Ordered magnetic fields around radio galaxies: evidence for interaction with the environment

0.8 MB·English

by  D. Guidetti

Mon.Not.R.Astron.Soc.000,1–21(2002) Printed11January2011 (MNLATEXstylefilev2.2)
Ordered magnetic fields around radio galaxies: evidence for
interaction with the environment
1 D. Guidetti⋆1,2,3, R.A. Laing 1, A.H. Bridle 4, P. Parma 2, L. Gregorini 3,2
1
0 1EuropeanSouthernObservatory,Karl-Schwarzschild-Straße2,D-85748Garching-bei-Mu¨nchen,Germany
2 2INAF–IstitutodiRadioastronomia,viaGobetti101,I-40129Bologna,Italy
3DipartimentodiAstronomia,Univ.Bologna,viaRanzani1,I–40127Bologna,Italy
n
4NationalRadioAstronomyObservatory,EdgemontRoad,Charlottesville,VA22903-2475,U.S.A.
a
J

0
1 Accepted.Received;inoriginalform

]
O
ABSTRACT
C
WepresentdetailedimagingofFaradayrotationanddepolarizationfortheradiogalaxies
.
h 0206+35,3C270,3C353andM84,basedonVeryLargeArrayobservationsatmultiplefre-
p
quenciesintherange1365to8440MHz.Allofthesourcesshowhighlyanisotropicbanded
-
o rotation measure (RM) structureswith contoursof constant RM perpendicularto the major
r axesoftheirradiolobes.AllexceptM84alsohaveregionsinwhichtheRMfluctuationshave
t
s lower amplitude and appear isotropic. We give a comprehensive description of the banded
a RMphenomenonandpresentaninitialattempttointerpretitasaconsequenceofinteractions
[
between the sources and their surroundings. We show that the material responsible for the

1 Faradayrotation is in frontof the radio emission and thatthe bandsare likely to be caused
v bymagnetizedplasmawhichhasbeencompressedbytheexpandingradiolobes.Wepresent
7 a simple model for the compression of a uniformly-magnetizedexternalmedium and show
0 thatRMbandsofapproximatelytherightamplitudecanbeproduced,butforonlyforspecial
8 initialconditions.Atwo-dimensionalmagneticstructureinwhichthefieldlinesareafamily
1 ofellipsesdrapedaroundthe leadingedgeofthelobecanproduceRM bandsin thecorrect
.
1 orientationforanysourceorientation.We also reportthefirstdetectionsofrimsofhighde-
0 polarization at the edges of the inner radio lobes of M84 and 3C270. These are spatially
1 coincidentwithshellsofenhancedX-raysurfacebrightness,inwhichboththefieldstrength
1 and the thermal gas density are likely to be increased by compression. The fields must be
: tangledonsmallscales.
v
i
X Keywords: –galaxies:magneticfields–radiocontinuum:galaxies–(galaxies:)intergalactic
medium–X-rays:galaxies:clusters
r
a
1 INTRODUCTION by linearly polarized radiation travelling through a magnetized
medium,andcanbedescribedbythetwofollowingrelations:
Thedetectionofdiffusesynchrotronemission(radiohalos)onMpc
scales in an increasing number of galaxy clusters provides good ∆Ψ[rad] =Ψ(λ)[rad] − Ψ0[rad] =λ2[m2]RM[radm−2], (1)
evidence for a distributed magnetic field of µGauss strength in
with
the hot intracluster medium (ICM; see e.g. Ferrarietal. 2008 for
areview).ImagingofFaradayrotationoflinearly-polarizedradio L[kpc]
emission from embedded and background sources confirms that RM[radm−2] =812Z ne[cm−3]Bz[µG]dz[kpc], (2)
therearefieldsassociatedwiththermalplasmaalonglinesofsight 0
through the clusters (e.g. Carilli&Taylor 2002). Observations of whereΨ(λ)andΨ aretheE-vectorpositionangleoflinearlypo-
0
Faradayrotationcanalsobemadeforradiogalaxiesinsparseren- larizedradiationobservedatwavelengthλandtheintrinsicangle,
vironments,allowingthestudyofmagneticfieldsinenvironments respectively,n istheelectrongasdensity,B isthemagneticfield
e z
too sparse for radio halos to be detected (e.g. Laingetal. 2008; alongtheline-of-sight (B ),andListheintegrationpath. RMis
k
Guidettietal.2010). therotationmeasure.
The Faraday effect (Faraday 1846) is the rotation suffered Observations of Faraday rotation variations across extended
radiogalaxiesallowustoderiveinformationabouttheintegralof
thedensity-weightedline-of-sightfieldcomponent.Thehot(T ≃
⋆ E-mail:[email protected] 107 −108K)plasmaemitsintheX-rayenergybandviathermal
2 D. Guidettiet al.
bremsstrahlung. Whenhigh quality X-ray datafor aradio-source andinSection3webrieflysummarizethetechniquesusedtoanal-
environmentisavailable,itispossibletoinferthegasdensitydis- yse depolarization and two-dimensional variations of RM. Sec-
tributionandthereforetoseparateitfromthatofthemagneticfield, tions4and5presenttheRManddepolarizationimagesonwhich
subjecttosomeassumptionsabouttherelationoffieldstrengthand ouranalysisisbasedandcorrelationsbetweenthetwoquantities.In
density. Section6,weevaluatetheRMstructurefunctionsinregionswhere
Most of the RM images of radio galaxies published so far thefluctuationsappear tobeisotropicandderivethepower spec-
show patchy structures with no clear preferred direction, consis- tra. A simple model of the source-environment interaction which
tent with isotropic foreground fluctuations over a range of linear characterises the effects of compression of a magnetised IGM is
scales ranging from tens of kpc to <100pc (e.g. Govonietal. describedinSection7.ThiscanproduceRMbands,butonlyun-
∼
2006;Guidettietal.2008;Laingetal.2008;Guidettietal.2010). derimplausiblespecialinitialconditions.Empirical“draped”field
Numerical modelling has demonstrated that thistype of complex configurationswhichareabletoreproducethebandedRMdistri-
RM structure can be accurately reproduced if the magnetic field butionsareinvestigatedinSection8.InSection9,wespeculateon
is randomly variable with fluctuations on a wide range of spatial correlationsbetweenradiosourcemorphology,andRManisotropy,
scales, and isspread throughout the whole group or cluster envi- discussotherexamplesfromtheliterature,consider theeffectsof
ronment(e.g.Murgiaetal.2004;Govonietal.2006;Guidettietal. anisotropicforegroundFaradayscreenonthedetectabilityofRM
2008; Laingetal. 2008; Guidettietal. 2010; Vaccaetal. 2010). bandsandbrieflydiscusspossibleasymmetriesintheamplitudeof
Theseauthorsusedforwardmodelling,togetherwithestimatorsof theRMbandsbetweentheapproachingandrecedinglobes.Finally,
the spatial statistics of the RM distributions (structure and auto- Section10summarizesourconclusions.
