A Detailed Study of the Radio--FIR Correlation in NGC6946 with Herschel-PACS/SPIRE from KINGFISH

0.8 MB·English

by  F. S. Tabatabaei

Astronomy & Astrophysics manuscript no. 6946arxiv c ESO 2013
(cid:13)
January 30, 2013
A Detailed Study of the Radio–FIR Correlation in
NGC 6946 with Herschel-PACS/SPIRE from KINGFISH
F.S. Tabatabaei1, E. Schinnerer1, E.J. Murphy2, R. Beck3, B. Groves1, S. Meidt1, M. Krause3,
H-W. Rix1, K. Sandstrom1, A.F. Crocker4, M. Galametz5, G. Helou6, C.D. Wilson7,
R. Kennicutt5, D. Calzetti4, B. Draine8, G. Aniano8, D. Dale9, G. Dumas10, C.W.
Engelbracht11,12, K.D. Gordon13, J. Hinz11, K. Kreckel1, E. Montiel11, H. Roussel14
1 Max-Planck-Institut fu¨r Astronomie, K¨onigstuhl 17, 69117 Heidelberg, Germany
3 2 Observatories of theCarnegie Institution for Science, Pasadena, CA 91101, USA
1 3 Max-Planck Institut fu¨r Radioastronomie, Auf dem Hu¨gel 69, 53121 Bonn, Germany
0 4 Department of Astronomy,University of Massachusetts, Amherst, MA 01003, USA
2 5 Instituteof Astronomy,University of Cambridge, Madingley Road, Cambridge CB3 0HA,UK
6 Infrared Processing and Analysis Center, MS 100-22, Pasadena, CA 91125, USA
n
7 Department of Physics & Astronomy,McMaster University,Hamilton, Ontario L8S 4M1, Canada
a
J 8 Princeton University Observatory,Peyton Hall, Princeton, NJ 08544-1001, USA
9 Department of Physics & Astronomy,University of Wyoming, Laramie, WY 82071, USA
9 10 Institut de RadioAstronomie Millim´etrique, 38406 Grenoble, France
2 11 Steward Observatory,University of Arizona, 933 N. Cherry Ave., Tucson, AZ 85721, USA
12 Raytheon Company,1151 E. Hermans Road,Tucson, AZ 85756, USA
O] 13 Space Telescope Science Institute,3700 San Martin Drive,Baltimore, MD 21218, USA
14 Institutd’AstrophysiquedeParis,Universit´ePierreetMarieCurie(UPMC),CNRS(UMR7095),
C
75014 Paris, France
.
h
Preprint online version: January 30, 2013
p
- ABSTRACT
o
r
t We derive the distribution of the synchrotron spectral index across NGC6946 and investigate the
s
correlation between the radio continuum (synchrotron) and far-infrared (FIR) emission using the
a
[ KINGFISHHerschelPACSandSPIREdata.Theradio–FIRcorrelationisstudiedasafunctionofstar
formation rate, magnetic field strength, radiation field strength, and the total gas surface brightness.

1 The synchrotron emission follows both star-forming regions and the so-called magnetic arms present
v intheinter-armregions.Thesynchrotronspectralindexissteepestalongthemagneticarms(αn ∼1),
4 whileitisflatinplacesofgiantHiiregionsandinthecenterofthegalaxy(αn ∼0.6−0.7).Themapof
8 αn providesanobservationalevidenceforagingandenergylossofcosmicrayelectronspropagatingin
8 thediskofthegalaxy.Variationsinthesynchrotron–FIRcorrelationacrossthegalaxyareshowntobe
6 afunctionofbothstarformationandmagneticfields.Wefindthatthesynchrotronemissioncorrelates
. betterwithcoldratherthanwithwarmdustemission,whentheinterstellarradiationfieldisthemain
1
heating source of dust. The synchrotron–FIR correlation suggests a coupling between the magnetic
0
fieldandthegasdensity.NGC6946showsapower-lawbehaviorbetweenthetotal(turbulent)magnetic
3
field strength B and the star formation rate surface density ΣSFR with an index of 0.14(0.16)±0.01.
1
Thisindicatesanefficientproductionoftheturbulentmagneticfieldwiththeincreasinggasturbulence
:
v expectedinactivelystarformingregions.Moreover,itissuggestedthattheB-ΣSFR powerlawindexis
i similarfortheturbulentandthetotalfieldsinnormalgalaxies,whileitissteeperfortheturbulentthan
X
for thetotal fields in galaxies interacting with the cluster environment.The scale-by-scale analysis of
r thesynchrotron–FIRcorrelation indicatesthattheISMaffectsthepropagationofold/diffusedcosmic
a ray electrons, resulting in a diffusion coefficient of D0 =4.6×1028cm2s−1 for 2.2GeV CREs.
