(cid:16) × − 2∇ × − ∇× (cid:17) the α-effectwhenits energydensityapproachesthatofthe tur-
bulence;the constantξ is introducedto suggest formally some
inthreespatialdimensions,usingCartesiancoordinates(x,y,z),
of the uncertainty about the details of this feedback. The de-
where xandyarehorizontaldimensions,andthediscmidplane
pendenceofαonheight,definedby f(z),isimplicitlyoddwith
isatz = 0.Hereαandηaretheturbulenttransportcoefficients
respect to the midplane, with α increasing with z from 0 at
responsiblefortheα-effectandturbulentmagneticdiffusion,re- | | | |
z = 0toamaximumat z = h/2,andthendecreasingtozeroas
spectively,u is the large-scalevelocityfield, and the term with | |
z (rememberingthatweonlyexplicitlymodeltheregion
η allows for the turbulent diamagnetism associated with the | | → ∞
∇ z 0). Because of the symmetry of Eqs (1) and (2), if B is a
spatialvariationof the turbulentdiffusivity(Roberts& Soward ≥
solution,then Bisalsoasolution.
1975). In our standard case, our computational domain covers −
We take ξ = O(1), assuming that there is no catastrophic
theregion L (x,y) L, 0 z aL = z , whereais the
− ≤ ≤ ≤ ≤ max α-quenching(Brandenburg& Subramanian2005). The models
domain’saspectratio.Wetakeameshofsizen n n ,with
x× y× z werecomputedwithξ = 1,andthefieldstrengththenscalesas
uniformspacinginthehorizontaldirectionsandalso,separately,
ξ 1/2. The turbulent speed that enters B is taken to be equal
vertically.The maximumresolutionreadilyavailable to uswas − eq
to the speed of sound as adopted in the gas dynamical model.
n =n =200,n =31,andinordertoresolvesatisfactorilythe
x y z Thegasdensityρ(x,y,0)istakenfromthegasdynamicalmodel
solutionswetook L = 15kpcanda = 0.12,so z = 1.8kpc.
max describedinSect.3.1.Weextendthisawayfromz=0bywriting
(Thuswestudyonlytheinnerpartofthisunusuallylargebarred
galaxy.)Thetotalthicknessofgaslayerthathoststhelarge-scale ρ(x,y,0)
magnetic field is taken as 2h = 0.9kpc, compatible with the ρ(x,y,z)= . (4)
cosh(z/h)
thicknessofthediffusewarmgasintheMilkyWay.Ourproce- | |
dureistotime-stepthe xandycomponentsofEq.(1),andthen Themagnitudeofthegasdensityisrelativelyunimportantinour
tousethecondition B=0toupdateB .Werestrictourselves model(wheretheLorentzforceisnotincludedintotheNavier–
z
∇·
tosolutionsofeven(quadrupolar)paritywithrespecttothedisc Stokesequation)asitaffectsonlythemagnitudeofthemagnetic
planez = 0,andsothelatterstepisstraightforward,giventhat field in the steady state, via Eq.(2), butnotits spatial distribu-
B = 0 at z = 0. This is the same procedureused in the three- tion.Theonlyaspectwherethemagnitudeofgasdensityplaysa
z
Mossetal.:ModellingNGC1365 5
code at attainable numerical resolution. Thus Ω was softened
by introducing an explicit parabolic profile within a radius of
2.1kpc, with the maximumof Ω truncatedto 110kms 1kpc 1
− −
(ascomparedto1730kms 1kpc 1 atr = 0.013kpc,thesmall-
− −
est distance from the axis in the gas dynamical model used).
Thismodificationcan be expectedto reducethe magneticfield
strengthinregionsclosetothegalacticcentre,butasthisregion
isnotwellresolvedbytheradioobservations,wecannotinany
casemakeacomparisonbetweentheseandthecomputedmag-
neticfield.