correlationfunctionsoramulti-scalestatistic)toestimatethefield Throughout thispaper weassumeaΛCDMcosmology with
strength,itsrelationtothegasdensityanditspowerspectrum.The H =71kms−1Mpc−1,Ω =0.3,andΩ =0.7.
0 m Λ
techniqueofBayesianmaximumlikelihoodhasalsobeenusedfor
thispurpose(Enßlin&Vogt2005;Kuchar&Enßlin 2009).
Inordertoderivethethree-dimensionalmagneticfieldpower
2 THESAMPLE
spectrum,alloftheseauthorshadtoassumestatisticalisotropyfor
thefield,sinceonlythecomponentofthemagneticfieldalongthe High quality radio and X-ray data are available for all of the
line-of-sight contributes to the observed RM. This assumption is sources.InthisSectionwesummarizethoseoftheirobservational
consistentwiththeabsenceofapreferreddirectioninmostofthe propertieswhicharerelevanttoourRMstudy.Alistofthesources
RMimages. and their general parameters is given in Table1, while Table2
Incontrast,thepresentpaperreportsonanisotropicRMstruc- showstheX-rayparameterstakenfromtheliteratureandequipar-
tures,observedinlobedradiogalaxieslocatedindifferentenviron- titionparametersderivedfromourradioobservations.
ments,rangingfromasmallgrouptooneoftherichestclustersof ThesourceswereobservedwiththeVLAatseveralfrequen-
galaxies.TheRMimagesofradiogalaxiespresentedinthispaper cies,infullpolarizationmodeandwithmultipleconfigurationsso
showclearlyanisotropic“banded”patternsoverpartoralloftheir that the radio structure is well sampled. The VLA observations,
areas.Insomesources,thesebandedpatternscoexistwithregions datareductionanddetaileddescriptionsoftheradiostructuresare
ofisotropicrandomvariations.Themagneticfieldresponsiblefor givenfor0206+35andM84byLaingetal.(2011),for3C270by
theseRMpatternsmust,therefore,haveapreferreddirection. Laing,Guidetti&Bridle(2011),andfor3C353bySwain(1996).
OnesourcewhoseRMstructureisdominatedbybandsisal- All of the radio maps show a core, two sided jets and a double-
ready known: M84 (Laing&Bridle 1987). In addition, there is lobedstructurewithsharpbrightnessgradientsattheleadingedges
some evidence for RM bands in sources which also show strong ofbothlobes. Thesynchrotron minimumpressures areallsignif-
irregularfluctuations,suchasCygnusA(Carilli&Taylor2002).It icantly lower than the thermal pressures of the external medium
ispossible,however,thatsomeoftheclaimedbandscouldbedue (Table2).
toimperfectsamplingofanisotropicRMdistributionwithlarge- AllofthesourceshavebeenobservedinthesoftX-rayband
scalepower,andwereturntothisquestioninSection9.1. bymorethanonesatellite,allowingthedetectionofmultiplecom-
Thepresent paper presentsnew RMimagesofthreesources ponentsoncluster/groupandsub-galacticscales.TheX-raymor-
whichshowspectacularbandedstructures,togetherwithimproved phologiesarecharacterizedbyacompactsourcesurroundedbyex-
dataforM84.Theenvironmentsofallfoursourcesarewellchar- tendedemissionwithlowsurfacebrightness.Theformerincludesa
acterizedbymodernX-rayobservations,andwegivethefirstcom- non-thermalcontribution,fromthecoreandtheinnerregionsofthe
prehensivedescriptionofthebandedRMphenomenon.Wepresent radiojetsand,inthecaseof0206+35and3C270,athermalcom-
aninitialattempttointerpretthephenomenonasaconsequenceof ponent which is well fitted by a small core radius β model. The
source-environment interactions and to understand the difference lattercomponentisassociatedwiththediffuseintra-grouporintra-
betweenitandthemoreusualirregularRMstructure. clustermedium.Parametersforallofthethermalcomponents,de-
TheRMimagesreportedinthispaper arederivedfromnew rivedfromX-rayobservations,arelistedinTable2.Becauseofthe
orpreviouslyunpublishedarchiveVeryLargeArray(VLA)1 data irregularmorphologyofthehotgassurrounding3C353andM84,
for the nearby radio galaxies 0206+35, M84 (Laingetal. 2011), ithasnotbeenpossibletofitβmodelstotheirX-rayradialsurface
3C270(Laing,Guidetti&Bridle2011)and3C353(Swain,private brightnessprofiles.
communication;seeSwain1996).
Thepaperisorganizedasfollows.InSection2theradioand
2.1 0206+35(4C35.03)
X-ray properties of the sources under investigation are presented
0206+35 is an extended Fanaroff-Riley Class I (FRI;
Fanaroff&Riley 1974) radio source whose optical counter-
1 TheVeryLargeArrayisafacilityoftheNationalScienceFoundation, part,UGC11651,isaD-galaxy,amemberofadumb-bellsystem
operatedundercooperativeagreementbyAssociatedUniversities,Inc. atthecentreofagroupofgalaxies.Ataresolutionof1.2arcsecthe
Faradayrotationmeasurebandsacrossradiogalaxies 3
Figure1. X-rayimagesoverlaidwithradiocontoursforallsources:(a)0206+35:1385.1MHzVLAradiomapwith1.2arcsecFWHM;thecontoursarespaced
byfactorof2between0.06and15mJybeam−1.TheROSATPSPCimage(Worrall&Birkinshaw2000),issmoothedwithaGaussianofσ = 30arcsec.
