Radio polarization and magnetic field structure in M 101

1.8 MB·

by  E. M. Berkhuijsen

Astronomy&Astrophysicsmanuscriptno.m101.paper.v210116 cESO2016
(cid:13)
January26,2016
⋆
Radio polarization and magnetic field structure in M101
E.M.Berkhuijsen1,M.Urbanik2,R.Beck1,andJ.L.Han3
1 Max-Planck-InstitutfürRadioastronomie,AufdemHügel69,53121Bonn,Germany
e-mail:[email protected]
2 AstronomicalObservatory,JagiellonianUniversity,ul.Orla171,30-244Kraków,Poland
3 NationalAstronomicalObservatories,ChineseAcademyofSciences,A20DatunRoad,Beijing100012,China
Received7September2015/Accepted4January2016
6
1
0 ABSTRACT
2
WeobservedtotalandpolarizedradiocontinuumemissionfromthespiralgalaxyM101atλλ6.2cmand11.1cmwiththeEffelsberg
n
telescope.Theangularresolutionsare2.5(=5.4kpc)and4.4(=9.5kpc),respectively.Weusethesedatatostudyvariousemission
′ ′
a
componentsinM101andpropertiesofthemagneticfield.Separationofthermalandnon-thermalemissionshowsthatthethermal
J
emissioniscloselycorrelatedwiththespiralarms,whilethenon-thermalemissionismoresmoothlydistributedindicatingdiffusion

2 ofcosmicrayelectronsawayfromtheirplacesoforigin.TheradialdistributionofbothemissionshasabreaknearR=16kpc(=7.4),
′
2 whereitsteepenstoanexponentialscalelengthofL 5kpc,whichisabout2.5timessmallerthanatR < 16kpc.Thedistribution
ofthepolarizedemissionhasabroadmaximumnearR≃=12kpcandbeyondR=16kpcalsodecreaseswithL 5kpc.Itseemsthat

] nearR=16kpcamajorchangeinthestructureofM101takesplace,whichalsoaffectsthedistributionsofthes≃trengthoftherandom
A
andorderedmagneticfield.BeyondR=16kpctheradialscalelengthofbothfieldsisabout20kpc,whichimpliesthattheydecrease
G toabout 0.3µG at R= 70kpc, which isthelargest optical extent. Theequipartition strength of thetotal fieldranges fromnearly
10µGatR< 2kpcto4µGatR = 22 24kpc.AstherandomfielddominatesinM101(B /B 2.4),wavelength-independent
h. polarizationisthemainpolarizationm−echanism.WeshowthatenergeticeventscausingHirsanhellosrdof≃meandiameter<625pccould
p partly be responsible for this. At radii < 24kpc, the random magnetic field depends on the star formation rate/area, Σ , witha
SFR
- power-lawexponentofb = 0.28 0.02.Theorderedmagneticfieldisgenerallyalignedwiththespiralarmswithpitchanglesthat
o areabout8 largerthanthoseofH±ifilaments.
r ◦
t
s Key words. Galaxies: individual: M101 – galaxies: magnetic fields– galaxies: star formation – polarization - radio continuum:
a galaxies–radiationmechanisms:non-thermal
[

1
v1. Introduction (FUV)(Walleretal.1997),X-rays(Kuntzetal.2003),andmid-
1 infrared(mid-IR)(Jarrettetal.2013).Thesemapsshowacom-
7The Pinwheel galaxy, M101 (NGC5457) is a nearby spi- plicatedstructureofmanynarrow,patchyspiralarmswithlarge
1ral galaxy seen nearly face-on (see Table 1). It is an variationsinpitchangle.Themanylineararmsegmentsandthe
6SAB(rs)cdgalaxy(deVaucouleursetal.1976)containingmany
asymmetry of the large-scale structure are attributed to a col-
0Hii regions and several large Hii complexes. Sensitive opti-
lision with the satellite galaxy NGC5474 (Walleretal. 1997;
.cal imaging of Mihosetal. (2013) showed that in blue light
1 Kamphuis 1993; Mihosetal. 2012). Kenneyetal. (1991) de-
0the bright parts of M101 have a radius of about 8′on the tected a bar in the centre in CO, which is also seen in Hα
6sky (R25 = 8′), but that a weak optical disk can be traced and near-infrared (NIR), but density waves are weak in M101
1about three times further out (R = 25). However, the
29.5 ′ (Kamphuis1993).
:galaxy is strongly lopsided, which may be due to past en-
v Little isknownaboutthemagneticfieldin M101.Thefirst
counters with one or more of the six companions forming the
i radiocontiunummapswerepresentedbyIsraeletal.(1975)who
XM101 group (e.g. Karachentsev&Kudrya 2014; Mihosetal.
used aperture synthesis at wavelengthsλλ49.2, 21.2, and 6cm
ar2M01130;1Jhoags&beCeonmtbheess2u0b0je9c;tWofalmleraneytaol.p1ti9c9al7)s.tuTdhieesd.isWtaencheavtoe showing enhanced emission from spiral arms and Hii-region
complexes. Gräveetal. (1990) carried out a multi-wavelength
adoptedtheCepheiddistanceof D = 7.4 0.6Mpcderivedby
± study of M101 at λλ11.1, 6.3, 2.8, and 1.2cm with the 100m
Kelsonetal.(1996),whichisingoodagreementwiththecompi-
telescope at Effelsberg, leading to the first spectral index map
lationandnewmeasurementsofLee&Jang(2012).Somebasic
of the galaxy. At λ6.3cm they also obtained the first map of
parametersofM101relevanttoourworkarelistedinTable1.
polarized emission from M101, indicating the existence of an
M101 has been observed at many wavelengths. High-
ordered,large-scalemagneticfieldgenerallyorientedalongspi-
resolution maps have been presented in the emission lines
of atomic hydrogen (Hi) (Kamphuis 1993; Braun 1995; ralarms.However,thesensitivityofthesedatawereinsufficient
forfurtheranalysisofthefieldproperties.
Walteretal. 2008), CO(1-0) (Kenneyetal. 1991; Helferetal.
2003) , and ionized hydrogen (Hα) (Scowenetal. 1992; We observed M101 with the Effelsberg telescope at λλ6.2
Hoopesetal.2001),aswellasoftheemissioninfar-ultraviolet and11.1cmwithimprovedsensitivityintotalpowerandpolar-
ization.Our dataallow a detailedstudyofthe propertiesofthe
⋆ Based on observations with the 100 m telescope of the MPIfR at magnetic field in M101 after separation of the thermal (free-
Effelsberg free) and non-thermal (synchrotron) components of the radio
Articlenumber,page1of14
A&Aproofs:manuscriptno.m101.paper.v210116
Table1.AdoptedparametersonM101
Variable Value Reference
DistanceD(Mpc) 7.4(1 =2.15kpc) Kelsonetal.(1996)
′
Centreposition
(RA,Dec) 14h03m12s.77,54 20 54. 4 Israeletal.(1975)
2000 ◦ ′ ′′
Positionangle PA 38 Kamphuis(1993)
◦
Inclination ia 30 (face-oni=0 ) Kamphuis(1993)
◦ ◦
RadiusincolourB:R 8 Mihosetal.(2013)
25 ′
RadiusincolourB:R 25 Mihosetal.(2013)
29.5 ′
RadiusinHi 27 Kamphuis(1993)
′
Hubbletype SAB(rs)cd deVaucouleursetal.(1976)
Notes. (a) KamphuisderiveddifferentinclinationanglesforradiiR < 7 (27 )andR > 7 (25 inSWand40 inNE).Asourdataextendto
′ ◦ ′ ◦ ◦
R 15,weadoptedameanvalueofi=30 .