Key words. galaxies: individual: NGC6946 – radio continuum: galaxies – galaxies: magnetic field –
galaxies: ISM
1. Introduction
Send offprint requests to: F.S.Tabatabaei The correlation between the radio and far-infrared
[email protected] (FIR) emission of galaxies has been shown to be
1
Tabatabaei et al.: Radio–FIR correlation in NGC6946
largely invariant over more than 4 orders of mag- Table 1. General parameters adopted for
nitude in luminosity (e.g. Yun et al. 2001a) and NGC6946.
out to a redshift of z 3 (e.g. Sargent et al. 2010).
This correlation is con∼ventionally explained by the Position of nucleus RA=20h34m52.3s
ideathattheFIRandradioemissionarebothbeing (J2000) DEC=60◦09′14′′
drivenby the energyinput frommassive stars,and Position angle of major axis1 242◦
thus star formation. However, this connection is Inclination1 38◦ (0◦=face on)
complicated by the observationthat the FIR emis- Distance2 6.8Mpc3
sionconsistsofatleasttwocomponents;oneheated 1 Boomsma et al. (2008)
directlybymassivestars(i.e.the ‘warm’dustcom- 2 Karachentsev et al. (2000)
ponent), and one heated by the diffuse interstellar 3 1′=1.7kpcalong major axis
radiation field or ISRF (i.e. the ‘cold’ dust compo-
nent) (see e.g. Draine et al. 2007), which includes
the emission from the old stellar population (e.g.
Xu 1990; Bendo et al. 2010). been shown via detailed multi-scale analysis using
Similarly, the radio emission consists of two wavelet transformation (e.g. Hughes et al. 2006;
main components; the thermal, free-free emission Dumas et al. 2011). Murphy et al. (2006, 2008)
andnonthermalsynchrotronemission.Adirectcon- showed that recent massive SF could reduce these
nection between the free-free emission (of ther- dissimilaritiesduetogenerationofanewepisodeof
mal electrons in Hii regions) and young massive CREs,assumingthattheFIRemissionisattributed
stars is expected (e.g. Osterbrock & Stockhausen to dust heating by the same stars.
1960).Conversely,the connectionbetweenthe syn- Assuming the massive SF is as the source of
chrotronemissionand massivestars is complicated bothFIRandsynchrotronemission,Helou & Bicay
by the convection and diffusion of cosmic ray elec- (1993)andNiklas & Beck(1997)considereda cou-
trons (CREs) from their place of birth (supernova pling between magnetic field strengthand gas den-
remnants, SNRs) and by the magnetic fields that sity as the reason for the tight radio–FIR cor-
regulate the synchrotron emission in the interstel- relation in spite of the sensitive dependence of
lar medium (ISM). the synchrotron emission on the magnetic field.
Hence,warmdustemission/thermalradioemis- A modified version of this model was suggested
sioncanbedirectlyassociatedwithyoungstarsand by Hoernes et al. (1998) to explain the correla-
acorrelationbetweenwarmdustandthermalradio tion between the cold dust heated by the ISRF
emission is not surprising. On the other hand, the andthesynchrotronemission,whoseenergysources
connectionbetweencolddustemission/nonthermal are independent. The scale at which the corre-
synchrotron emission and massive stars (and thus lation breaks down provides an important con-
starformation)is less clear.A better correlationof strainton these models, explaining the scale where
the FIR with the thermal than the nonthermal ra- static pressure equilibrium between the gas and
dio emission has already been shown in the LMC, CREs/magnetic fields holds.
M31,andM33(Hughes et al.2006;Hoernes et al. Withinnearbygalaxies,variationsintheradio–
1998; Tabatabaei et al. 2007a). The CREs experi- FIR correlation have been shown to exist by sev-
ence various energy losses while interacting with eralauthors(e.g.Gordon et al.2004;Murphy et al.
matter and magnetic fields in the ISM, causing the 2006; Hughes et al. 2006; Murphy et al. 2008;
powerlawindexoftheirenergydistributiontovary. Dumas et al.2011) througha change in the q ratio
Significant variation of the nonthermal spectral in- (Helou et al.1985, see Sect.7.3 for definition) orin
dex was found in M33 with a flatter synchrotron the fitted slope. Furthermore, the smallest scale at
spectruminregionsofmassiveSFthanintheinter- which the radio–FIR correlation holds is not the
arm regions and the outer disk (Tabatabaei et al. same from one galaxy to another (Hughes et al.
2007b). 2006; Tabatabaei et al. 2007a; Dumas et al. 2011).