(b) M84: 1413.0MHz VLA radio map with 4.5arcsec FWHM; the contours are spaced by factor of 2 between 1 and 128mJy beam−1. TheChandra
(Finoguenov&Jones 2001) image is a wavelet reconstruction on angular scales from 4 up to 32arcsec. (c) 3C270: 1365.0MHz VLA radio map with
5.0arcsecFWHM;thecontoursarespacedbyfactorof2between0.45and58mJybeam−1.TheXMM-Newtonimage(Croston,Hardcastle&Birkinshaw
2005)issmoothedwithaGaussianofσ=26arcsec.(d)3C353:1385.0MHzVLAradiomapwith1.3arcsecFWHM;thecontoursarespacedbyfactorof
2between0.35and22mJybeam−1.TheXMM-Newtonimage(Goodgeretal.2008)issmoothedwithaGaussianofσ=30arcsec.TheChandraimageof
3C270isdisplayedinlogarithmicscale.
Table1.Generalopticalandradioproperties:Col.1:sourcename;Cols.2&3:position;Col.4:redshift;Col.5:conversionfromangulartospatialscalewith
theadoptedcosmology;Col.6:Fanaroff-Rileyclass;Col.7:thelargestangularsizeoftheradiosource;Col.8:radiopowerat1.4GHz;Col.9:angletothe
lineofsightofthejetaxis;Col.10:radiospectralindex;Col.11:environmentofthegalaxy;Col.12:reference.
source RA DEC z kpc/arcsec FRclass LAS logP1.4 θ env. ref.
[J2000] [J2000] [arcsec] [WHz−1] [degree]
0206+35(4C35.03) 020938.6 +354750 0.0377 0.739 I 90 24.8 40 group 1
3C353 172029.1 -005847 0.0304 0.601 II 186 26.3 90 poorcluster 2
3C270 121923.2 +054931 0.0075 0.151 I 580 24.4 90 group 3
M84 122503.7 +125313 0.0036 0.072 I 150 23.2 60 richcluster 3
Referencesfortheenvironmentalclassification:(1)Milleretal.(2002);(2)deVaucoleurs(1991);(3)Trageretal.(2000).
4 D. Guidettiet al.
Table2.X-rayandradioequipartitionparametersforallthesources.Col.1:sourcename;Col.2:X-rayenergyband;Col.3:averagethermaltemperature;
Cols.4,5,6and7,8,9best-fittingcoreradii,centraldensitiesandβparametersfortheouterandinnerβmodels,respectively;Col.10:averagethermalpressure
atthemidpointoftheradiolobes;Cols.11&12:minimumsynchrotronpressureandcorrespondingmagneticfield;Col.13:referencesfortheX-raymodels.
source band kT rcxout n0out βout rcxin n0in βin P0 Pmin BPmin ref.
[keV] [keV] [kpc] [cm−3] [kpc] [cm−3] [dynecm−2] [dynecm−2] µG
0206+35 0.2-2.5 1.3+1.3 22.2 2.4×10−3 0.35 0.85 0.42 0.70 9.6×10−12 4.31×10−13 5.70 1,2
−0.3
3C353 ” 4.33+0.25 1.66×10−12 11.2 3
−0.24
3C270 0.3-7.0 1.45+0.23 36.8 7.7×10−3 0.30 1.1 0.34 0.64 5.75×10−12 1.64×10−13 3.71 4
−0.01
M84 0.6-7.0 0.6+0.05 5.28±0.08 0.42 1.40±0.03 1.70×10−11 1.07×10−12 9.00 5
−0.05
References:(1)Worrall&Birkinshaw(2000);(2)Worrall,Birkinshaw&Hardcastle(2001);(3)Iwasawaetal.(2000);(4)Crostonetal.(2008);(5)(Finoguenov&Jones 2001).
radioemissionshowsacore,withsmoothtwo-sidedjetsalignedin matefortheinclinationofthejetsis≈90◦(Swain,Bridle&Baum
theNW-SEdirection and surrounded by adiffuseand symmetric 1998).Theeasternjetisslightlybrighterandendsinawell-defined
halo. Laing&Bridle (2011b) have estimated that the jets are hot spot. The radio lobes have markedly different morphologies:
inclined by ≈40◦ withrespect tothelineof sight, withthemain theeasternlobeisroundwithsharpedges,whilethewesternlobeis
(approaching)jetintheNWdirection. elongatedwithanirregularshape.Thelocationofthesourcewithin
0206+35 has been observed with both the ROSAT theclusterisofparticularinterestforthisworkandmightaccount
PSPC and HRI instruments (Worrall&Birkinshaw for the different shapes of the lobes. Fig.1(d) shows the XMM-
1994, 2000; Trussonietal. 1997) and with Chandra Newton image overlaid on the radio contours. The image shows
(Worrall,Birkinshaw&Hardcastle 2001). The X-ray emission onlytheNWpartofthecluster,butitisclearthattheradiosource
consistsofacompactsourcesurroundedbyagalacticatmosphere liesontheedgeoftheX-rayemittinggasdistribution.sothatthe
which merges into the much more extended intra-group gas. The roundeasternlobeisencounteringahigherexternaldensityandis
radius of the extended halo observed by the ROSAT PSPC is probablyalsobehindalargercolumnofFaraday-rotatingmaterial
≈2.5arcmin (Fig. 1a). The ROSAT and ChandraX-ray surface (Iwasawaetal.2000,Goodgeretal.2008).Inparticular,theimage
brightnessprofilesarewellfitbythecombinationofβmodelswith publishedbyGoodgeretal.(2008)showsthatthegasdensitygra-
two different core radii and a power-law component (Hardcastle, dientpersistsonlargerscales.
privatecommunication;Table2).