Further,wecontinuedthevelocityfieldabovethediscbyin-
troducingz-dependenceintothehorizontalvelocitycomponents
via
u(x,y,0)
u(x,y,z)= , (6)
cosh(z/1.2kpc)
| |
andu =0everywhere.
z
Inordertomodela galaxysurroundedbynear-vacuum,we
allow themagneticdiffusivityto becomelargehighin thehalo
(Sokoloff&Shukurov1990),
1, z h,
| |≤
η=η01+(η1−1)"1−exp −1|z.5|−kphc!#2 , |z|>h,
whereη andη areconstants;thusη=η nearthediscmidplane
0 1 0
andη η η inthehaloregion(z >h).Weadoptedanominal
0 1
→ | |
η = 2 – larger values led to numerical difficulties. A conven-
1
tionalvalue of η is 1026cm2s 1; however,we also considered
0 −
models with values larger than that – see Table 1. In order to
reproduce polarized radio maps of NGC 1365 in sufficient de-
tail,wehadtointroducefurtherspatialvariationinη.Following
Moss et al. (2001), we have assumed that the turbulent diffu-
Fig.3. (a): The rotation curves used in the paper: that from
sivityisenhancedbytheshearofthenonaxisymmetricvelocity
Lindbladetal.(1996) (solid;asinFig. 2a), andonemorecon-
accordingto
sistent with more recent CO observations (Sofue et al. 1999)
(dashed; as in Fig. 2b,c). The plot assumes the distance of S ∂u ∂u
η 1+ f , S = x + y ,
dNdiiGaugsCrao1mf3c6fo5orrotottahtbieoenr2o0itsaMtRiopcnc≈acsur1ivn4eskLpisnch.dob(wblan)d:ieTntha(eal.)li(nw1e9iat9rh6r)te.hsTeohnseaanmrcaee- w0h∝ere SmaxηSismtahxe!maximum v(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)a∂lyue(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) of(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)S∂x. T(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)he effect of fη , 0
line style. From bottom to top: Ω κ/2, Ω, and Ω + κ/2 in is, firstly, to broaden magnetic structures near the spiral arms,
units of kms 1kpc 1. The resonan−ces are located at the in- and,secondly,toreducethecentralpeakofmagneticfield.The
− −
tersections with the horizontal lines corresponding to Ω = valuesof f adoptedareshowninTable1.Wedidnotconsider
p η
16.16kms 1kpc 1 (solid) and 17kms 1kpc 1 (dashed). The asimilarenhancementinαasMossetal.(2001)foundittobe
− − − −
smallscalestructureintheΩ κ/2curvesisanartefactofplot- unimportant.Thevaluesof fη thatweresufficienttoproducere-
ting. ± alisticmagneticfieldsinspiralarmwerestilltoosmalltoreduce
the central maximum of magnetic field to an acceptable level.
Therefore,weintroducedanadditionalenhancementofηinthe
roleistheFaradaydepolarizationand,hence,themodelleddis- centralpartofthegalaxy,multiplyingη byq exp( r2/2r2);the
tributionofpolarizedintensity.Thiseffectis,however,relatively 0 η − η
valuesofq andr aregiveninTable1foreachmodelstudied.
η η
weakatλ = 3–6cmanditisplausiblethatotherdepolarization
Clearly,wehavemadeanumberofratherarbitrarychoices,
effects(e.g.,Faradaydispersion)aremoreimportantinthereal
in particular when extending the two dimensional gas dynam-
galaxy.ThegasdensityinourmodelisshowninFig.4.
ical model into three dimensions. Our overallimpression from
The gasvelocityin the plane z = 0, u(x,y,0),is also taken
asubstantialnumberofnumericalexperimentsisthattheover-
from the gas dynamical model. For convenience, we split this
allnatureofourresultsdoesnotdependverystronglyonthese
intorotationalandnon-circularparts,
choices.