′ ◦
∼
continuum emission. In this paper, we study the strength and Table2.Systemparameters
regularityofthe magneticfield,depolarizationeffectsandtheir
origin,theinfluenceofstarformationonthestrengthoftheran- λ11.1cm λ6.2cm
dom field, and the relationship between the orientation of the Feed Singlehorn Dualhorn
orderedfieldandspiralarms. SystemTemperature(K) 45 30
The observations and reduction procedures are described CentreFrequency(GHz) 2.7 4.85
in Sect. 2. In Sect. 3.1 we present the resulting maps and in Bandwidth(MHz) 40 300
Sect. 3.2 we separate thermal/non-thermalemission and derive Half-powerbeamwidth 4.′4 2.′5
radial scale lengths of the various emission components. The σI(mJy/beamarea) 1.20 0.50
discussion in Sect. 4 consists of severalparts. Sect. 4.1 shows σPI (mJy/beamarea) 0.54 0.07
theradialdistributionofthemagneticfieldstrengthsandthede-
pendenceof the randomfield onthe star formationrate (SFR);
respectively.Finally,thePImapwascorrectedforpositivenoise
Sect.4.2discussesFaradayrotationmeasuresanddepolarization
bias(Wardle&Kronberg1974).
effectsinM101;Sect.4.3describesthelarge-scalestructureof
Weobservedthesamefieldatλ6.2cmasatλ11.1cm,using
the ordered magnetic field, the alignment with Hiarms, and a
the dual-horn system. Because the beams of the two horns are
modeltoexplainthealignment.Finally,wesummarizeourcon-
separatedby8.12inazimuth,thegalaxycanonlybescannedin
clusionsinSect.5. ′
azimuth.Withascanspeedof60 perminuteandascansepara-
′
tionin elevationof 1 , onecoveragetookabout51minutes.In
′
all,weobtained20coverages.
2. Observationsanddatareduction
The dual-horn system is less sensitive to interference and
weather changes than the single-horn system because distur-
M101wasobservedatthefrequencies2.7GHz(λ11.1cm)and
bances are largely removed in the difference (i.e. time aligned
4.85GHz (λ6.2cm) with receiver systems in the 100m Effels-
and then subtracted) maps of the two horns. During data pro-
bergtelescope between July and December 1997.At these fre-
cessingwithNOD2,weremovedresidualinterferencefromthe
quencies the half-power beamwidths are 4.4 and 2.5, respec-
′ ′ differenceI,Q,andUmaps,adjustedthebaselevelofeachscan,
tively. The system parameters are listed in Table 2. The point
restoredtheskymapfromthedifferencemapsusingthemethod
sources 3C286 and 3C138 were observed for calibrations of
byEmersonetal.(1979),andtransformedthemapstoequatorial
flux density and polarization angle. We adopted S = 5.8Jy
11 coordinates.Mapsfromallcoverageswerethencombinedtothe
andS = 3.8Jy for3C138,andS = 10.4JyandS = 7.5Jy
6 11 6 finalI,Q,andU mapsusingtheNOD2routineTURBOPLAIT.
for3C286,respectively(Ottetal.1994;Ferninietal.1997).
We reached a noise level of σ = 0.50mJy/beamareafor the I
Weobservedalargefieldof51 51 atλ11.1cmtoenable I
proper base level determination. T′h×e fie′ld was centred on the mapandofσPI = 0.07mJy/beamareaforthe PI map,whichis
nearlythreetimesbetterinIandmorethantentimesbetterinPI
galaxy(seeTable1)andalternatelyscannedinRAandDEC.We
thanwasobtainedbyGräveetal.(1990).Again,thePImapwas
used a single horn,a scan speed of 60 per minute,and a scan
′ correctedforpositivenoisebias(Wardle&Kronberg1974).The
separationof1.5 inDEC(orRA)betweenscans,whichisabout
′ estimatederrorintheabsoluteflux-densityscaleis5percentand
one-third of the beamwidth, as needed for complete sampling
instrumentalpolarizationintheextendedemissionisnegligible.
ofthe emission.We obtained14coverages,halfofwhichwere
scanned in RA and the other half in DEC. Each coveragetook
about40minutes. 3. Results
We carried out the data processing with the NOD2 pack-
3.1.Totalemissionandpolarizedemission
age (Haslam 1974). After removal of strong interference and
adjustment of base levels of individual scans, final maps in The distribution of the total radio emission from M101 at λ
Stokes I, Q, and U were made with the baseline optimiz- 6.2cm (Fig. 1) is asymmetric. The eastern half has a steep
ing procedure described by Emerson&Gräve (1988). After brightness gradient towards the outside, while in the western
combining all coverages, we reached noise levels of σI = half the emission falls off more gradually beyond the west-
1.20mJy/beamareaand σPI = 0.54mJy/beamareafor the maps ern spiral arms. This reflects the optical asymmetry in M101
of totalintensity (I) and polarizedintensity(PI = pQ2+U2), withthewesternarmsextendingtoaconsiderablylargerradius
Articlenumber,page2of14
E.M.Berkhuijsenetal.:PolarizedemissionfromM101
M101 4.85 GHz Effelsberg Total Intensity + B-Vectors HPBW=2.5’ M101 HI + 4.85 GHz Polarized Intensity + B-Vectors HPBW=2.5’
0.5 1.0 1.5 mJy/beam (PI)
54 30
54 30
25
0)
0
20 25
J
Declination ( 20 ation (J2000) 20
n
15 cli
e
D
15
10
10
14 04 30 00 03 30 00 02 30 00
Right ascension (J2000)
Fig.1.TotalemissionandapparentB-vectorsofthepolarizedemission
14 04 30 00 03 30 00 02 30 00
(definedasE-vectorsrotatedby90 )fromM101observedatλ 6.2cm Right Ascension (J2000)
◦
overlaidontheopticalimageofSandage(1961).Thecontourlevelsare
Fig.2. Greyscaleplot of theobserved intensity of polarized emission
1,2,4,8,12,16,and24mJy/beamarea.Avectorof1′ lengthcorre- fromM101atλ6.2cmandapparentB-vectors(E+90 ,notcorrected
spondstoapolarizedintensityof1mJy/beamarea.Thenoiselevelsare ◦
forFaradayrotation)withlengthproportionaltothedegreeofpolariza-
0.5mJy/beamareain I and 0.07mJy/beamareain PI.The beamwidth
tion.Avectorof1 lengthcorrespondsto20%.ThenoiselevelinPIis
′
of2.′5isshowninthelowerrightcorner.Asquare-rootscalehasbeen 0.07mJy/beamarea.Contours show thebrightness distributionof Hi
appliedtotheopticalimagetoshowlowsurfacebrightnessstructures
ofBraun(1995).Thecontourlevelsofcolumndensityare(10,15,20,
moreclearly. and25)1020 cm 2.Thebeamwidthof2.5isshowninthelowerright
− ′
corner.
than the eastern arms. The maximum located 1.5 NE of the
′ perpartoftheminimumisonacrossingofseveralthinarmsjust
centre coincides with backgroundsource number 20 in the list
northoftheinnermostarmAnotherdepressioninthepolarized
of Israeletal. (1975); the emission from the nucleus is much
intensity occurs about 5 south-west of the centre. It does not
weaker.Otherbrightnesspeakscoincidewithlargestar-forming ′
correspondtoanyparticularopticalorHαfeature,butcoincides
complexesin the western arms as well as with two large com-
plexesin the eastern armsand the giantHii regionNGC5471 withanextendedminimumintheHi mapofBraun(1995)be-
tweentwomajorspiralarms.