The critical dependence of the synchrotron As the variations in the radio–FIR correlation
emission on both magnetic fields and CRE prop- are possibly due to a range of different conditions
agation could cause the nonlinearity in the such as the star formation rate (SFR), magnetic
synchrotron-FIR correlation seen globally for fields,CREpropagation,radiationfieldandheating
galaxy samples (e.g. Niklas 1997a). Propagation sources of dust, this correlation can be used as a
of the CREs can also cause dissimilarities of the tool to study the unknown interplay between the
synchrotron and FIR morphologies particularly on ISM components and SF. These are addressed in
small scales. For instance, Galactic SNRs do not this paper through a detailed study of the radio–
seem to be well-correlated with the FIR emission FIR correlation in NGC6946.
(e.g. Cohen et al. 1984). Moreover, within a few NGC6946 is one of the largest spiral galax-
100pcofthestar-formingOrionnebula,nocorrela- ies on the sky at a distance of 6.8Mpc
tion exists (Boulanger & Perault 1988). In nearby (Karachentsev et al.2000).Itslowinclination(38◦)
galaxies, a lack of correlation on small scales has makes it ideal for mapping various astrophysical
2
Tabatabaei et al.: Radio–FIR correlation in NGC6946
properties across the galaxy (Table 1). NGC6946 Aniano et al. (2011) and resampled to a common
shows a multiple spiral structure with an excep- pixel size of 6′′ ( 170pc).
∼
tionally bright arm in the north-eastof the galaxy. The radio continuum (RC) data at 3.5 and
Having several bright giant Hii regions, this Sc 20cm are presented in Beck (1991) and Beck
(SABc) galaxy has active SF as well as strong (2007). At 3.5cm, NGC6946 was observed with
magnetic fields as traced by linearly polarized the 100-mEffelsberg telescope of the MPIfR1. The
observations (Beck & Hoernes 1996). The global 20cm data were obtained from observations with
star-formation rate is 7.1M⊙yr−1 (as listed by the Very Large Array (VLA2) corrected for miss-
≃
Kennicutt et al. 2011, assuming a Kroupa IMF ing short spacings using the Effelsberg data at
and a mass range of 0.1-100 M⊙). The dynam- 20cm. To trace the orderedmagnetic field, the lin-
ical mass of this galaxy is 1.9 1011M⊙ early polarized intensity data at 6cm presented in
≃ ×
(Crosthwaite & Turner 2007). This galaxy harbors Beck & Hoernes(1996) wereused.The averagede-
amildstarburstnucleus(e.g. Ball et al.1985)and gree of polarization is 30% for the entire galaxy.
≃
there is no strong evidence for AGN activity (e.g. To investigate the connection between the neu-
Tsai et al. 2006). tral gas and the magnetic field, we used the to-
Frick et al. (2001) presented the wavelet analy- tal gas (HI + H2) mass surface density map which
sis of the radio and mid-infrared (ISOCAM LW3) was derived using the VLA data of the HI-21cm
emission in NGC6946. Here we study this corre- line (obtained as part of THINGS, Walter et al.
lation for dust emission at FIR wavelengths with 2008) and the IRAM 30-m CO(2-1) data from
Herschel-PACS and SPIRE from the KINGFISH the HERACLES survey as detailed in Bigiel et al.
project (Key Insights on Nearby Galaxies: a Far- (2008) and Leroy et al. (2009).
Infrared Survey with Herschel, Kennicutt et al. We used the Hα map of NGC6946 observed
2011) and using various approaches. withtheKPNO0.9mina23′ 23′fieldofviewand
The paper is organizedas follows. The relevant with 0.69′′ pixel−1 (resolution×of 1.5′′), subtracted
data sets are described in Sect. 2. After deriving for the continuum (Ferguson et al. 1998) and fore-
the maps of the free-free and synchrotron emis- ground stars. The contribution from the [NII] line
sions (Sect. 3), we derive the distribution of the emission was subtracted following Kennicutt et al.
synchrotron spectral index in Sect. 4. We map the (2008). The Hα emission is corrected for attenu-
magnetic field strength in Sect. 5. The radio–FIR ation by the Galactic cirrus using the extinction
correlation is calculated using various approaches value given by Schlegel et al. (1998). The Hα map
i.e. the q-method, classical pixel-by-pixel correla- has a calibration uncertainty of 20%.
tion, and as a function of spatial scale in Sect. 6. The radio and Hα maps wer≃e smoothed to 18′′
Wefurtherdiscussthecorrelationsversusmagnetic resolution (using a Gaussian kernel). All the maps
fields,SFR,radiationfieldandgasdensity(Sect.7). were normalized to the same grid, geometry, and
Finally, we summarize the results in Sect. 8. size before comparison.