Atz = z , andon x,y = L, theboundaryconditionsare
u(x,y,0)=Ω(r)rφ+v(x,y,0), (5) max ±
B = B = 0.Onz = 0,∂B /∂z = ∂B /∂z = 0, B = 0,andso
x y x y z
respectively,whebrer =(x2+y2)1/2isaxialdistance. theintegrationof B = 0givesthevaluesof Bz onthe other
∇·
Wethenintroducedtwosignificantmodifications.Wefound boundaries. These are conservative boundary conditions on B
x
that, in the gas dynamical model, Ω(r) increases very rapidly and B , in that they will increase the field gradients and thus
y
towardsthe rotationaxis(veryapproximately,as 1/r).The gas raisethethresholdfordynamoactiontooccur.
dynamicalmodelmodelappearstohandlethisfeaturesatisfacto- We nondimensionalize the problem in terms of the length
rily,butitcausessignificantnumericalproblemsforthedynamo L = 15kpc, time h2/η and magnetic field B . Given that the
0 eq
6 Mossetal.:ModellingNGC1365
velocityfield,includingtheangularvelocity,isgivenbythedy- 0 5 10 16 21
namicalmodel,theonlyfreedynamoparameterisα ;thecorre- 15
spondingdimensionlessparameteris ∗
α h
Rα = η∗ , (7) 10
0
whereα isdefinedinEq.(3).Thedynamoactionpreventsmag-
netic fie∗ld from decay for values of R exceeding about 1 for
α 5
η =1026cm2s 1;thecriticalvalueofR increasesroughlypro-
0 − α
portionallytoη .
0
Henceforth,wewillusedimensionlessvariables,unlessex- c)
p 0
plicitly otherwise stated; the units of gas number density and k
(
magneticfieldstrengthare44cm 3and30µG,respectively. y
−
−5
4. Results
Thegasdynamicanddynamomodelsdescribedabovetogether
yieldthegasdensityandthedistributionofthelarge-scalemag- −10
netic field in the galaxy. The distribution of magnetic field in
thegalaxyplaneresultingfromModel2(introducedinTable1),
whichwearguebelowtobeourbestmodel,isshowninFig.4. −15
Giventhedistributionofthecosmicrays,wecannowconstruct −15 −10 −5 0 5 10 15
syntheticradioobservablesin ordertoassess thequalityof the x (kpc)
model.We havecomputedsyntheticradiopolarizationmapsat
wavelengthsof 3.5cm and 6.2cm using the dynamo generated
Fig.4.Energydensitycontoursandvectorsoftheregularmag-
magnetic field and the gas density, and compared them with
netic field B from Model 2 (see Table 1), both at z = 0, are
the observedradiomaps.Detailsof thisprocedurearegivenin
showntogetherwithgasnumberdensityrepresentedwithshades
AppendixA. Since we do not modelturbulentmagnetic fields,
of grey. The contours shown correspond to approximately 0.1,
weareunabletocalculatethetotalradiointensityandtoestimate
0.6 and 3.0 times the r.m.s. value; the length of the vectors is
thedegreeofpolarizationfromthemodel.
proportionaltoB2.Thescalebaratthetopoftheframerefersto
Weconsideredseveralmodelsforthenumberdensityofcos-
thegasnumberdensityintheunitsofhydrogenatomspercm3.
micrays,n ,whichwediscussinSect.5.1.Forallbutoneofthe
cr
dynamomodelslistedinTable1wefindthatthesimplestpossi-
blechoice,n =const,providesthebestfittotheobserveddata,
cr
Weusedtwomaintechniquestocomparethesyntheticmaps
regardlessoftheotherquantitiesadopted.Thelargervalueofr
η
with observations and therefore to select the optimal magnetic
in Model 1 producesa relatively weak magnetic field through-
field model. We chose to use the λ6.2cm map of polarized in-
outalargecentralregioncomparedwiththatattheendsofthe
tensity in the analysis since it has the best signal-to-noise ra-
bar. In order to fit the observed central peaks of polarized in-
tio. All model data, including synthetic radio maps, have been
tensity,P,animplausiblenon-uniformdistributionofn would
cr
smoothed(intermsoftheStokesparametersQandU)tomatch
berequiredin thismodel.Specifically,thecosmic raydistribu-
the resolution of the observations.In Sect. 4.2 we comparethe
tion required to reconcile this model with observations would
distributions of polarized intensity on cuts along various paths
haveahighpeakwithin3kpcofthecentrewheremagneticfield
in the plane of the sky. In Sect. 4.3 we analyse the difference
strengthisminimum.Fortheotherdynamomodels,anyplausi-
betweenthecomputedandobservedpolarizedintensitiesintwo
blenon-uniformdistributionofn producestoostrongacentral
cr
dimensions.Inaddition,wecomparetheorientationsofthemag-
maximumof P relativetoall otherstructures.Inparticular,the
neticB-vectorsobtainedfromtheobservedandsyntheticStokes
polarized intensity in the spiral arms is almost lost in models
parameters(Sect.4.5).