at RA=14h04m28s.6, Dec=54 23 40. 3. The south-easternex-
◦ ′ ′′ TheapparentpolarizationB-vectors(definedasobservedE-
tension has no optical counterpart; inspection of a larger field
vectors rotated by 90 ) at λ6.2cm form a very regular spiral
in the digitized sky survey (DSS) and of the deep survey of ◦
pattern(Figs.1and2).Despitethemoderateresolution,theap-
Mihosetal.(2013)didnotshowanyopticalemissionalongthis
parentmagneticfieldorientationsfollowtheopticalspiralarms.
feature. It consists of several background sources unrelated to
Thesamemagneticpatternisobservedatλ11.1cm(Fig.3).The
M101.Checkingthecatalogueoffaintimagesoftheradiosky
similarorientationsofthevectorssuggestthatFaradayrotation
attwentycm(FIRST),we foundtwocompactsourcescoincid-
betweenthesefrequenciesissmall(seeSect.4.2.1).
ingwiththeuppermaximumintheextensionandthreesources
with the lower maximum. The strong source in the north-west
ontheedgeofthefieldalsoisabackgroundsource. 3.2.Thermalandnon-thermalemission
Theasymmetryintotalemissionandtheextensiontowards
Beforefurtheranalysingourdata,we subtractedfourunrelated
the south are also visible in the map at λ11.1cm (Fig. 3). The
pointsourcesfromthetotalpowermapsatλλ6.2and11.1cm.
extendedmaximumnearthecentreisclearlydisplacedfromthe
Wethensmoothedtheλ6.2cmmapsinIandPItoabeamwidth
nucleusbecauseofthebackgroundsourcementionedbefore.In
of2.7andthoseat11.1cmto5.0,whichimprovedthesensitiv-
the western disk, the radio contours show some emission en- ′ ′
itiesatλ6.2cmtoσ(σ )=0.460(0.065)mJy/beamareaandat
hancementatthepositionofalargestar-formingcomplexinthe I PI
λ11.1cmtoσ (σ )=1.05(0.47)mJy/beamarea.
spiralarm;theemissionisalsoenhancedonNGC5471. I PI
For the separation of thermal and non-thermalcomponents
The distribution of polarized emission from M101 at
ofthetotalemissionweneedamapofthetotalspectralindexα
λ6.2cmshowsthesameeast-westasymmetryasthetotalemis- andthenon-thermalspectralindexα 1.Gräveetal.(1990)de-
n
sion(Fig.2).Thebrightestpeakislocatedat5 eastoftheop-
′ rivedaspectralindexmapbetweenλλ49.2cmand2.8cmat1.5
′
tical centre on the inside of the outer eastern arm. The inner-
resolution(see theirfigure5a).Aftersmoothingtheλλ49.2cm
mostdiskisdepolarizedbyvariouseffects(seeSect.4.2.1).The
and2.8cmmapstotheresolutionsof2.7and5.0,whichcon-
′ ′
size of the southern part of this minimum corresponds to the
siderablyreducedthenoise,wecalculatedmapsoftotalspectral
areabelowthecentralbarandinnermostspiralarmsseeninHα
(Scowenetal.1992)andCO(Kenneyetal.1991),whiletheup- 1 WeusetheconventionS ν α
−
∝
Articlenumber,page3of14
A&Aproofs:manuscriptno.m101.paper.v210116
M101 2.7 GHz Total + Polarized Intensity + B-Vectors HPBW=4.4’ M101 4.85 GHz Thermal Intensity + H-alpha HPBW=2.7’
2 4 mJy/beam (PI)
54 30
54 40 28
26
35 00) 24
0
2
J
n ( 22
o
30 ati 20
n
cli
De 18
25
16
0)
0
20 14
on (J 20 12
ati
n
Decli 15 14 04 30 00 0R3ig 3h0t Ascensi0o0n (J200002) 30 00
Fig. 4. Distribution of the thermal radio emission from M101 at
10 λ6.2cmoverlaidonagreyscaleplotoftheHαemissionofHoopesetal.
(2001) smoothed to the same beamwidth of 2.7 (shown in the
′
lower left corner). Contour levels are (1, 2, 3, 4, 6, 8, and 12)
05 1.5mJy/beamarea. The noise level is about 0.5mJy/beamarea. Th×e
white plus shows the position of the optical centre. The strong
source near the eastern border of the map is the Hii-region complex
00
NGC5471.
14 05 00 04 30 00 03 30 00 02 30 00 01 30 00 M101 4.85 GHz Nonthermal Intensity + Nonthermal pol % HPBW=2.7’
Right Ascension (J2000) 10 20 30 40%
Fig. 3. Distribution of the total emission and apparent B-vectors
(E+90 , not corrected for Faraday rotation) of polarized emission
◦ 54 30
from M101 observed at λ11.1cm, overlaid on a greyscale image of
the polarized intensity. Contour levels are 3, 6, 12, 24, 36, 48, and 28
72 mJy/beamarea,avectorof1′ lengthcorrespondstoapolarizedin- 26
tIeannsidty0.o5f41m.5Jmy/Jbye/abmeaamreaarienaP.TI.hTehneoibseealmevweildstahreof1.42.′m4Jisy/sbheoawmnairneathine 2000) 24
lowerrightcorner. n (J 22
o
ati 20
n
cli
De 18
index at our resolutions for all points above the noise level in
16
bothmaps.Thespectralindexvariesfromabout0.6intheinner
partto0.9or1.0atlargeradii.Thelargedifferenceinλbetween 14
the mapsandthe low noise yielderrorsin the α map of<0.02 12
within7arcminfromthecentre,whichslowlyincreaseto<0.1
furtherout. 14 04 30 00 03 30 00 02 30 00
Right Ascension (J2000)
Gräveetal.(1990)determinedαandαnwiththemethodde- Fig.5.Distributionofthenon-thermalemissionfromM101atλ6.2cm
scribedbyKleinetal.(1984),usingtheintegratedfluxdensities (contours) superimposed onto the non-thermal degree of polarization
forR < 14 attenfrequencies.Theyfoundα = 0.72 0.04and (greyscale).Contourlevelsare1,2,4,6,8,and12mJy/beamarea.The
′
α =0.92 0.18.Furthermore,Gräveetal.(1990)ob±servedthat centrepositionisindicatedwithaplus.Themaximumintheemission
n
α becomes±about 0.9 in the outer parts of M101 where all the NEofthecentreisduetothebackgroundsourcenumber20inthelistof
Israeletal.(1975).Thenoiselevelinthenon-thermalintensityisabout
emissionisnon-thermal,andtheyfoundthataftersubtractionof
thebrightHiiregionsαalsobecomesabout0.9intheinnerparts. 0.5mJy/beamarea. In the centre region, strong depolarization causes
verylownon-thermalpolarizationdegrees.Thebeamwidthis2.7.
Soα mustbecloseto0.9.FollowingGräveetal.(1990),wein- ′
n
tegrated our λλ6.2 and 11.1cm maps over the area R < 14 ,
′
yielding S = 310 20mJy and S = 480 30mJy. These
6 11 In Fig. 4 we compare the distribution of thermal emission
± ±
values are less than 8% lower than those listed by Gräveetal.
at λ6.2cm with that of the Hα emission (Hoopesetal. 2001)
(1990) butagree withinerrors.Thereforewe adoptedthevalue
smoothedto the same beam size. Maxima in the radio thermal
ofα =0.92 0.10forourstudy.
n emissionfromM101agreewellwiththoseintheHαemission.