3. Thermal/nonthermal separation
2. Data
Constraints on the origin and propagation of cos-
mic rays can be achieved by studying the varia-
Table 2 summarizes the data used in this work.
tion in the spectral index of the synchrotron emis-
NGC6946 was observed with the Herschel Space
sion across external galaxies. To determine the
Observatory as part of the KINGFISH project
variation in the nonthermal radio spectral index,
(Kennicutt et al. 2011) and was described in
we separate the thermal and nonthermal compo-
detail in Dale et al. (2012) and Aniano et al.
nents usingathermalradiotracer(TRT)approach
(2012). Observations with the PACS instrument
in which one of the hydrogen recombination lines
(Poglitsch et al. 2010) were carried out at 70, 100,
is used as a template for the free-free emission
160µm in the Scan-Map mode. The PACS images
(see e.g. Dickinson et al. 2003; Tabatabaei et al.
were reduced by the Scanamorphos data reduction
2007b). For NGC6946, we use the Hα line emis-
pipeline (Roussel et al. 2010; Roussel 2012), ver-
sion which is the brightest recombination line data
sion 12.5. Scanamorphos version 12.5 includes the
available. Both the free-free and the Hα emission
latest PACS calibration available and aims to pre-
are linearly proportional to the number of ioniz-
serve the low surface brightness diffuse emission.
ing photons produced by massive stars, assuming
The 250µm map was observed with the SPIRE in-
strument (Griffin et al. 2010) and reduced using
the HIPE version spire-5.0.1894. The data were 1 The 100–m telescope at Effelsberg is operated by
subtracted for the sky as detailed in Aniano et al.
theMax-Planck-Institutfu¨r Radioastronomie (MPIfR)
(2012). on behalf of theMax–Planck–Gesellschaft.
The 70, 100, 160 and 250µm images were 2 The VLA is a facility of the National Radio
convolved from their native PSFs to a Gaussian Astronomy Observatory. The NRAO is operated by
PSF with 18′′ FWHM using the kernels from Associated Universities, Inc., under contract with the
National Science Foundation.
3
Tabatabaei et al.: Radio–FIR correlation in NGC6946
Table 2. Images of NGC6946 used in this study.
Wavelength Resolution rms noise Telescope
20cm 15′′ 23µJy/beam VLA+Effelsberg 1
3.5cm 15′′ 50µJy/beam VLA+Effelsberg2
250µm 18′′ 0.7MJysr−1 Herschel-SPIRE3
160µm 12′′ 2.2MJysr−1 Herschel-PACS3
100µm 8′′ 5MJysr−1 Herschel-PACS3
70µm 6′′ 5MJysr−1 Herschel-PACS3
6563˚A(Hα) 1.5′′ 0.06µerg s−1cm−2sr−1 KPNO4
HI-21cm 6′′ 1.4Jy/beamms−1 VLA 5
CO(2-1) 13′′ 0.06Kkms−1 IRAM-30m 6
1 Beck (1991, 2007)
2 Beck (2007)
3 Kennicuttet al. (2011)
4 Ferguson et al. (1998)
5 Walter et al. (2008)
6 Leroy et al. (2009)
that the Hα emitting medium is optically thick to The map of σ is equivalent to a map of the
ionizing Lyman photons (Osterbrock 1989; Rubin dust optical depth at Hα wavelengths given by
1968, see also Sect. 3.2). However, the observed τ =σκ where κ is the dustopacity.Taking
Hα Hα Hα
Hα emission may suffer from extinction by dust intoaccountbothabsorptionandscattering,κ =
Hα
which will lead to an underestimate of the free- 2.187 104cm2g−1, assuming a Milky-Way value
×
free emission. Hence, following Tabatabaei et al. of the total/selective extinction ratio of R =3.1
v
(2007b) and Tabatabaei & Berkhuijsen (2010), we (Weingartner & Draine 2001). The distribution of
first investigate the dust content of NGC6946 in τ over the disk of NGC6946 overlaid with con-
Hα
an attempt to de-redden the observed Hα emis- tours of the Hα emission is shown in Fig. 1. We
sion. Then we compare our de-reddening method note that the dust mass from modeling the SED
with the one based on a combination of the total at 18” resolution may be overestimated by 20%
∼
infrared(TIR)andHαluminosity(Kennicutt et al. due to the lack of longer wavelength constraints
2009). (Aniano et al. 2012).
Regions with considerable dust opacity (τ >
Hα
0.7) follow narrow dust lanes along the spiral arms
3.1. De-reddening of the Hα emission
(e.g.thenarrowlaneintheinneredgeofthebright
Following Draine & Li (2007), the interstellar optical arm) and are found mainly in the inner
dust heating has been modeled in NGC6946 disk. High opacity dust is found in the center of
(Aniano et al. 2012) assuming a δ-function in ra- the galaxy with τ 5. This corresponds to
Hα
≃
diationfieldintensity, U,coupledwithapower-law a silicate optical depth of τ 0.5 which is in
9.7
≃
distribution U <U <U , agreement with Smith et al. (2007). In the cen-
min max
tral 60pc which is much smaller than our resolu-
dMdust/dU =Mdust (1 γ)δ(U Umin) tion,∼much larger estimates of the extinction have
h − − (1) beenfoundusingtotalgasmasses(Schinnerer et al.