withnon-uniformn ,beingfarweakerthanthatwithin1–2kpc
cr
of the centre. Since we have truncated the angular velocity at To rotate the modelgalaxyto the positionof NGC 1365in
r < 2.1kpc, the untruncateddifferentialrotation would lead to the sky, we took the inclinationangle i = 46◦ and the position
anevenstrongerdiscrepancy. angle of the galaxy’smajor axis (i.e the intersectionof the sky
Oursyntheticmapsdonotincludeanydepolarizationeffects planeandthegalaxyplane)PA=222◦,whicharethoseassumed
due to random magnetic fields (see Burn 1966; Sokoloff et al. inobtainingtherotationcurveforour(favoured)gasdynamical
1998),althoughtheyallowfullyfordepolarizationbytheregu- model.Resultsarequitesensitivetothesevalues,anditispos-
larmagneticfields(differentialFaradayrotationandbeamdepo- siblethatareappraisalcouldresultinnoticeablechanges.
larization).InordertoincludeFaradaydepolarizationeffectsdue
tothelarge-scalemagneticfield,weassumedanominalconstant
4.1.Syntheticpolarizationmaps
ionizationfractionof X = n /n = 0.1,correspondingto ather-
e
malelectrondensityof0.1ofthetotalgasdensityobtainedfrom Overall, Model 2 (specified in Table 1) appears to provide the
thegasdynamicalsimulationsasdescribedinSect.3.2.Guided bestfittotheobservedpolarizationmap;Model4isonlyslightly
byanalogywiththeMilkyWay,wheretheaveragetotalgasden- worse – see Sect. 4.2. Contoursof B2 shown in Fig. 4 indicate
sityis1cm 3whereasthethermalelectrondensityis0.03cm 3, thattheregularmagneticfieldisstrongerinthebarregionwhere
− −
asmallervalueofXmightbeappropriate.WeshowresultsforX gasdensityislarge,andoutsidetheregionsofhighdensityinthe
closetothisvalueinSect.4.1.InSect.5.5,wediscusstheeffect spiralarms.Therearemagneticfeaturesapparentlyunrelatedto
ofvariationsinX andarguethat0.01< X <0.2. thedensitydistribution[e.g.,thosepassingthroughthepositions
∼ ∼
Mossetal.:ModellingNGC1365 7
150 200
(a)
150
100
P 100
50
50
)
c
e
cs 0 0
r
a
(
y −100 0 100
distance from centre (arcsec)
−50
300
(b)
250
−100
200
P 150
−150
−150 −100 −50 0 50 100 150 100
x (arcsec)
50
Fig.5. Asyntheticmapofpolarizedsynchrotronintensity(con-
0
tours)andpolarizationplanesatλ6.2cm,resultingfromModel2
−100 0 100
(seeTable1)assumingthatn =const,areshownsuperimposed
cr distance from centre (arcsec)
on the optical image of the galaxy NGC 1365 (shown in only
a few shades of grey for clarity). The synthetic map has been 300 (c)
smoothedtotheresolutionof25 tomatchthatoftheobserved
′′ 250
map shown in Fig. 1. The contour levels shown are approxi-
mately (1,3,6,12,32) P /45, where P is the maximum
max max 200
×
ofPinthesyntheticmap.Dashedlinesshowthepositionofcuts
discussedinSect.4.2. P 150
100
(x,y) ( 5,8),(5, 8)];they are presumably formed by a lo-
50
≈ − −
cally enhanced velocity shear. The magnetic field has a deep
minimum within the bar, mainly producedby the density defi- 0
ciencyinthatregion.Otherimportantfeaturesclearlyvisiblein −100 0 100
Fig. 4 are the magnetic field enhancementsin the dustlane re- distance from centre (arcsec)
gion,wheremagneticfieldisamplifiedbybothcompressionand