±
Fortheseparationofthermal/non-thermalemissiononlypix- InFig.5weshowthedistributionofthenon-thermalemis-
elsinthespectralindexmapwithrealisticvaluesofαwereused. sion from M101, NTH, at λ6.2cm (contours) superimposed
Ifα 0.1theemissionisfullythermalandfullynon-thermalif onto the degree of non-thermal polarization p = PI/NTH
n
≤
α α ;elsewherethethermalfractioniscalculated.Theresult- (greyscale).TheNTHhasalargerextentthanthethermalemis-
n
≥
ingthermalemissionisthensubtractedfromthetotalemissionto sion, especially to the north. The strong emission 1.5 NE of
′
obtainthenon-thermalemission.InSect.3.2.1wediscusshow the centre is from the background source number 20 listed by
thermalandnon-thermalemissiondependontheuncertaintyof Israeletal. (1975); the emission from the nucleusitself is very
0.1inα . weak.TheNTHisslightlyenhancedonthebrightestspiralarms
n
Articlenumber,page4of14
E.M.Berkhuijsenetal.:PolarizedemissionfromM101
Table3.IntegratedfluxdensitiesofM101forR<14 (=30kpc) M101 Radial Scale Lengths at 6.2 cm
′
Component λ6.2cm Systematicerror
I (mJy) 310 20 —
TH(mJy) 140±15 30 10000
± ±
f 0.45 0.06 0.1
th
NTH (mJy) 170 ±15 ±30 m ]
± ± a
PI(mJy) 28 3 — e
b
p 0.1±6 0.02 0.03 y/
n ± ± µJ
Notes.Errorsincolumn2arestatisticalerrors;thoseincolumn3arise m) [ 1000
fromanuncertaintyof0.10inα (seeSect.3.2.1). c
n 2
6.
y(
sit
n
and on the star formation complex in the south-west, which is nte 100 I
visible in Fig. 4. The values of p gradually increase from the I NTH
n TH/2
centre outwards and degrees of more than 40% are reached in
PI
the south. On the star formationcomplexin the south-west, p
n
hasaminimumof< 10%.
Theintegratedfluxdensitiesofthethermal(TH),NTH,and 10
0 5 10 15 20 25 30
polarized (PI) emission at λ6.2cm are listed in Table 3, to-
Radius [kpc]
gether with the average thermal fraction f = TH/I and the
th
Fig.6.Averageintensityin2kpc-wideringsintheplaneofM101ofI
mean value of p = PI/NTH. About 50% of the TH comes
fromthefivegianntHiiregioncomplexesobservedbyIsraeletal. andtheemissioncomponentsNTH,THandPIplottedagainstgalacto-
centricradius.Forclarity,intensitiesofTHarehalved.Errorsarestan-
(1975).ThefluxdensityofTHand f maybeoverestimatedby
th darddeviations.NotethechangeintheslopesnearR=16kpc.Dashed
20–25% because we used a constant value of α , which is too
n linesshowthefitsgivingtheexponential radialscalelengthslistedin
large for star-forming regions(Tabatabaeietal. 2007a, 2013a). Table4.
In this case, NTH (p ) is underestimated (overestimated) by
n
nearly 20%. For further interpretation, a more realistic separa-
tion of thermal/non-thermalemission is required, i.e. by deter-
miningthethermalemissionfromextinction-correctedHαdata, phenomena indicate a major change in the structure of M101
which does not need the assumption of a constant value of αn nearR=16kpc.
throughoutthegalaxy(Tabatabaeietal.2007a).
TheradialdistributionsofI andtheemissioncomponentsin Abreakinthescalelengthoftheradiocontinuumemission
M101 at λ6.2cm are shown in Fig. 6. The deep central min- neartheradiuswherethestarformationvanisheshasalsobeen
imum in PI is clearly visible, but NTH and TH similarly de- found in M33 (Tabatabaeietal. 2007b), M51 (Mulcahyetal.
crease with increasing radius. We do not show TH and NTH 2014)andIC342(Beck2015).TheIRemissionfromM33also
points for R > 24kpc because at these large radii the TH shows a break at this radius. Hence, a break in the radial scale
and NTH maps are no longer complete, which make the ra- length of emission components near the radius where the star
dial averages unreliable. In each of the curves a break is visi- formation comes to an end may be a general phenomenon in
blenearR=16kpc.Therefore,weseparatelydeterminedexpo- galaxies.
nential radial scale lengths L for the intervals R = 0 16kpc,
−
R = 16 24kpcand R = 16 30kpc(for I and PI) by fitting
− −
theintensities,weightedbytheirerrors,toI(R)=a exp( R/L). 3.2.1. Theeffectofanerrorinα onTHandNTH
· − n
ForPIonlyLatlargeRcouldbedetermined.Theresultingscale
lengthsaregiveninTable4.AtR=0 16kpc,NTH decreases
moreslowly(L=13.0 1.4kpc)thanT−H(L=10.2 1.0kpc),as We repeated the thermal/non-thermalseparation for αn = 0.82
isexpectedifcosmicr±ayelectronsdiffuseawayfro±mtheirbirth andαn =1.02toinvestigatehowsensitiveTH and NTH areto
theerrorinα .Figure7showstheradialvariationofthethermal
placesinstar-formingregions.However,beyondR = 16kpcall n
emissionforthesecasesandforα =0.92.Thedifferencefrom
threecomponentshavethesameradialscalelengthofL 5kpc, n
suggestingthatintheouterdiskthecosmicrayelectrons≃escape ourstandardcaseistypically20%,hence,theerrorinαn causes
a systematic error of 20% in TH and a similar error in NTH.
intothehaloofM101.
Asthenon-thermaldegreeofpolarizationis p = PI/NTH, p
n n
Mihosetal.(2013)foundachangeintheradialscalelength
also has a 20% systematic error (see Table 3). The resulting
of the optical surface brightness at R = 7 9, which is the
′ ′ systematicerrorsinthescalelengthsaregiveninTable4.
−
sameradiusasthebreakintheradioprofiles.Thispositionnear
R = 16kpc(=7.′4)correspondstotheradiuswheretheinclina- InFig.7wealsoshowtheradialprofileoftheHαemission
tion angle changes and the Higas starts deviating from differ- observed by Hoopesetal. (2001), scaled to TH for α = 0.92
n
entialrotation (Kamphuis1993). BeyondR = 7′ the gasstarts atR = 16 18kpc.Apartfromthe inner6kpcthe profilesare
flaringwithvelocitycomponentsperpendiculartothemidplane almost iden−tical. The discrepancy near the centre is due to the
ofM101. combinationofextinctioninHαandapossibleoverestimateof
The change in scale length near R = 16kpc, which is seen THonthemanyHii regionsinthisareainM101.Thiscompari-
in the distributions of thermal and non-thermal radio emission son,andtheoverlayinFig.4,showthatourthermal/non-thermal
and optical surface brightness, is accompanied by a change in separationyieldsagoodestimateofthedistributionofthether-
thevelocitystructurenearthesameradius.Takentogether,these malemissioninthegalaxy.