α 1
+ γ − U−α , 2006).
Um1−inα−Um1−axα i Figure 1 also shows that the Hii complexes are
where U is normalized to the local Galactic inter- dustier in the inner disk (with τHα &1.4) than
stellar radiationfield, Mdust is the total dust mass, in the outer parts (with τHα .0.6) of NGC6946.
and (1 γ) is the portion of the dust heated by Across the galaxy, the mean value of τHα is 0.43
the diff−use interstellar radiation field defined by 0.04(medianof 0.34 0.04).Therefore,apartfrom±
±
U = U . The minimum and maximum interstel- thecenter,NGC6946isalmosttransparenttopho-
min
larradiationfieldintensitiesspan0.01<U <30 tons with λ 6563˚A propagating towards us.
min ≃
and 3 < logU < 8 (see Dale et al. 2001, Theτ derivedcanthenbeusedtocorrectthe
max Hα
2012). Fitting this modelto the dust SEDcovering Hαemissionforattenuationbydust,takingintoac-
the wavelength range between 3.5µm and 250µm, counttheeffective fractionofdustactuallyabsorb-
pixel-by-pixel,resultsinthe18′′maps(with6′′pix- ingtheHαphotons.Sincethesephotonsareusually
els) of the dust mass surface density (σ), the dis- emitted from sources within the galaxy, the total
tribution of the radiation fields (U), and the total dust thickness τ only provides an upper limit.
Hα
infrared (TIR) luminosity emitted by the dust. Following Dickinson et al. (2003), we set the effec-
4
Tabatabaei et al.: Radio–FIR correlation in NGC6946
Fig.1. Left: Dust optical depth at Hα wavelength τ overlaid with contours of the Hα emission from
Hα
NGC6946.Contourlevelsare1,3,6,15,30,40µerg s−1cm−2sr−1.Thebarattherightshowsthevalues
of τ . Right: Radiation field U map (mass-weighted mean starlight heating intensity) of NGC6946 in
Hα
units of radiation field in solar neighborhood U⊙ (Aniano et al. 2012), indicated by the bar at the right
of the image. The beam area is shown in the lower left corners.
tive thickness to τ = f τ with f being the (Kennicutt et al.2009).Interestingly,thisapproach
eff d Hα d
×
dust fractionactually absorbingthe Hα; the atten- is linearly correlated with the de-reddening using
uation factor for the Hα flux is then e−τeff. At our τeff (Fig.2),withanoffsetof0.19dexandadisper-
resolutionof18′′ 530pc,onemayassumethatthe sion of0.14dex.Figure 2 showsthat at the highest
≃
Hαemittingionizedgasisuniformlymixedwiththe luminosities, the corrected Hα values agree, corre-
dust, which would imply f 0.5. Considering the sponding to the calibrationof the secondapproach
d
≃
fact that the ionized gas has a larger extent than specificallytostar-formingregions.Outsideofthese
the dust, Dickinson et al. (2003) found a smaller regions, the Hα-TIR ratio approach overestimates
effective factor (f =0.33)basedona cosecantlaw thecorrectionappliedtotheobservedHα,probably
d
modeling. We also adopt f = 0.33 for NGC6946. because of contributions from other dust-heating
d
We notethatthis choicebarelyinfluencesthe ther- sources. Masking out the diffuse emission in the
malfractionofthe radioemission,due to the small inter-arm regions and outer disk (i.e., considering
τ (Sect. 3.2). onlythespiralarmsandSFregions),boththeoffset
Hα
and dispersion reduces to 0.11dex and hence both
Of course, it would be preferable not to use
methodsagreewithintheuncertainties( 20%due
a uniform value fd for the whole galaxy, but one tocalibration).Thislikelyindicatesthat∼thediffuse
thatisadaptedtothe geometry(wellmixeddiffuse
mediumorshell-likeinHiiregions, Witt & Gordon dust is not heated by the UV radiation of ionizing
stars.
2000) and the dust column density. However, this
would require specifying the location of the stel-
lar sources and the absorbing dust along the line
3.2. Distribution of the free-free and synchrotron
of sight and solving the radiative transfer problem
emission
with massive numerical computations which is far
from our first order approximation.