Fig.6. Cuts, at position angle 31 passing through the galac-
◦
shear,andtheprominentcentralpeak. −
tic centre (left to right in the plots corresponds moving from
The synthetic polarization map for this model is shown in
south-easttonorth-westinthesky),throughpolarizedintensity
Fig.5.Thiscanbecompareddirectlywiththeobservedmapin mapsatλ6.2cmsmoothedtoHPBW=25 ,for(a)theobserved
′′
theright-hand-panelofFig.1;themaps(andallothermapswe
map,andsyntheticmapsfrom(b)Model2and(c)Model4,both
show)areatasimilarscaletofacilitatethecomparison;wemake for n = const. In panels(b) and (c), the synthetic profiles for
cr
this comparison more quantitatively in Sect. 4.3. Our models
λ6.2cm and λ3.5cm are shown solid and dotted, respectively;
havea highdegreeofsymmetry,whereasthe ‘real’NGC1365 thedifferenceisduetoFaradayandbeamdepolarizationforthe
isonlyapproximatelysymmetric;sincetheobservedmaplooks assumed ionization degree X = 0.1. The units of P are as in
more regular on the eastern side, we shall mostly refer to that
Fig. 1 for (a) and arbitrary in (b) and (c), but adjusted to fit a
part of the galaxy unless stated otherwise. Despite the differ- similarrange.Thedottedprofilesforλ3.5cmwithX = 0.1also
ence in symmetry,there is broadagreementbetweenthese two correspondtoPatλ6.2cmwithX =0.032.
maps; for example, both have a deep minimum of P near the
bar’s major axis where gas density is low, and both have the
magneticspiralarmsdisplacedfromthegaseousones(although
bothmagneticarmsaredisplacedtolargerradiiinthesynthetic ical model underestimates significantly the amount of molecu-
map, only one arm is so displaced in the observed map). The lar gas in the bar region. Synthetic P is large both to the north
minimumofthesynthetic Pinthebar(correspondingalsotoa and southof the bar majoraxis. In particular,the modelrepro-
minimum of magnetic field within the bar, as seen in Fig. 4), ducesamaximumof Pupstreamofthebarmajoraxis,centred
is broader than of the observations (see Sect. 4.2). The rea- intheλ6.2cmmapofFig.1at(RA=03h33min40sec,Dec=
son for this is the very low gas density in this region, lead- 36 0900 ). These maxima apparentlyarise fromslightly en-
◦ ′ ′′
−
ing to weaker magnetic fields via Eq. (2). This feature is fur- hanced velocity shear (that locally amplifies magnetic field)
ther discussed in Sect. 6 where we argue that the gas dynam- rather than from local density maxima. We also note maxima
8 Mossetal.:ModellingNGC1365
200
(a) 200 (a)
150
150
100
P P 100
50 50
0 0
−150 −100 −50 0 50 100 150 −150 −100 −50 0 50 100 150
distance from centre (arcsec) distance from centre (arcsec)
250
(b) (b)
250
200
200
150
150
P P
100
100
50 50
−150 −100 −50 0 50 100 150 −150 −100 −50 0 50 100 150
distance from centre (arcsec) distance from centre (arcsec)
(c) (c)
250 200
200
150
P 150 P
100
100
50
50
−150 −100 −50 0 50 100 150 −150 −100 −50 0 50 100 150
distance from centre (arcsec) distance from centre (arcsec)
Fig.7.AsinFig.6,butatpositionangle0 (lefttorightissouth Fig.8. As in Fig. 6, but at position angle 90 (left to right is
◦ ◦
−
tonorthinthesky). easttowestinthesky).