2.2 3C270
2.4 M84
3C270isaradiosourceclassifiedasFRIinmostoftheliterature,
M84 is a giant elliptical galaxy located in the Virgo Cluster at
althoughinfact,thetwolobeshavedifferentFRclassificationsat
about400kpcfromthecore.Opticalemission-lineimagingshows
lowresolution(Laing,Guidetti&Bridle2011).Theopticalcoun-
adiskofionizedgasaroundthenucleus,withamaximumdetected
terpartisthegiantellipticalgalaxyNGC4261,locatedatthecentre extent of 20×7arcsec2 (Hansen,Norgaard-Nielsen&Jorgensen
of a nearby group. The radio source has a symmetrical structure
1985;Baumetal.1988;Boweretal.1997,2000).Theradioemis-
with a bright core and twin jets, extending E-W and completely
sionofM84(3C272.1)hasanangularextensionofabout3arcmin
surroundedbylobes.Thelowjet/counter-jetratioindicatesthatthe
(≃ 11kpc) and shows an unresolved core in the nucleus of the
jets are close to the plane of the sky, with the Western side ap-
galaxy,tworesolvedjetsandapairofwidelobes(Laing&Bridle
proaching(Laing,Guidetti&Bridle2011).
1987;Laingetal.2011).Theinclinationtotheline-of-sightofthe
The XMM-Newton image (Fig.1c) shows a disturbed dis- innerjetaxisis∼60◦,withthenorthernjetapproaching,butthere
tribution with regions of low surface-brightness (cavities) at
is a noticeable bend in the counter-jet very close to the nucleus,
the positions of both radio lobes. A recent Chandra ob-
which complicates modelling (Laing&Bridle 2011b). After this
servation (Worralletal. 2010) shows “wedges” of low X-
bend, the jets remain straight for ≈40arcsec, then both of them
ray surface brightness surrounding the inner jets (see also bend eastwards by ∼90◦ and fade into the radio emission of the
Croston,Hardcastle&Birkinshaw 2005, Finoguenovetal. 2006,
lobes.
Jethaetal.2007,Crostonetal.2008).Theoverall surface bright-
ThemorphologyoftheX-rayemissionhasaH-shapemadeup
ness profile is accurately reproduced by a point source con-
of shells of compressed gas surrounding cavities coincident with
volved with the Chandra point spread function plus a double
both the radio lobes (Finoguenovetal. 2008; Finoguenovetal.
β model (Crostonetal. 2008, projb model). Crostonetal. 2008
2006; Finoguenov&Jones 2001). This shape, together with the
found no evidence for a temperature gradient in thehot gas. The
fact that the initial bending of the radio jets has the same direc-
group is characterized by high temperature and low luminosity
tionandisquitesymmetrical,suggestsacombinationofinteraction
(Finoguenovetal.2006),whichtakentogetherprovideaveryhigh
withtheradioplasmaandmotionofthegalaxywithinthecluster
levelofentropy. Thismightbeafurthersignofalargedegreeof
(Finoguenov&Jones 2001).TheratiobetweentheX-raysurface
impactoftheAGNontheenvironment.
brightnessoftheshellsofthecompressedgasandtheirsurround-
ingsis≈3andisalmostconstantaroundthesource.Theshellsare
regionsofenhancedpressureanddensityandlowentropy:theam-
2.3 3C353
plitudeofthedensityenhancements(afactorof≈3)suggeststhat
3C353isanextendedFRIIradiosourceidentifiedwithaD-galaxy theyareproducedbyweakshockwaves(MachnumberM∼1.3)
embedded at theperipheryof aclusterof galaxies.Thebest esti- drivenbytheexpandinglobes(Finoguenovetal.2006).
Faradayrotationmeasurebandsacrossradiogalaxies 5
Figure2.RMimagesforallsources:(a)0206+35;(b)M84;(c)3C270;(d)3C353.Theangularresolutionandthelinearscaleofeachmapareshowninthe
individualpanels.
3 ANALYSISOFRMANDDEPOLARIZATIONIMAGES Sincek ∝ |∇RM|2,Eq.3clearlyillustratesthathigherRMgra-
dientsacrossthebeamgeneratehigherkvaluesandinturnhigher
Forafully-resolvedforegroundFaradayscreen,theλ2 relationof
depolarization.
Eq.2holdsexactlyandthereisnochangeofdegreeofpolarization,
p, with wavelength. Even in the presence of a small gradient of Our observational analysis is based on the following proce-
RMacrossthebeam,λ2rotationisobservedoverawiderangeof dure.WefirstproducedRMandBurnlawkimagesattwodiffer-
polarization angle. In this case, the emission tends to depolarize ent angular resolutions for each source and searched for regions
withincreasingwavelength,followingtheBurnlaw(Burn1966): withhighk orcorrelatedRMandk values, whichcouldindicate
p(λ)=p(0)exp(−kλ4), (3) thepresenceofinternalFaradayrotationand/orstrongRMgradi-
entsacrossthebeam.Inregionswithlowkwherethevariationsof
where p(0) is the intrinsic value of the degree of polarization RMareplausiblyisotropicandrandom,wethenusedthestructure
andk=2|∇RM|2σ2,withFWHM = 2σ(2ln2)1/2 (Burn1966; function(definedinEq.4)toderivethepowerspectrumoftheRM
Tribble1991;Laingetal.2008). fluctuations.Finally,toinvestigatethedepolarizationintheareasof
6 D. Guidettiet al.
Figure3.BurnlawkimagesforallsourcesatthesameangularresolutionsasfortheRMimages:(a)0206+35at1.2arcsecFWHM;(b)M84at4.5arcsec
FWHM;(c)3C270at5arcsecFWHM;(d)3C353at1.3arcsecFWHM.Thecorrespondingintegrateddepolarization(DP;Section5)isindicatedonthetop
rightangleofeachpanel.Thecolourscaleisthesameforalldisplays.