Articlenumber,page5of14
A&Aproofs:manuscriptno.m101.paper.v210116
M101 Comparison of thermal and H_alpha emission M101 EQUIPARTITION MAGNETIC FIELD STRENGTHS
10
m]10000
a
Jy/be µG ]
micro h [ BB__troant
ON [ strengt B_ord
SI d
L EMIS 1000 etic fiel
RMA TH alpha_n=0.92 Magn
E TH alpha_n=0.82 lower line
H
T TH alpha_n=1.02 upper line
H_alpha scaled at R=17kpc
1
0 5 10 15 20 25 0 5 10 15 20 25
RADIUS [kpc] Radius [kpc]
Fig.7.Averageintensityin2kpc-wideradialringsintheplaneofM101 Fig.8. Variationwithgalacto-centric radius of the equipartition mag-
ofTH derivedwithαn =0.92(solidline)andwithαn=0.82and1.02 neticfieldstrengths Btot, Bran,and Bordaveragedin2kpc-wideringsin
(dottedlines),plottedagainstgalacto-centricradius.Theerrorsonthe theplaneofM101.ThereisachangeinslopenearR=16kpc.Dashed
dotted lines are the same as on the solid line, but are not shown for linesrepresenttheexponentialfitsyieldingtheradialscalelengthsgiven
clarity. The red line shows the radial distribution of the Hα emission inTable4
(Hoopesetal.2001),scaledtoTH derivedwithα =0.92atthering .
n
R=16 18kpc.Notetheclosecorresponcencebetweenthetwodistri-
−
butionsatR>6kpc.Thediscrepancyinthecentralpartmaybedueto
extinctioninHαandapossibleoverestimateofTHonHiiregions.
(Sect. 3.2) and a scale height of the non-thermal emission of
1kpc, leading to L = 2/cos(i) = 2.3kpc. Fig. 8 shows the
nth
4. Discussion radial distributions of B , B , and B in 2kpc-wide rings
tot ran ord
around the centre for R < 24kpc. 3 The total field strength is
We now employ the non-thermal and polarized emission com-
nearly10µGnearthecentreanddropstoabout4µGinthering
ponentsderivedintheforegoingsectionsforananalysisofvar-
R=22 24kpc.ThemeanfieldstrengthsintheareaR<24kpc
ious properties of the magnetic field in M101. We show how −
are B = 6.4µG, B = 5.9µGand B = 2.5µG. With
tot ran ord
magneticfieldstrengthsdecreasewithincreasingdistancetothe
B /B = 2.4, the magnetic field in M101 is highly random
ran ord
centre and how the random magnetic field depends on the star
likein,forexampleIC342(Beck2015).
formationrate per unitarea,Σ . We discussFaradayrotation
SFR
measuresanddepolarizationeffects, andlookatthelarge-scale InFig.8thebreakintheslopeofthecurvesnearR=16kpc
structureoftheorderedfield. is very clear. Like in Sect. 3.2, we calculated the exponen-
tial radial scale lengths for the two intervals R < 16kpc and
R = 16 24kpc. Table 4 shows that the magnetic fields have
4.1.Magneticfieldstrengthsandstarformationrate verylong−scalelengthsof34 45kpc atR < 16kpcandabout
−
20kpc at larger radii. In the inner region, B is low due to
4.1.1. Radialdistributionofmagneticfieldstrengths ord
the depolarization;therefore, the scale length of B is signif-
tot
From the radial variations of the surface brightnesses of NTH icantlylargerthan thatof B ((B )2 = (B )2 +(B )2).In
ran tot ran ord
and PI at λ6.2cm presentedin Fig. 6, we calculated the mean the outer region, B and B have the same scale length. If
ran ord
equipartition strengths of the total (B ), ordered(B ), 2 and thisscalelengthremainsthesameouttotheradiusofthemax-
tot ord
random (B ) magnetic field using the code BFIELD of M. imalobservedopticalextentofR 70kpc (vanDokkumetal.
ran
Krause based on equation (3) of Beck&Krause (2005). The 2014) and of the Hi gas of the e≃xtension in the southwest of
code also requires the non-thermal spectral index α , the non- R = 90pc (Mihosetal. 2012), the field strengths will have
n
thermaldegreeofpolarization p ,thelineofsight L through droppedtoabout0.3µGand0.2µG,respectively.Hence,thein-
n nth
the emitting medium, and the ratio of the energy densities of tragroupmagneticfieldstrengthisprobablysmallerthan0.3µG,
protonsandelectronsK,heretakenas100.We usedα = 0.92 whichissimilartothevalueestimatedforalocalgroupofirreg-
n
ulardwarfgalaxies(Chyz˙yetal.2011).
2 Ordered magnetic fields as traced by linearly polarized emission
can be either regular fields, preserving their direction over large
scales (leading to both polarized emission and rotation measure), or
anisotropicrandom fieldswithmultiplerandomfieldreversalswithin 3 As field strength scales with the power 1/(3+α ) of K, L , and
n nth
the telescope beam, caused by shear and/or compression of isotropic NTH,errorsinthesequantitiesandobservationalerrorsinNTH have
random fields (leading to polarized emission but not to rotation mea- littleeffectonthederivedfieldstrengths.Theuncertaintyof0.1inα =
n
sure).Toobservationallydistinguishbetweenthesefundamentallydif- 0.92leadstolessthan2%changesin B and B atR < 16kpcand
tot ran
ferent types of magnetic field, additional Faraday rotation data is lessthan5%errorsatlargerradii.Onlythesystematicerrorin B is
ord
needed. about17%duetothesystematicerrorinp (seeSect.3.2.1).
n
Articlenumber,page6of14
E.M.Berkhuijsenetal.:PolarizedemissionfromM101
Table4.ExponentialradialscalelengthsL[kpc]ofsurfacebrightness M101 Σ vs. Radius
SFR
atλ6.2cmandmagneticfieldstrength.Errorsarestatisticalerrors.The
numbersimmediatelybelowNTH,TH,andthefieldstrengthsaresys-
tematic errors in case α = 1.02 (first one) or 0.82 (second one), re-
n
spectively. The ratio between the scale lengths of B and NTH at
tot
R = 16 24kpc is(3+α ), whichisexpected if p isconstant. Be- 10
causep −increasesatR=0n 16kpc,theratiobetweennthescalelengths
of BtotanndNTHislesstha−n(3+αn). -2c ]
p
I R=110.5−116.k0pc R=41.76−02.45k˙pc R=51.26−03.03kpc -1Gyr
NTH 13.0±1.4 5.1±0.7 —±– M o
PI +0.—2±−–0.5 +50.1.2±−00.2.2 4.7—–0.3 [ R
TH 10.2 1.0 4.7±0.8 —±– SF
+0.1±0.3 +0.4± 0.1 —– Σ
− − 1
B 45.5 3.6 19.8 2.9 —–
tot
± ±
+2.3 3.3 +2.0 1.5 —–
− −
B 33.9 1.9 19.5 3.6 —–
ran
± ±
1.2+0.2 +2.8 1.8 —–
− − 0 5 10 15 20 25
Bord —– 21.1 0.8 —– Radius [kpc]
±
—– 1.7+0.6 —–
− Fig.9. Radial variation of the mean star formation rateper unit area,
Σ ,in2kpc-wideringsintheplaneofM101.Theshapeofthecurve
SFR,j
isthesameasthatofthethermalemissioninFig.6.Errorsarestandard
4.1.2. Dependenceofmagneticfieldstrengthonstar deviations.DashedlinesshowthefitsgivingthescalelengthsofTHin
formationrate Table4.