of P near the ends of the bar and the beginning of the spiral length(seeSect.2)andhastobetakenintoaccountwhencom-
arms, at (RA = 03h33 min45sec,Dec = 36 0815 ) and paring the model and observations. We use cuts through the
◦ ′ ′′
−
(RA=03h33min28sec,Dec= 36 0830 ).Wenotethatthe centre of the galaxy at position angles PA = 0 , 90 and
− ◦ ′ ′′ ◦ − ◦
observedtotalemission (notshownhere;see Beck etal. 2005) 31 , where PA is measured counterclockwise from the north
◦
−
isrelatedtogasdensityinaratherstraightforwardmannerbeing as shown in Fig. 5. (The angle 31 is chosen so that the cut
◦
−
correlatedwiththegasdensity.Thefactthatthisisnotthecase goes throughthe spiral arms; this correspondsroughlyto a di-
with the polarizedintensity (as seen in both observedand syn- agonal in the computationalframe of Fig. 4.) The positions of
theticmaps)confirmsthattheobservedregularmagneticfieldis these cuts are shown in Fig. 5. The synthetic P has been nor-
notfrozenintothegas,apparentlybeingaffectedbythedynamo malized to make the mean difference between that and the ob-
action. served P approximately zero. We have superimposed another
profilefromcutsthroughsyntheticmapswhichrepresentsboth
P at λ3.5cm with our favoured value of X = 0.1, and also
4.2.Cutsthroughpolarizationmaps
at λ6.2cm with X = 0.032 (incidentally, this is close to the
mean ionization degree of the warm diffuse gas in the Milky
We found that comparisons can be usefully quantified and de-
tailedusingthecutsintheskyplanementionedabove.Weshow Way). The coincidence of these two cuts is due to equivalent
cuts only through the map at λ6.2cm because this map has Faradaydepolarization,whichdependsdirectlyon thequantity
higher signal-to-noise ratio and includes the large-scale emis- ψ(z) λ2X ∞nB dzalongthelineofsighttowardsanobserver
∝ z k
sion fully. However, depolarization is significant at this wave- (see AppendRixA). Here B is the line of sightfield component
k
Mossetal.:ModellingNGC1365 9
and n = Xn, therefore λ2X = const identifies equivalence in correspondinglyhigherspeedofsound,whichwouldallow the
e
depolarization.We seethatthisvalueisaboutthesameinboth turbulentspeedtobelargerthanelsewhere.
cases(i.e.6.22 0.032 3.52 0.1).Thedifferencebetweenthe TheModel2cutatPA= 31 (Fig.6),whichpassesthrough
◦
× ≈ × −
polarizationforthesetwopossibilitiesisthenjustaλ-dependent thespiralarms,showsanencouragingagreementwithobserva-
scalefactor. tions.Forexample,Bhasamaximumslightlyoutsidethenorth-
The cuts are presented in Figs 6, 7 and 8 for the best-fit ernarminboththismodelandtherealgalaxy.However,theout-
Model 2 and also for Model 4. The latter model has the back- ermostmaximaproducedbythespiralarmsareslightlytoofar
ground turbulent magnetic diffusivity η enhanced by a factor awayfromthecentreinthemodel.AsillustratedinFig.6(b),the
0
of 2.Thisleadsto a significantlysmoother,less structureddis- relativeheightsofthepeaksatλ6.2cmaresignificantlyaffected
tribution of P. Thus, comparison of Models 2 and 4 allows us byFaradayrotationevenfor X = 0.1,wheretheyclearlydiffer
to suggest that the effective turbulent magnetic diffusivity in bymorethanjustascalefactorbetweenλ6.2cmandλ3.5cm.
the interstellar gas of barred galaxies is, on average, close to ThecutatPA = 0(Fig.7)exhibitssimilardegreeofagree-
η = 1026cm2s 1. This value is typical of spiral galaxies in ment with the observations. The main deficiency of the model
0 −
generalandis thatobtainedif the turbulentspeed v is close to here is the too narrowdistributionof P (the magneticstructure
t
10kms 1andtheturbulentscaleisaboutl=0.1kpc;η 1lv. ofthemodelistoopooroutsidethebar)andtheminimumistoo
− 0 ≃ 3 t
Ourmodelneglectsdepolarizationdueto randommagnetic deepnearthecentreofthecut.