isotropicRM,andhencethemagneticfieldpoweronsmallscales, WeassumeRMpowerspectraoftheform:
wemadenumericalsimulationsoftheBurnlawkusingthemodel
Cˆ(f ) = C f−q f ≤f
powerspectrumwithdifferentminimumscalesandcomparedthe ⊥ 0 ⊥ ⊥ max
resultswiththedata. = 0 f⊥ >fmax
Thestructurefunctionisdefinedby
wheref isascalar spatialfrequency andfittheobserved struc-
⊥
turefunction(includingtheeffectoftheobservingbeam)usingthe
S(r⊥)=<[RM(r⊥+r′⊥)−RM(r′⊥)]2 > (4) Hankel-transform method described by Laingetal. (2008) to de-
rivetheamplitude,C andtheslope,q.ToconstraintheRMstruc-
0
(Simonetti,Cordes&Spangler 1984; Minter&Spangler 1996) tureonscalessmallerthanthebeamwidth,weestimatedthemini-
wherer andr′ arevectorsintheplaneoftheskyandhiisan mumscaleofthebestfittedfieldpowerspectrum,Λ =1/f ,
⊥ ⊥ min max
averageoverr′ . whichpredictsameanvalueofkconsistentwiththeobservedone.
⊥
Faradayrotationmeasurebandsacrossradiogalaxies 7
quencytoderivetheresidualsathighresolution.Then,wefitthe
Table3.Frequencies,bandwidthsandangularresolutionsusedintheRM
andBurnlawkimagesdiscussedinSects.4and5,respectively. residualswithoutallowinganynπambiguitiesandaddedtheresult-
ingRM’stothevaluesdeterminedatlowresolution.Thisprocedure
source ν ∆ν beam allowedustoobtainanRMmapof0206+35freeofsignificantde-
[MHz] [MHz] [arcsec] viationsfromλ2 rotationand fullyconsistent withthe1.2-arcsec
measurements.
0206+35 1385.1 25 1.2
Wehaveverifiedthatthepolarizationanglesaccuratelyfollow
1464.9 25
therelation∆Ψ ∝ λ2overthefullrangeofpositionangleessen-
4885.1 50
tiallyeverywhereexceptforsmallareasaroundtheoptically-thick
3C353 1385.0 12.5 1.3
1665.0 12.5 cores:representativeplotsofΨagainstλ2for0206+35areshown
4866.3 12.5 inFig.4.Thelackofdeviationsfromλ2rotationinalloftheradio
8439.9 12.5 galaxies is fully consistent with our assumption that the Faraday
3C270 1365.0 25 1.65 rotatingmediumismostlyexternaltothesources.
1412.0 12.5 TheRMmapsareshown inFig.2. Thetypical rmserror on
4860.1 100 thefit is≈2radm−2. Nocorrection for theGalacticcontribution
1365.0 25 5.0
hasbeenapplied.
1412.0 12.5
All of the RM maps show two-dimensional patterns, RM
1646.0 25
bands, acrossthelobeswithcharacteristicwidthsrangingfrom3
4860.1 100
to12kpc.Multiplebandsparalleltoeachotherareobservedinthe
M84 1413.0 25 1.65
4885.1 50 westernlobeof0206+35,theeasternlobeof3C353andthesouth-
1385.1 50 4.5 ernlobeofM84.
1413.0 25 Inallcases,theiso-RMcontoursarestraightandperpendicu-
1464.9 50 lartothemajoraxesofthelobestoaverygoodapproximation:the
4885.1 50 very straight and well-defined bands in the eastern lobes of both
0206+35 (Fig.2a) and 3C353 (Fig.2d) are particularly striking.
TheentireareaofM84appearstobecoveredbyabandedstructure,
Inthispaper,weareprimarilyinterestedinestimatingtheRM whileinthecentralpartsof0206+35and3C270andthewestern
powerspectrumoverlimitedareas,andwemadenoattempttode- lobe of 3C353, regions of isotropic and random RM fluctuations
terminetheouterscaleoffluctuations. arealsopresent.
Theuseofthestructurefunctiontogether withtheBurnlaw WealsoderivedprofilesofhRMialongtheradioaxisofeach
k represents a powerful technique to investigate the RM power source, averaging over boxes a few beamwidths long (parallel to
spectrum over a wide range of spatial scales (Laingetal. 2008; the axes), but extended perpendicular to them to cover the entire
Guidettietal.2010).Thetwoquantitiesarecomplementary,inthat width of the source. The boxes are all large enough to contain
thestructurefunctionallowsustodeterminethepowerspectrumof many independent points. The profiles are shown in Fig.5. For
thefluctuationsonscaleslargerthanthebeamwidth,whiletheBurn each radio galaxy, we also plot an estimate of the Galactic con-
lawkconstrainsfluctuationsofRMbelowtheresolutionlimit. tributiontotheRMderivedfromaweightedmeanoftheintegrated
RM’s for non-cluster radio sources within a surrounding area of
10deg2 (Simard-Normandinetal. 1981). In all cases, both posi-
tiveandnegativefluctuationswithrespecttotheGalacticvalueare
4 ROTATIONMEASUREIMAGES
present.
The RM images and associated rms errors were produced by In 0206+35 (Fig.2a), the largest-amplitude bands are in the
weighted least-squares fitting to the observed polarization angles outerpartsofthelobes,withapossiblelow-levelbandjusttothe
Ψ(λ)asafunctionofλ2 (Eq.1)atthreeorfourfrequencies(Ta- NWofthecore.Themostprominentband(withthemostnegative
ble3,seealsoLaingetal.2011andLaing,Guidetti&Bridle2011) RMvalues)isintheeastern(receding)lobe,about15kpcfromthe
usingtheRMtaskintheAIPSpackage. core (Fig.5a). Its amplitude with respect to the Galactic value is
Each RM map was calculated only at pixels with rms about40radm−2.Thisbandmustbeassociatedwithastrongor-
polarization-angle uncertainties <10◦ at all frequencies. We re- deredmagneticfieldcomponentalongthelineofsight.Ifcorrected
feronlytothelower-resolutionRMandk imagesfor3C270and fortheGalacticcontribution,thetwoadjacentbandsintheeastern
M84(Table3),asthey show moreof thefaint, extended regions lobewouldhaveRMwithoppositesignsandthefieldcomponent
ofthesesourcesandarefullyconsistentwiththehigher-resolution alongthelineofsightmustthereforereverse.