Since supernova explosions, SNRs, and stellar winds are the
principal actors stirring up the ISM, and hence producing ran- haveasystematicerrorof20%.ThethermalemissionandΣSFR
dom magnetic fields, a relationship between the random mag- of M33, however, do not contain such a systematic error be-
netic field B and the mean star formation rate per unit area, causetheywerebothderivedfromextinction-correctedHαdata
ran
Σ , is expected. This has indeed been found for the galax- (Tabatabaeietal.2007a;Berkhuijsenetal.2013).
SFR
ies NGC4254 (Chyzy 2008) and NGC6946 (Tabatabaeietal. In M101 the values of ΣSFR,j range from nearly
2013b) as well as for the global values of a sample of nearby 14M Gyr 1pc 2 at R < 2kpc to about 0.8M Gyr 1pc 2
− − − −
galaxies(e.g.Heesenetal.(2014)).Belowweshowthatarela- at R⊙ = 22 24kpc, which is in good agre⊙ement with
−
tionshipalsoexistsinM101. the range derived by Zasov&Abramova (2006, fig. 1) from
Asthermalradioemissionisfree-freeemissionfromgasion- UV and FIR data. Suzukietal. (2010, fig. 8a) found val-
izedbymassivestars,thepresent-dayΣ isproportionaltothe ues of 5 100M Gyr 1pc 2 in spiral arms, and the map
SFR − −
thermal surface brightness. Therefore, we evaluated the mean of Σ of−Leroye⊙tal. (2012, fig. 20) shows values of about
SFR
valueofΣ inM101bycomparingthethermalsurfacebright- 16M Gyr 1pc 2 near the centre and of 0.6M Gyr 1pc 2 in
SFR − − − −
nessatλ21cm, s ,withthatofM33,forwhichΣ isknown spiral⊙arms. Hence, the radial distribution of Σ ⊙ in Fig. 9 is
21 SFR SFR,j
(seeBerkhuijsenetal.2013,table6), consistentwithotherestimatesintheliterature.
In Fig. 10 the mean valuesof B in 2kpc–wide ringsare
ran
Σ (M101)= s21(M101)Σ (M33). (1) plottedagainstthe correspondingmean valuesof ΣSFR for R =
SFR SFR
s (M33) 0 24kpc.Apower-lawfittothepointsyields
21
−
AtdistanceDwehaves21 =S214D2/R2,whereS21isthether- Bran =(3.98±0.12)ΣS0F.R28±0.02. (3)
malfluxdensityoftheareawithinradiusR.WithD = 7.4Mpc,
Theuncertaintyinα causesasystematicerrorintheexponent
S =TH =160 13mJywithinR=30kpc(calculatedfrom n
21 21 ± of 0.02.
TH6 in Table 3) for M101 and D = 0.84Mpc, S21 = 420mJy ≤By using the values in 2kpc-wide rings, our fit refers to
withinR=5kpcandΣ =3.0 0.6M Gyr 1pc 2 forM33,
we find Σ (M101) =SFR2.5 0±.2M G⊙yr 1p−c 2 −for the area a correlation on large scales. In spite of this, the exponent of
R < 30kpScFR(R < 14′). We t±hen use⊙d the−λ6c−m thermal map s0c.2a8les±b0y.0C2hyiszyin(2g0o0o8d) aagnrdeeTmabeanttabwaietihetthaol.se(2f0o1u3nbd),ownhsomdael-l
of M101 to find∼the mean Σ in the 2kpc-wide rings used
SFR,j rivedexponentsof0.26 0.01forNGC4254and0.16 0.01for
before ± ±
NGC6946, respectively, using pixel-to-pixel correlations. The
TH smallexponentfoundforNGC6946isattributedtothefastcos-
6,j
ΣSFR,j = ΣSFR(M101), (2) micraydiffusioninthisgalaxy.
TH
6
Asdiscussedabove,theradialdistributionsofmagneticfield
whereTH andTH arethemeanthermalintensityforring j strengthinFig.8showabreaknearR=16kpccausingdifferent
6,j 6
and R < 30kpc, respectively. We present Σ as a function scalelengthsforR < 16kpcandR > 16kpc.Wecalculatedthe
SFR,j
of radius in Fig. 9. Since Σ TH, the shape of the curve exponentbinB Σb fromthescalelengthsatR<16kpcand
SFR ∝ ∝ SFR
isthesameasthatofTH inFig.6.Thethermalemissionfrom R=16 24kpc,giveninTable4,asb= L /L ,whereL =
SFR B SFR
−
M101hasasystematicerrorof20%becauseoftheuncertainty L . As can be seen in Table 5, the values of b agree within
TH
in α (see Sect. 3.2.1); therefore, Σ (M101) and Σ also errors. Although the power law between B and Σ at R <
n SFR SFR,j ran SFR
Articlenumber,page7of14
A&Aproofs:manuscriptno.m101.paper.v210116
M101 B vs. Σ for R = 0 - 24 kpc M101 Effelsberg RM (11.1 cm, 6.2 cm) HPBW=5’
RAN SFR
10 0 20 rad/m**2 40
9
54 30
8
25
G ] 7 000)
2
µ J
[RAN 6 eclination ( 20
B 5 D
15
4
3 10
14 04 30 00 03 30 00 02 30 00
Right Ascension (J2000)
2
0 5 10 15
Fig.11.DistributionofFaradayrotationmeasureRM(11,6)(greyscale
Σ [M Gyr -1 pc -2] andcontours) inM101betweenλ11.1cmand λ6.2cm.Thedataare
SFR o
convolvedtoacommonbeamwidthof5 showninthelowerleftcorner.
Fig. 10. Dependence of the turbulent magnetic field strength B on ′
ran Contourlevelsare-10,0,10,20,30,and40radm 2.Theuncertainty
thestarformationrateperunitarea,Σ .Thepointsrepresentaverage −
SFR inRM(11,6) isabout 10 15radm 2. The cross shows the centre of
valuesin2-kpcwideringsintheplaneofM101.Thedashedlineshows − −
M101.
thepower-lawfitforR<24kpcgiveninthetext.Statisticalerrorsof1
σareshownforΣ ,butarenegligblein B .
SFR ran
4.2.Rotationmeasuresanddepolarization
Table5.Power-lawexponentsbinB Σb fromb= L /L .Sys-
∝ SFR SFR B
tematic errors in b due to the uncertainty in α are smaller than the In Fig. 11 we present the distribution of the Faraday rota-
n
statisticalerrors tion measures between λ11.1cm and λ6.2cm, RM(11,6). Af-
ter smoothing the PI(6cm) map to the 5 beamwidth of the
′
Fieldtype R=0 16kpc R=16 24kpc PI map at 11cm, RM(11,6) was calculated for all data points
− −
Btot 0.22 0.03 0.24 0.05 above 2.3 times the noise in both maps. The ambiguity of
± ±
Bran 0.30±0.03 0.24±0.07 367 radm−2 does not influence these results. East of the ma-
Bord —– 0.22±0.03 jor axis RM(11,6) varies smoothly around 20radm−2, but in
the western part strong gradients in RM(11,6) occur. A com-
parison with Fig. 4 shows that RM(11,6) is not correlated
16kpc maybe somewhatsteeper than thatat R = 16 24kpc, with the thermal emission from ionized gas that mainly orig-
thefitforR=0 24kpcshowninFig.10withb=0.28− 0.02is inates from discrete Hiiregions with small volume filling fac-
withinerrorsfor−bothradialranges.AtR >16kpc, Bor±d isalso tors. Only the maximum in RM(11,6) > 40radm−2 near the
correlatedwithΣ ,whichisnotthecaseinNGC4254(Chyzy south-western major axis coincides with intense thermal emis-
SFR
2008)andNGC6946(Tabatabaeietal.2013b).However,these sion.Hence,RM(11,6)arisesinthediffuseionizedgasinM101.