fieldswhichcanreducethevalueofPinthecentralpartsmore ThecutatPA= 90 inthesyntheticmap,showninFig.8,
◦
−
stronglythanintheoutergalaxyandthereforeaffecttherelative hasacentralmaximumthatistoonarrow(oroff-centreminima
height of the central peaks in Figs 6–8. Depolarization due to that are too broad). This difference results in the deep minima
internalFaradaydispersionreducesthedegreeofpolarizationto in the difference parameter δ discussed in Sect. 4.3. The sharp
minimumintheobservedcutnearthecentreisaresultofbeam
1 e S depolarization;it occursin thesyntheticcutsas well, butisre-
p= p − − , (8)
0 S movedbysmoothing.
Model 2 seems to be almost optimal. The model could
whereS = 2σ2 λ4 withσ2 = 2C2 b2 n2 dLthevarianceof be fine tuned by changing η and r within the ranges (1–
RM RM 1h ih ei 0 η
the Faraday rotation measure. HereC1 is the dimensionalcon- 2) 1026cm2s−1 and1.5–3,respectively.Forexample,thesec-
stant appearing in the definition of the Faraday rotation mea- ond×arypeaksinthePA=0cutdecreaseinstrengthinModel4.
sure (see AppendixA), b is the turbulentmagneticfield, angu- Further,increasingn byafactorof2withinthecentral1.5kpc
cr
larbracketsdenoteaveraging(thefluctuationsinmagneticfield wouldmakethecentralpeakhigher.However,wehavenotmade
and thermal electron density are assumed to be uncorrelated), suchposthocadjustments.
d is the turbulentscale and L is the pathlength(Sokoloffet al.
1998).Thebestavailableestimateoftherandommagneticfield
in the central region of NGC 1365, b 40µG, follows from 4.3.Thedifferencemaps
≃
the total synchrotron intensity assuming equipartition between
To obtaina globalcomparisonofthe modelsandobservations,
cosmicraysandmagneticfields(seehoweverSect.5.1foradis-
we producedmaps of the difference between the observed and
cussionofthevalidityofthisassumption).Forn = 0.03cm 3,
e − synthetic polarization at λ6.2cm, with the synthetic polariza-
d = 0.1kpc, L = 1kpcandλ = 6.2cm, wethenobtainS 6,
tionscaledtomakethemeandifferenceapproximatelyzero;this
≃
implying that this mechanism can depolarize the central peak
measurewasfurthernormalizedbydividingthedifferencebythe
significantly, giving p/p 0.2. Since the height of the sec-
0 appropriatelynormalizednoiseleveloftheobservedmapgiving
≃
ondarypeakshouldalsobeaffectedbydepolarization,albeitto
a lesser extent, we expect that the ratio of the two peaks will (1.4P/P ) (P/P )
bereducedbyafactorsmallerthanfive.Wenote,however,that δ= max model− max obs . (9)
(σ /P )
P max obs
this estimate is uncertain since the number density of thermal
electrons, their filling factor, turbulentscale and other parame- Thus, all comparisonswere performedpointwise after their re-
ters are not knownwell enough.An alternative is to assess the ductiontothecommonresolution25 –thisisquiteastringent
′′
importanceofthisdepolarizationeffectbycomparingpolarized testofthemodel.TheresultisshowninFig.9forModel2.
intensitiesatλ6.2cmandλ3.5cm.Theratioofthecentralpeak Since the models– unlikethe realgalaxy– possess perfect
tothesecondaryonesatλ3.5cmisabout6–8,asopposedto2–3 symmetry,the differencecan hardlybe uniformlysmall: a per-
atλ6.2cm.ThedifferencecanbeattributedtoFaradaydepolar- fectfitinonehalfofthegalaxywouldproducesignificantsys-
ization(bybothregularandrandommagneticfields).Assuming tematic discrepancyin the other half. With this caveat, the dif-
thatFaradaydepolarizationatλ3.5cmisnegligible,weconclude ferencemapshowsanacceptableglobalagreementofthemodel
thatitcanreducethedegreeofpolarizationatλ6.2cmbyafac- with observations, in that it does not show much of the basic
toraslargeas4,whichisconsistentwiththeanalyticalestimate. morphologicalelements of the galaxy.The normalized relative
We conclude that the relative height of the central peak in the differenceisabout6–14infourspotsobservedtotheeast,south
syntheticcutsofFigs6–8wouldbereducedbyFaradaydisper- and north-west of the galactic centre, indicating that synthetic
sion,althoughthisisdifficulttoestimateaccurately. polarized intensity is too small upstream of the dust lanes and
Given the above uncertainties in the amountof depolariza- at two positions at the inner edge of the western spiral arm.