Using the corrected Hα emission from the first ap-
In another approach, assuming that the dust proach, we derive the intrinsic Hα intensity, I ,
0
is mainly heated by the massive stars, we cor- according to I = I0 e−τeff. Integration of the de-
rected the Hα emission by combining it with the reddenedHαmapouttoaradiusof11.9kpc(414′′)
TIR (integrated dust luminosity in the 8-1000µm yields a luminosity of L = (3.46 0.05)
Hα
wavelength range): Hα =Hα + 0.0024 TIR 1041ergs−1 that is higher than the fo±reground×-
corr obs
5
Tabatabaei et al.: Radio–FIR correlation in NGC6946
Fig.3. Free-free (left) and synchrotron emission (right) from NGC6946 at 3.5cm (top) and 20cm (bot-
tom). The angular resolution is 18′′ (shown in the lower left corner of the panels) with a grid size of 6′′.
The bars at the right of the images show the intensity values in mJy/beam. Note that the areas are not
the same at 20cm and 3.5cm due to their different observedfields. At 20cm the synchrotronemission is
overlaid with contours of linearly polarized intensity (Beck & Hoernes 1996). The contour levels are 70,
120, 160µJy/beam.
corrected luminosity by 20%. A similar increase where the electron temperature, T , is in units of
e4
in the Hα flux has been≃derived in other nearby 104K, and EM in cm−6 pc. The emission measure
galaxies, M33 ( 13%, Tabatabaei et al. 2007b) is relatedto the continuum opticalthickness, τ , of
c
≃
and M31 ( 30%, Tabatabaei & Berkhuijsen the ionized gas by
≃
2010).
Dickinson et al. (2003) showed that the Hα τc =3.278×10−7aTe−41.35νG−H2.z1(1+0.08)EM, (3)
emitting medium in our Galaxy is optically thick
with a 1 (Dickinson et al. 2003). The factor
to ionizing Lyman photons (case B, Osterbrock ≃
1989) not only for Hii regions (τ 103 1010) (1+0.08)takes into account the contribution from
Lyα ∼ − singly ionized He. The brightness temperature of
but also for faint Hα features at intermediate and
the radio continuum (free-free) emission, T , then
high Galactic latitudes (τ 1 30). Assuming b
Lyα ∼ − follows from
thesameconditionappliesforNGC6946,theemis-
sion measure (EM) follows from the Hα intensity T =T (1 e−τc) . (4)
(in units of ergcm−2s−1 sr−1) via the expression b e −
(Valls-Gabaud 1998) : Eq. (4) with Eqs.(2) and (3) gives:
Tb =Te(1 e−AIHα),
IHα =9.41×10−8Te−41.01710−0T.0e249 EM , (2) (cid:26)A=3.763−aνG−H2.z1Te−40.3100T.0e249. (5)
6
Tabatabaei et al.: Radio–FIR correlation in NGC6946
Table 3.Globalradiocontinuumfluxdensitiesand
thermal fractions in NGC6946.
λ Observed Free-free Thermal
(cm) fluxdensity flux density fraction
(mJy) (mJy) %
3.5 422±65 78± 10 18.4±3.7
20 1444± 215 97± 13 6.7±1.3
tion factor of f = 0.3. For a uniform distribution
d
of dust and ionized gas (f = 0.5), the thermal
d
fractions increase to about 21% and 8% at 3.5 and
20cm, respectively.
Fig.2. Hα luminosity de-reddened based on τ
eff 4. Synchrotron spectral index
versusde-reddeningusingtheTIRluminosity.Also
shown are the lines of 1:1 correspondence (dashed) Usingthenonthermalradiofluxesat3.5and20cm,
and Y=X - 0.19 (solid). we obtained the spectral index of the nonthermal
radio emission. This was only computed for pixels
with flux densities of at least three times the rms
Hence, the free-free emission can be derived noiseatbothfrequencies.Thesynchrotronspectral
separately at each radio wavelength. The result- index,α ,showsasmoothvariationacrossthedisk
n
ing distributions of the intensity of the free-free of NGC6946 (Fig. 4). The greenish color in Fig. 4
emission in mJy/beam at 3.5 and 20cm are shown corresponds to the synchrotron emission with flat
in (Fig. 3, left panels) for3 T = 104K. Using a spectrum (α . 0.7), and the reddish color to the
e n
constant electron temperature is supported by the regionswithasteepspectrum(α &0.9),i.e.emis-
n
shallow metallicity gradient found in this galaxy sion from lower-energyCREs. The flat spectrum is
(Moustakas et al. 2010). Subtracting the free-free found in giant Hii regions and the steep spectrum
emission from the observed radio continuum emis- intheinter-armregions,theeasternpartofthecen-
sion results in a map of the synchrotron emission tral galaxy, and the south of the major axis where
(Fig. 3, right panels). α =1.0 0.1.Asshowninthehistogramrepresen-
n
±
The synchrotron maps exhibit diffuse emission tation (Fig. 5), the median value of α across the
n
extending to large radii indicating diffusion and galaxy is 0.81 with a dispersion of 0.18. Figure 5
propagationoftheCREs.Strongsynchrotronemis- also presentsa histogramofthe ‘observed’spectral
sion emerges from the galaxy center, giant star- index α (obtained using the observedradio data at
forming regions, and spiral arms, which could be 3.5 and 20cm, i.e., contaminated by the free-free
due to stronger magnetic fields and/or young- emission), for comparison,with α 0.7 on the av-
≃
energetic CREs close to the star-forming regions. erage and with a dispersion of 0.16.