authorsusedpixel-topixelcorrelationsforthewholegalaxy,in ThisisalsothecaseinM31(Berkhuijsenetal.2003)andM51
which a possible weak dependence in the outer part may have (Fletcheretal.2011).
beenlost. The ratio of the non-thermal degree of polarization at
Sincethe totalmagneticfield containsa largerandomfrac- λ11.1cm and λ6.2cm yields the Faraday depolarization be-
tion, Btot is correlatedwith ΣSFR as well, but with a somewhat tween these wavelengths, DPn(11,6) = pn(11) / pn(6), as the
smaller exponentthan B (see Table 5). This is also the case wavelength-independentpolarizationcancels.Theuncertaintyin
ran
inNGC6946(Tabatabaeietal.2013b).Furthermore,significant αncausesasystematicerrorof20%inpn(6),12%inpn(11),and
correlations between the global values of Btot and ΣSFR have 10%in DPn(11,6).Thedistributionof DPn(11,6)acrossM101
beenfoundforasmallsampleofLocalGroupdwarfswithb = isshowninFig.12. DPn(11,6)generallyisclosetounity,vary-
0.30 0.04 (Chyz˙yetal. 2011), for 17 low-mass, Magellanic- ing between about 0.7 and 1.3. This means that depolarization
type ±and peculiar galaxies with b = 0.25 0.02 (Jurusiketal. byFaradayeffectsissmall.InSect.4.2.1weestimatewhichde-
2014), for a sample of 17 galaxies with±b = 0.30 0.02 polarizationmechanismsareimportantinM101.
±
(Heesenetal.2014),andforasampleof20nearbyspiralgalax- IncomparingFig.11andFig.12onegetstheimpressionthat
ies with b = 0.19 0.03 (VanEcketal. 2015). It would be contourlevelsofRMareoftenperpendiculartocontourlevelsof
±
interesting to see if the observed variation in the exponent b DP .ThisisespeciallyclearinFig.13wherebothcontoursets
n
couldberelatedtotheconsiderablevariationinthedependence areshown.ContoursofRMandDP tendtobeperpendicularto
n
of the local star formation rate on the total gas surface density each otherat their crossingpoints. This suggeststhatgradients
(Bigieletal. 2008), on variations in the dependence of B on in RM are a significant cause of Faraday depolarization. This
tot
thetotalgasvolumedensity,and/oronvariationsincosmicray phenomenonwas also observed in M51 (Horellouetal. 1992)
diffusion(fastdiffusioncausesasmallexponent). andM31(Berkhuijsenetal.2003).
Articlenumber,page8of14
E.M.Berkhuijsenetal.:PolarizedemissionfromM101
M101 Effelsberg Nonthermal DP (11.1 cm, 6.2 cm) HPBW=5’ valueofRM .Theazimuthalprofilesforthetworingsareshown
0.8 1.0 1.2 1.4 1.6 f
inFig.14andFig.15.
Theprofilesfortheinnerring(Fig.14)showlittlevariation
withazimuth.Thenon-thermaldegreesofpolarizationp (6)and
n
p (11) are nearly the same and DP (11,6) remains close to 1.
54 30 n n
Hence, Faraday depolarizationis unimportantand the low val-
ues of p 0.1 must be due to wavelength-independent po-
n
larization 4≃. The top panel shows that in all sectors B dom-
ran
25
2000) tionmatepsaanselB)riasn/gBenoredra≃lly2.5smaanldl,Bburatn/chBatontg≃es0f.r9o.mRMi(1151,r6a)d(mbot2-
J −
n ( to 15radm 2 between Az = 210 and Az =≃ 240 . Fig-
natio 20 ure≃11−shows a−strong gradient in RM◦(11,6) in these s◦ectors,
ecli which causes the depression in PI south-west of the centre in
D
Fig.2.Thisareaiscoincidentwithanextendedminimuminthe
15 Hi mapofBraun(1995).
In the outer ring (Fig. 15) the situation is more complex.
From Az = 90 to Az = 180 , the non-thermal polarization
◦ ◦
percentagesareincreasedandshowa pronouncedmaximumat
10
Az= 150 .Inthesesectors p (11)< p (6)andDP (11,6)<1,
◦ n n n
14 04 30 00 03 30 00 02 30 00 indicating Faraday depolarization. In the same interval the or-
Right Ascension (J2000)
deredfieldstrength B isincreasedand B /B hasdropped
ord ran ord
Fig. 12. Distribution of the non-thermal depolarization, to 1. In sector Az = 210 B suddenlyincreases by 2µG.
◦ ran
DPn(11,6)=pn(6)/pn(11), in M101. Contour levels are 0.6, 0.8, Th≃is is caused by the large Hii complex south-westof the nu-
1.0,1.2,1.4,and1.6.TheuncertaintyinDPn(11,6)increasesfrom0.1 cleusthatisvisibleasabrightsourceinboththermalandnon-
nearthecentreto0.3intheouterparts.Theangularresolutionis5.
′ thermalintensity(i.e.see Fig.4).RM(11,6)issmallinallsec-
i
tors(< 20 radm 2),apartfromthesectorat Az = 300 where
M101 Effelsberg RM + Nonthermal DP (11.1 cm, 6.2 cm) HPBW=5’ itisstro|ngl|ynega−tivewithnearly 60radm 2.Thissec◦torcon-
−
tains a strong decrease in RM(11−,6) around RA=14h02m45s,
DEC=54 28 35 (see Fig. 11). Here p (6) and p (11) reach a
54 30 ◦ ′ ′′ n n
minimumoflessthan0.1and B /B becomes 4.Themin-
ran ord
≃
imuminthepolarizationdegreesisduetowavelengthindepen-
dentpolarizationas p (6) p (11).
n n
25 ≃
0) We discuss the wavelength-independentpolarization in the
0
20 inner ring in the next section. Here we estimate whether Fara-
J
n ( daydepolarizationcouldexplain p (6)and p (11)inthesector
o n n
ati 20 at Az = 150 in the outer ring, where DP (11,6) 0.8 (see
eclin Fig.15). ◦ n ≃
D
InternalFaradaydispersionusuallyisthestrongestFaraday
15 effect,forwhichBurn(1966)andSokoloffetal.(1998)givethe
expression
p (λ)= p (1 exp( 2S))/2S, (4)
n 0
10 − −
where S = σ2 λ4 and p = 0.75 is the maximum degree
14 04 30 00 03 30 00 02 30 00 RM 0
Right Ascension (J2000) of polarization 5; σ is the standard deviation of the intrin-
RM
Fig.13. Contoursof RM(11,6) (thickbluelines) and DPn(11,6) (thin sicrotationmeasureRMi.Forthewavelengthsofλλ6.2cmand
redlines)inM101superimposed.Thinandthicklinestendtobeper- 11.1cm,wefindthatσRM =40radm−2 givestheobservedvalue
pendiculartoeachotherattheircrossingpoints.Thebeamwidthis5. of DP (11,6) 0.8. This value of σ is similar to those in
′ n RM
NGC6946(Be≃ck 2007) and IC342 (Beck 2015) of 38radm 2
−
and55radm 2,respectively.