versions.TheRMimageofM84isconsistentwiththatshownby M84 (Fig.2b) displays an ordered RM pattern across the
Laing&Bridle(1987),butisderivedfromfour-frequencydataand whole source, with two wide bands of opposite sign having the
hasahighersignal-to-noiseratio. highestabsoluteRMvalues.Thereisalsoanabruptchangeofsign
In the fainter regions of 0206+35 (for which only three fre- acrosstheradiocore(seealsoLaing&Bridle1987).Thenegative
quencies are available and the signal-to-noise ratio is relatively bandinthenorthernlobe(associatedwiththeapproachingjet)has
low), the RM task occasionally failedto determine the nπ ambi- alargeramplitudewithrespecttotheGalacticvaluethanthecor-
guitiesinpositionanglecorrectly.Inordertoremovetheseanoma- responding(positive)featureinthesouthernlobe(Fig.5c).
lies,wefirstproducedalower-resolution,buthighsignal-to-noise 3C270(Fig.2c)showstwolargebands:oneonthefrontend
RMimagebyconvolvingthe1.2arcsecRMmaptoabeamwidthof of the eastern lobe, the other in the middle of the western lobe.
5arcsecFWHM.Fromthismapwederivedthepolarization-angle The bands have opposite signs and contain the extreme positive
rotationsateachofthethreefrequenciesandsubtractedthemfrom andnegativevaluesoftheobservedRM.Thepeakpositivevalueis
the observed 1.2arcsec polarization angle maps at the same fre- withintheeasternbandattheextremeendofthelobe(Fig.5e).
8 D. Guidettiet al.
The RM structure of 3C353 (Fig.2d) is highly asymmetric. thesouthernjet(Fig.3b).Thereisnocorrespondingfeatureinthe
The eastern lobe shows a strong pattern, made up of four bands, RMimage(Fig.2b).Thedepolarizationislikelytobeassociated
withverystraightiso-RMcontourswhicharealmostexactlyper- with one of the shells of compressed gas visible in the Chandra
pendiculartothesourceaxis.Asin0206+35,adjacentbandshave image(Fig.1b),implyingsignificantmagnetizationwithinhomo-
RMwithopposite signsoncecorrectedfortheGalacticcontribu- geneousfieldand/ordensitystructureonscalesmuchsmallerthan
tion(Fig.5g).Incontrast,theRMdistributioninthewesternlobe thebeamwidth,apparentlyindependentofthelarger-scalefieldre-
showsnosignofanybandedstructure,andisconsistentwithran- sponsiblefortheRMbands.Thispictureissupportedbythegood
domfluctuationssuperimposedonanalmostlinearprofile.Itseems spatialcoincidenceofthehighkregionwithashellofcompressed
verylikelythatthedifferencesinRMmorphologyandaxialratio gas,asillustratedintheoverlayofthe4.5arcsecBurnlawkimage
arebothrelatedtotheexternaldensitygradient(Fig.1d). onthecontoursoftheChandradata(Fig.6(a)).Coolergasassoci-
In Table 4 the relevant geometrical features (size, distance atedwiththeemission-linediskmightalsoberesponsible,butthere
fromtheradiocore,hRMi)fortheRMbandsarelisted. isnoevidenceforspatialcoincidencebetweenenhanced depolar-
izationand Hαemission(Hansen,Norgaard-Nielsen&Jorgensen
1985). Despite the complex morphology of the X-ray emission
around M84, its k profile is very symmetrical, with the highest
5 DEPOLARIZATION
valuesatthecentre(Fig.5(d)).
In this section, we use “depolarization” in its conventional sense 3C270 also shows areas of very strong depolarization
tomean“decreaseofdegreeofpolarizationwithincreasingwave- (k ∼550rad2m−4,correspondingtoDP=0.35)closetothecore
length” and define DP = p /p . Using the Faraday and surrounding the inner and northern parts of both the radio
1.4GHz 4.9GHz
code (Murgiaetal. 2004), we produced images of Burn law k lobes.AsforM84,theareasofhighk arecoincidentwithridges
by weighted least-squares fitting to lnp(λ) as a function of λ4 intheX-rayemissionwhichformtheboundariesofthecavitysur-
(Eq.3). Onlydatawithsignal-to-noise ratio>4inP ateach fre- roundingthelobes(Fig.6(b)).TheinnerpartsofthisX-raystruc-
quencywereincludedinthefits.TheBurnlawkimageswerepro- ture are described in more detail by Worralletal. (2010), whose
duced with the same angular resolutions as the RM images. The recenthigh-resolutionChandraimageclearlyreveals“wedges”of
1.65arcsec resolution Burn law k maps for M84 and 3C270 are low brightness surrounding the radio jets. As in M84, the most
consistentwiththelow-resolutionones,butaddnoadditionaldetail likely explanation is that a shell of denser gas immediately sur-
andarequitenoisy.Thiscouldleadtosignificantlybiasedestimates roundingtheradiolobesismagnetized,withsignificantfluctuations
forthemeanvaluesofkoverlargeareas(Laingetal.2008).There- of field strength and density on scales smaller than our 5-arcsec
fore,asfortheRMmaps,weusedonlytheBurnlawkimagesat beam, uncorrelated with the RM bands. The k profile of 3C270
lowresolutionforthesetwosources. (Fig.5(f))isvery symmetrical, suggesting that the magnetic-field
TheBurnlawkmapsareshowninFig.3.Allofthesources anddensitydistributionsarealsosymmetricalandconsistentwith
showlowaveragevaluesofk(i.e.slightdepolarization),suggest- anorientationclosetotheplaneofthesky.Thelargestvaluesofk
ing littleRM power on small scales. Withthe possible exception areobservedinthecentre,coincidentwiththefeaturesnotedear-
of the narrow filaments of high k in the eastern lobe of 3C353 lierandwiththebulkoftheX-rayemission(thehighk valuesin
(which might result from partially resolved RM gradients at the thetwooutermostbinshavelowsignal-to-noiseandarenotsignif-
band edges), none of the images show any obvious structure re- icant).