tion,allthreecutsforModel2aresimilartothoseobserved.In Otherwise, δ < 4 across the whole field of view. Given the
particular, the relative heights of the peaks in P and, more im- limitedscop|e|o∼fourmodel(e.g.,itdoesnotincludeanyturbu-
portantly,thepositionsofbothmaximaandminimaareremark- lentmagneticfieldswhichcanproducepolarizedradioemission
ably realistic. The characteristic feature of this model is that η where they are anisotropic), we consider this degree of agree-
is further enhanced by a factor of q 3 in the inner region menttobeacceptable.WediscussinSect.5.1acosmicraydis-
η
of NGC 1365, r < 3kpc. This enhanc≃ement can be due to a tribution that would provide perfect fit of Model 2 to observa-
higher rate of star∼formation, and hence more hot gas, with a tions.
10 Mossetal.:ModellingNGC1365
150
100
50
)
c
e
s
c 0
r
a
(

y
−50
−100
−150
−150 −100 −50 0 50 100 150
x (arcsec)
Fig.9.Thedifferenceδbetweennormalizedsyntheticandobservedpolarizationmapsatλ6.2cm, asdefinedin Eq.(9),superim-
posedontheopticalimageofNGC1365.Thecontourspacingis2,withthezerocontourshownsolid,negativevaluesofδdashed,
andpositive,dotted.
4.4.Faradayrotation so that modes with odd values of m do not occur in the mod-
elled magnetic field. The contribution of the m = 1 mode to
Wecanusepolarizedintensity(asinthecomparisonsabove)to
those Fourier expansions is more important than just produc-
probethedistributionofthelarge-scalemagneticfieldstrength,
ing the overall asymmetry. In particular, superposition of vari-
and also to deduce the orientation of the magnetic field in the
ous azimuthalmodes produceslocal magnetic features at kilo-
plane of the sky (via polarization vectors). However, knowl-
parsec scale which are lost if only even modes are retained in
edgeofthisquantitydoesnotdeterminethefielddirection.The
the observedstructure to facilitate comparison with the model.
FaradayrotationmeasureRMissensitivetothedirectionofthe
Therefore,wedidnotfinditusefultocomparethemodelledand
magneticfield,buttheobservedRMmapisverypatchybecause
observed magnetic structures in this manner. (The presence of
ofthelowersignal-to-noiseratioatλ3.5cm.Therefore,weused
unmodelledodd-m structure was also a feature of our study of
RMdataonlytoestablishaminimumacceptabledegreeofgas
NGC1097inMossetal.2001.)
ionization.
Weinsteadcomparedirectlytheorientationofthemagnetic
field vectors in the observed and synthetic polarization maps.
Comparison of two-dimensional vector fields is difficult. We
4.5.Magneticfieldstructure
couldapproachthisbytakingcutsthroughmapsofthemagnetic
An analysis of the observed global magnetic structure in fieldorientationangles,aswasdonewiththepolarizedintensity.
NGC1365thatissensitivetothedirectionofmagneticfieldwas However,asmallshiftinafeaturesuchasashockfrontcanre-
performedbyBecketal.(2005)byfittingthepolarizationangles sult in drastic differences between any such cuts made parallel
obtainedfrommulti-frequencyobservations.Thisanalysispro- tothefront.
videsthelarge-scalemagneticfieldexpandedintoFourierseries InFig.10weshowtheorientationofboththesyntheticand
in the azimuthal angle. Their results indicate the presence of a observedmagneticfieldvectorsobtaineddirectlyfromthecor-
significantcomponentwiththeazimuthalwavenumberm=1at responding Stokes parameters; points below 3 times the r.m.s.
almostall distancesfrom the galactic centre.However,our un- noise levelare neglected in the observedmaps. Agreementbe-
derlying gas dynamical model has even symmetry in azimuth, tween modeland observationsis reasonable in the top left and