−
4.2.1. DepolarizationmechanismsinM101 Although σ = 40radm 2 can explain DP = 0.8, the
RM − n
valuesof p (6)=0.73and p (11) = 0.50resulting fromEq.4,
Inordertounderstandwhichmechanismsarecausingthedepo- n n
are much higher than those observed, which are p (6) = 0.39
larizationinM101,wecalculatedthemeanvaluesofDP (11,6) n
n
and p (11) = 0.31. Therefore, the value of p 0.40 is
in30 -widesectorsintworadialringsintheplaneofthegalaxy: n n
◦ ≃
aninnerringatR=2.5 7.5(=5.4–16.1kpc)andanouterring the result of wavelength-independent polarization. This rather
′ ′
atR = 7.5 12.5(=16−.1–26.9kpc).Forthesamesectors,we high value could partly come from anisotropic magnetic fields
′ ′
− (Fletcheretal. 2011) (see Sect. 4.2.2). Thusin the sector Az =
also calculatedthemeanvaluesof B , B and B ,of p (6)
tot ran ord n
and p (11), and of the intrinsic rotation measure, RM(11,6)= 150◦ in the outer ring the combination of Faraday dispersion
n i
RM(11,6)–RM , where RM is the rotation measure of the
f f 4 Insteadof wavelength-independent depolarization weuse themore
Galacticforeground.WeestimatedRM = 15 5radm 2 from
f ± − accurate description of wavelength-independent polarization (see
the mean RM(11,6) in the two rings. The rotation measures of Sokoloffetal. (1998)), emerging from ordered fields (at small wave-
the three polarized point sources located within 30′ from the lengths)orfromshearedorcompressedrandommagneticfieldsinthe
centreofM101varybetween2 10radm−2 and9 6radm−2 emissionregion(seeSect.4.2.2).
± ±
(Oppermannetal. 2012), which is in fair agreement with our 5 p =(1+α )/(5/3+α )=0.74 0.09forα =0.92.
0 n n ± n
Articlenumber,page9of14
A&Aproofs:manuscriptno.m101.paper.v210116
andwavelength-independentpolarizationcanexplaintheobser- M101 Ring R = 2.’5 - 7.’5
8
vations,wherethelatteristhedominantpolarizationmechanism.
It is interesting to see whether the value of σRM = G]6
m40edraiudmmi−n2Mis1c0o1n.siWsteenctawnietshtitmheaptero<penretie>s,otfhtehaevmeraaggneeetole-ciotrnoinc µB [24
densityalongthelineofsight(in cm−3),usingtherelation 0
0.3 p_n (6)
σRM = 0.81 < ne > Bran,a pLiond/ f, (5) _n 0.2 p_n (11)
p
where B is the strength of the component of the isotropic 0.1
ran,a
random field along the line of sight (in µG); L is the path 0
ion
length through the layer of diffuse gas (in pc) containing ion- 6 )
1,
ized cells with a typical size of d = 50pc, which is the coher- 1
ence length of turbulence in the ISM (Ohno&Shibata 1993; _n ( 1
P
Berkhuijsenetal. 2006); and f is their volume filling factor D
0
aolfo1ngkpLci,onL.ioFno=r a2n0e0x0p/oncoens(tii)al=sc2a3l0e0hpecig,hwthoefrethweeioansiszuemdelatyheart 11,6) 300
we see polarized emission from both sides of the disk. With _i (
B = B √1/3 = 1.6 µG and f = 0.5 (Berkhuijsenetal. M-30
ran,a ran R
2006)wefind< n >= 0.06 cm 3,whichisaboutthreetimes
e − -60
higher than found near the sun (Berkhuijsen&Müller 2008). 0 90 180 270 360
Azimuthal angle [deg]
However,a smaller filling factor or a larger size of the ionized
Fig. 14. Variation with azimuthal angle in the plane of M101 of the
cellswouldbring< n > closertotheMWvalue.
e meanvalueofseveral variables, calculatedin30 -widesectorsinthe
Alternatively,wemayestimate< n > fromthemaximum ◦
e radial ring R = 2.5 7.5. The azimuthal angle is counted counter
intrinsicrotationmeasureintheouterringusing ′ − ′
clockwisefromthenorthernmajoraxis.Toppanel:Equipartitionmag-
netic field strengths B (black dots), B (red crosses) and B
RM = 0.81 < n > B L , (6) tot ran ord
i e ord,a ion (greencircles).Uppermiddlepanel:Non-thermalpolarizationpercent-
agesp (6)andp (11).Lowermiddlepanel:Non-thermaldepolarization
n n
where Bord,a = Bord sin(i) is the strength of the orderedmag- DPn(11,6).Bottompanel:IntrinsicrotationmeasureRMi(11,6).Aller-
neticfieldcomponentalongthelineofsight,assumedtobereg- ror bars are statistical errors of one σ. The uncertainty in α causes
n
ular. With RM = 18 radm 2, B = 3.1 µG (see Fig. 15), systematic errors of 17% in B , 20% in p (6), 12% in p (11), and
i − ord ord n n
and L =|2300|pc, we have < n >= 0.006 cm 3, which is 10%inDP (11,6).
ion e − n
about one-third of the value near the sun. The difference be-
tween the two estimates of < n >suggests that the observed
e
polarized emission mainly travels through thin, diffuse ionized M101 Ring R = 7.’5 - 12.’5
gas,whereasthedepolarizationbyFaradaydispersionismainly 8
causedbythedenser,ionizedclouds.However,weshouldregard G ]6
tfiheilsdloowbsveravlueedoinf<ponlaeri>zedasemaliosswioenrliismaitniisfoptarortpoicf(thsheeoarrdeedreodr µB [24
compressedfield),whichdoesnotcontributetoFaradayrotation
0
andRMi(Fletcheretal.2011). 0.3 p_n (6)
We conclude that the low degrees of polarization in M101 p_n (11)
are mainly caused by dispersion of polarization angles by p_n0.2
random magnetic fields in the emission regions, leading to 0.1
wavelength-independent polarization. Faraday dispersion also 0
playsarole,butonlyinsomeregions. 6 )
1,
n (1 1
_
P
4.2.2. Whatcauseswavelength-independentpolarization? D
0
30
In the foregoing Section, we showed that wavelength- 6)
innidsmepeinndMen1t0p1o.lWareizantoiownesistimthatee umnadienr wpohliacrhizcaitriocunmmstaenchceas- M_i (11,-300
wavelength-independentpolarizationwith p = 0.1is obtained R
n -60
intheinnerring(R=2.5-7.5)(Fig.14). 0 90 180 270 360
′ ′
Azimuthal angle [deg]
InM51,Fletcheretal.(2011)foundthatmostofthepolar-
izedradioemissionfromthedisk,observedatshortwavelengths, Fig.15.SameasFig.14fortheradialringR=7.′5 12.′5inM101.
−
arisesfromanisotropicrandommagneticfieldsthatdonotcon-
tribute to the rotationmeasure.Thismay be a generalproperty
For case (a), we use Eq.(24) of Sokoloffetal. (1998) for
ofgalaxydisks,andthelowvaluesofRM inM101suggestthat
i wavelength-independent polarization in a partly ordered mag-
anisotropicmagneticfieldsmaybeimportant.Therefore,wedis-
neticfield,
cusstwopossibilities(recallfootnote2toSect.4.1.1):
(a) polarization by an ordered (regular and/or anisotropic ran-
B2
dom)field;and p = p ord,p , (7)
(b)polarizationbyapurelyanisotropicrandomfield. n 0 B2 +σ2
ord,p r
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