latedtotheRMbands.Foreachsource,wehavealsocomparedthe In the Burn law k image of 3C353, there is evidence for a
RMandBurnlawkvaluesderivedbyaveragingovermanysmall straightandknottyregionofhighdepolarization≈20kpclongand
boxes covering theemission, and we findno correlationbetween extending westwards from the core. This region does not appear
them. toberelatedeithertothejetsortoanyother radiofeature.Asin
Wealsoderivedprofilesofk(Fig.5b,d,fandh)withthesame M84and3C270,theRMappearsquitesmoothovertheareashow-
setsofboxesasfortheRMprofilesinthesameFigure.Thesecon- inghighdepolarization,againsuggestingthattherearetwoscales
firmthatthevaluesofkmeasuredinthecentresoftheRMbands ofstructure,onemuchsmallerthanthebeam,butproducingzero
arealwayslow,butthatthereislittleevidenceforanydetailedcor- meanRMandtheotherverywellresolved.In3C353,thereisas
relation. yetnoevidenceforhotorcoolionizedgasassociatedwiththeen-
The signal-to-noise ratiofor 0206+35 isrelativelylow com- hanceddepolarization(contaminationfromtheverybrightnuclear
paredwiththatoftheotherthreesources, particularlyat4.9GHz X-rayemissionaffectsanareaof1arcminradiusaroundthecore;
(we need to use a small beam to resolve the bands), and this is Iwasawaetal.2000,Goodgeretal.2008).
reflectedinthehighproportionofblankedpixelsonthek image. Thekprofileof3C353(Fig.5(h))showsamarkedasymme-
Themostobviousfeatureofthisimage(Fig.3a),anapparentdiffer- try,withmuchhighervaluesintheEast.Thisisinthesamesenseas
enceinmeankbetweenthehigh-brightnessjets(lessdepolarized) thedifferenceofRMfluctuationamplitudes(Fig.5(g))andisalso
andthesurroundingemission,islikelytobeanartefactcausedby consistentwiththeeasternlobebeingembeddedinhigher-density
our blanking strategy: pointswhere thepolarized signal islow at gas.Therelativelyhighvaluesofkwithin20kpcofthenucleusin
4.9GHz are blanked preferentially, so the remainder show artifi- theWesternlobearedueprimarilytothediscreteregionidentified
ciallyhighpolarizationatthisfrequency.Forthesamereason,the earlier.
apparentminimuminkatthecentreofthedeep,negativeRMband
(Fig.5aandb)isprobablynotsignificant.Theaveragedvaluesof
kfor0206+35arealreadyverylow,however,andarelikelytobe
6 ROTATIONMEASURESTRUCTUREFUNCTIONS
slightlyoverestimated,soresidualRMfluctuationsonscalesbelow
the1.2-arcsecbeamwidthmustbeverysmall. We calculated RM structure function for discrete regions of the
M84 shows onelocalised areaof verystrong depolarization sourceswheretheRMfluctuationsappeartobeisotropicandran-
(k ∼500rad2m−4, corresponding to DP = 0.38) at the base of domandforwhichweexpectthespatialvariationsofforeground
Faradayrotationmeasurebandsacrossradiogalaxies 9
Table4.PropertiesoftheRMbands:Col.1sourcename;Cols.2&3:overallhRMiandσRM;Col.4:GalactichRMi;Col.5:hRMiforeachband;Col.
6:distanceofthebandmidpointfromtheradiocore(positivedistancesareinthewesterndirectionforallsources,exceptforM84,wheretheyareinthe
northerndirection);Col.7:widthoftheband;Col.8:maximumbandamplitude.
source hRMi σRM RMG bandhRMi dc width A
[radm−2] [radm−2] [kpc] [kpc] [radm−2]
0206+35(4C35.03) −77 23 −72
−140 -15 10 40
−60 -27 4
34 22 6
51 8 4
3C353 −56 24 −69
122 -12 5 50
102 -19 4
-40 -23 4
100 -26 4
3C270 14 10 12
−8 20 12 10
32 37 11
M84 −2 15 2
−27 1 3 10
22 -6 6
thermalgasdensity,rmsmagneticfieldstrengthandpathlengthto effectsoflarge-scalevariationsinpathlengthorfieldstrength(cf.
bereasonablysmall.Theseare:theinner26arcsecofthereceding Guidettietal.2010).
(Eastern)lobeof0206+35,theinner100arcsecof3C270andthe InordertoconstrainRMstructureonspatialscalesbelowthe
inner 40arcsec of thewesternlobeof 3C353. Theselectedareas beamwidth, we estimated the depolarization as described in Sec-
of0206+35and3C270arebothwithinthecoreradiiofthelarger- tion3.ThefittedkvaluesarelistedinTable5.Westressthatthese
scalebetamodelsthatdescribethegroup-scaleX-rayemissionand values refer only to areas with isotropic fluctuations, and cannot
thegalaxy-scalecomponentsaretoosmalltoaffecttheRMstatis- usefullybecomparedwiththeintegrateddepolarizationsquotedin
ticssignificantly(Table2).In3C353,theselectedareawaschosen inFig.2.
to be small compared with the scale of X-ray variations seen in For M84, using the Burn law k analysis and assuming that
Fig.1(d).Inallthreecases,theforegroundfluctuationsshouldbe variation of Faraday rotation across the 1.65-arcsec beam causes
fairlyhomogeneous. TherearenosuitableregionsinM84,which theresidualdepolarization,wefindthatΛ <0.1kpcforanyrea-
min∼
isentirelycoveredbythebandedRMpattern. sonableRMpowerspectrum.