Interestingly, the so called ’magnetic arms’ traced
bythelinearlypolarizedintensity(Beck & Hoernes
4.1. Synchrotron spectral index versus star formation
1996) are clearly visible in the 20cm synchrotron
map. The fact that they are less prominent at In the star-forming regions, the synchrotron spec-
3.5cm implies that these arms are filled by older trum is relatively flat with an average index of
and lower energetic CREs (see Sect 4.2). The ther- α =0.65 0.10,the typicalspectral index of young
n
mal free-free map, onthe other hand, exhibits nar- CREs in±SF regions (in supernova remnants, α is
n
row spiral arms dominated by the star-forming re- about 0.5 onthe averageand couldeven be flatter,
gions. see e.g. Gordon et al. 1999; Reynolds et al. 2012;
Integrating the observed, synchrotronand free- Longair 1994, and references therein). Table 4 lists
freemapsintheplaneofthegalaxy(i=38◦)around α in9giantHiiregionsannotatedinFig.4,(called
the center out to a radius of 324′′(9.2kpc), we ob- Ennuc following the nomenclature and location pre-
tainthetotalfluxdensitiesandthermalfractionsat sented in Murphy et al. 2010). Enuc2 and Enuc3
3.5 and 20cm (Table 3). The thermal fractions are have a relatively steep spectrum which could be
about 18% and 7% at 3.5 and 20cm, respectively. due to an energy loss of CREs in a magneto-ionic
As mentioned before, we assumed a dust attenua- medium along the line of sight seen at the position
oftheseHiiregions.ThisispossibleforEnuc3since
3 Smaller values of Te are reported from the mea- this source is adjacentto the strong northern mag-
netic arm (see below). In the neighborhood of the
surements in the Milky Way (e.g. Haffneret al. 1999;
Madsen et al. 2006). Assuming Te = 7000K, the ther- Enuc2,however,nostrongpolarizedemissionisde-
mal fraction would decrease byabout 23%. tected. The estimated spectral index of this source
7
Tabatabaei et al.: Radio–FIR correlation in NGC6946
Fig.5.Histogramofthe observedradiocontinuum
(gray) and synchrotron spectral index (black) in
NGC6946.
Table 4. Thermal fractions and synchrotron spec-
tral index of the giant Hii regions shown in Fig. 4.
Object ft3h.5cm ft2h0cm αn
(%) (%)
Enuc1 50±2 26±1 0.66±0.03
Enuc2 80±4 41±2 0.90±0.08
Enuc3 73±3 34±2 0.86±0.07
Enuc4 41±2 26±1 0.48±0.05
Enuc5 68±1 34±1 0.75±0.05
Enuc6 49±3 23±2 0.70±0.03
Enuc7 56±2 27±2 0.74±0.04
Enuc8 47±2 20±1 0.54±0.02
Enuc9 48±5 23±3 0.70±0.03
the giant Hii regions in Table 4, which is steeper
Fig.4. Synchrotron spectral index map of than our finding and equals to the average α
n
NGC6946 overlaid with contours of the lin- for the entire galaxy. One contributing factor to
early polarized emission at 6cm (top) tracing the their steeper indices could be a result of assum-
ordered magnetic field in the sky plane with the ing a fixed ISM density for the extranuclear re-
same levels as in Fig.3 and of bright Hα sources gions of 0.1cm−3 (motivated by their beam size
(bottom). The Hα contour levels are 18, 24, 35, area of 30′′ 0.9kpc), leading to dominant syn-
and 47% of the maximum intensity. The 9 giant chrotron and∼IC losses rather than the ionization
Hii regions are indicated (Table 4). The bars at and bremsstrahlung cooling mechanisms of CREs
the right of the images show the values of the (and hence a rather steep spectrum for these ob-
synchrotronspectral index. jects). In the present work, we determine α at
n
a smaller beam size of 0.5kpc (the scale of the
∼
giant SF regions in NGC6946 Kennicutt & Evans
2012)andwithoutanyassumptionontheISMden-
could be affected by an underestimate of the ob- sity and/or cooling mechanism of CREs. On these
served3.5cmemission,since this sourcesits onthe scales, more energetic CREs and/or stronger mag-
edge of the 3.5cm observed field (primary beam). netic fields close to the SF regionsprovidethe syn-
chrotronemissionwith a flatter α on the average.