The structure functions, corrected for uncorrelated random
noisebysubtracting2σ2 (Simonettietal.1984),areshownin
noise
Fig.7.Alloftheobservedstructurefunctionscorrespondtopower 7 ROTATION-MEASUREBANDSFROMCOMPRESSION
spectra of approximately power-law form over all or most of the
It is clear from the fact that the observed RM bands are perpen-
rangeofspatialfrequencieswesample.Weinitiallyassumedthat
dicular to the lobe axes that they must be associated with an in-
thepowerspectrumwasdescribedbyEq.5withnohigh-frequency
teraction between an expanding radio source and the gas imme-
cut-off (f → ∞) and made least-squares fitsto the structure
max diatelysurrounding it.Oneinevitablemechanismisenhancement
functions,weightedbyerrorsderivedfrommultiplerealizationsof
offieldanddensitybytheshockorcompressionwavesurrounding
thepowerspectrumontheobservinggrid,asdescribedindetailby
thesource.2TheimplicationofthepresenceofcavitiesintheX-ray
Laingetal.(2008)andGuidettietal.(2010).
gasdistributioncoincidentwiththeradiolobesisthatthesources
Thebest-fittingslopesq andamplitudesC aregiveninTa- areinteractingstronglywiththethermalgas,displacingratherthan
0
ble5. All of the fitted power spectra are quite flat and have low mixing withit (seeMcNamara&Nulsen 2007 for areview). For
amplitudes,implyingthatthereislittlepowerintheisotropicand the sources in the present paper, the X-ray observations of M84
randomcomponentofrotationmeasure.Indeed,theamplitudesof (Finoguenovetal. 2008,Fig.1b)and3C270(Crostonetal.2008,
thelargest-scaleRMfluctuationssampledinthisanalysisisafew Fig.1c)showcavitiesandarcsofenhancedbrightness,correspond-
timeslessthanthatofthebands(seeTables4and5).Thissuggests ing to shells of compressed gas bounded by weak shocks. The
thatthefieldresponsibleforthebandsisstrongeraswellasmore strengthofanypre-existingfieldintheIGM,whichwillbefrozen
orderedthanthatresponsiblefortheisotropicfluctuations. intothegas,willalsobeenhanced intheshells.Wethereforeex-
pectasignificantenhancementinRM.Amoreextremeexampleof
The structure functions for 0206+35 and 3C353 rise mono- thiseffectwilloccuriftheexpansionoftheradiosourceishighly
tonically, indicating that the outer scale for the random fluctua- supersonic,inwhichcasetherewillbeastrongbow-shockaheadof
tions must be larger than the maximum separations we sample.
For 3C270, the structure function levels out at r ≈ 100arcsec
⊥
(15kpc; Fig. 7d). This could be the outer scale of the field fluc- 2 Analternativemechanismisthegenerationofnon-linearsurfacewaves
tuations, but a better understanding of the geometry and external (Bicknell,Cameron&Gingold 1990).Itisunlikely thatthis canproduce
densitydistributionwouldbeneededbeforewecouldruleoutthe large-scalebands,forthereasonsgiveninSection9.5.
10 D. Guidettiet al.
Table5.Powerspectrumparametersfortheindividualsub-regions.Col.1:sourcename;Col.2:angularresolution;Col.3:slopeq:Col.4:amplitudeC0;
Col.5:minimumscale;Col.6:amplitudeofthelargescaleisotropiccomponent;Col.7:observedmeank;Col.8:predictedmeank.Thepowerspectrumhas
notbeencomputedforM84(seeSection6).
Source FWHM q logC0 Λmin Aiso kobs ksyn
[arcsec] [kpc] [radm−2] [rad2m−4] [rad2m−4]
0206+35 1.2 2.1 0.77 2 10 37 40
3C270 1.65 2.7 0.90 0.3 5 30 26
5.0 2.7 0.90 0.3 5 71 64
3C353 1.3 3.1 0.99 0.1 10 38 33
M84 1.65 <0.1 25
4.5 <0.1 43
0206+35
Figure4.PlotsofE-vectorpositionangleΨagainstλ2atrepresentativepointsofthe1.2arcsecRMmapof0206+35.FitstotherelationΨ(λ)=Ψ0+RMλ2
areshown.ThevaluesofRMaregivenintheindividualpanels.
thelobe,behindwhichboththedensityandthefieldbecomemuch lackof detection of strong shocks in theX-raydatafor the other
higher.Regardlessofthestrengthoftheshock,thefieldismodified sources.
sothatonlythecomponent intheplaneoftheshockisamplified
Inthissection,weinvestigatehowtheRMcouldbeaffected
andthepost-shockfieldtendsbecomeorderedparalleltotheshock
bycompression.Weconsideradeliberatelyoversimplifiedpicture
surface.
in which the radio source expands into an IGM with an initially
uniform magnetic field, B. This is the most favourable situation
Theevidencesofarsuggeststhatshocksaroundradiosources
forthegenerationoflarge-scale,anisotropicRMstructures:inre-
of both FR classes are generally weak (e.g. Formanetal. 2005,
ality,thepre-existingfieldislikelytobehighlydisordered,oreven
Wilsonetal.2006,Nulsenetal.2005).Thereareonlytwoexam-
isotropic,becauseofturbulenceinthethermalgas.Westressthat
ples inwhich highly supersonic expansion has been inferred: the
wehavenottriedtogenerateaself-consistentmodelforthemag-
southern lobe of CentaurusA (M ≈ 8; Kraftetal. 2003) and
neticfieldandthermaldensity,butrathertoillustratethegeneric
NGC3801(M≈4;Crostonetal.2007).Thereisnoevidencethat
effectsofcompressionontheRMstructure.
the sources described in the present paper are significantly over-
pressured compared with the surrounding IGM (indeed, the syn- Inthismodeltheradiolobeisanellipsoidwithitsmajoraxis
chrotronminimumpressure issystematicallylowerthanthether- alongthejetandissurroundedbyasphericalshellofcompressed
malpressureoftheIGM;Table 2).Thesidewaysexpansionofthe material.Thisshelliscentredatthemid-pointofthelobe(Fig.8)
lobesisthereforeunlikelytobehighlysupersonic.TheshockMach and has a stand-off distance equal to 1/3 of the lobe semi-major
numberestimatedforallthesourcesfromrampressurebalancein axis at the leading edge (the radius of the spherical compression
theforwarddirectionisalso≈1.3.Thisestimateisconsistentwith isthereforeequalto4/3ofthelobesemi-majoraxis).Inthecom-
thatforM84madebyFinoguenovetal.(2006)andalsowiththe pressedregion,thethermaldensityandthemagneticfieldcompo-