Consideringsynchrotron,inverse-Compton,ion- n
ization,andbremsstrahlungcoolingmechanismsof Table4alsoliststhethermalfractionsat3.5cm
CREs as well as using a prescription for the es- and20cmintheseextranuclearHiicomplexes.The
cape of these particles, Murphy et al. (2010) mod- thermalfractionsat3.5cmarehigherthanthoseat
eled the radio SEDs and found an α 0.8 for 20cmbyafactorofabouttwo(apartfromEnuc4).
n
≃
8
Tabatabaei et al.: Radio–FIR correlation in NGC6946
4.2. Synchrotron spectral index versus magnetic
fields
The magnetic fields in NGC6946 have been
extensively studied by Beck & Hoernes (1996),
Rohde et al. (1999), and Beck (2007). The con-
tours in Fig. 4 show the linearly polarized inten-
sity (PI) at 6.3cm which determines the strength
of the ordered magnetic field in the plane of the
sky (see e.g. Tabatabaei et al. 2008). Interestingly,
there is a good correspondence between the steep
synchrotronemissionandthePI,particularlyalong
the northernmagneticarm(Beck & Hoernes 1996)
and also along the strong ordered magnetic field
in the central disk (anisotropic turbulent magnetic
field, Beck 2007). In these regions, the spectral
index of α = 1.0 0.1 indicates that CREs
n
±
suffer strong synchrotron losses propagating along
NGC6946’s ordered magnetic field.
Overall, the synchrotron spectral index map
agrees with the energy loss theory of relativistic
electrons propagating away from their origin in
star-forming regions in the ISM (e.g. see Chapter
18ofLongair1994;Biermann et al.2001).The dif-
ference in α in star-formingregions and along the
n
magnetic arms in NGC6946 is similar to that pre-
dictedbyFletcher et al.(2011)forthespiralgalaxy
M51.
5. Maps of total and turbulent magnetic
fields
The strength of the total magnetic field B can
tot
be derived from the total synchrotron intensity.
Assuming equipartition between the energy densi-
ties of the magnetic field and cosmic rays (ε =
CR
ε =B2 /8π):
Btot tot
Btot =C(αn,K,L) In αn1+3, (6) Fig.6. Strength of the total Btot (top) and tur-
bulent B (bottom) magnetic fields in NGC6946.
(cid:2) (cid:3) tur
where I is the nonthermal intensity and C is a The bars at the top of each image show the mag-
n
function of α , K the ratio between the num- netic field strength in µGauss.
n
ber densities of cosmic ray protons and elec-
trons, and L the pathlength through the syn-
chrotron emitting medium (see Beck & Krause lent magnetic field B 4. Using this intensity with
tur
2005; Tabatabaei et al. 2008). Using the maps of Eq. (6) yields the distribution of B across the
tur
I and α obtained from the TRT method and as- galaxy. Similar to B , B is higher in places of
n n tot tur
suming that the magnetic field is parallel to the star-formingregions(Fig.6,bottom).Wenotethat
plane of the galaxy (inclination of i = 38◦ and po- any ordered field which is not resolved and depo-
sition angle of the major axis of PA=242◦), B larized within the beam would contribute to the
tot
isderivedacrossthe galaxy.Inourcalculations,we turbulentmagneticfield.Inotherwords,wecannot
applyvaluesofK 100(Beck & Krause2005)and distinguishbetweenunresolvedstructuresoftheor-
≃
L 1kpc/cosi. Figure 6 shows strong B in the dered field and truly turbulent fields for structures
tot
≃
centralregionofthe galaxy,the arms andthe star- smaller than the beam.
forming regions. Themagneticfieldstrengthestimatedusingthe
As a fraction of the polarizedintensity PI is re- ‘standard method’ for thermal/nonthermalsepara-
lated to the strength of the orderedmagnetic field,
and the nonthermal intensity I to the total mag-
n 4 In a completely ordered magnetic field, the maxi-
netic field in the plane of the sky, I (PI/0.75)
n
− mum degree of linear polarization is about 0.75 (e.g.
gives the nonthermal emission due to the turbu-
Westfold 1959)
9
Tabatabaei et al.: Radio–FIR correlation in NGC6946
tion, i.e. assuming a fixed synchrotron spectral in- values are large (> 33) indicating that the fitted
dex (see Appendix A), is similar to the TRT es- slopesarestatistically significant.With coefficients
timate (within 10% difference) in the spiral arms, of r 0.8, good correlations hold between the
c
and is underestimated by 35% in the giant Hii re- FIRba≥ndsandobservedradio(RC)/free-freeemis-
gions, and 45% in the nucleus. This is because, in sion.The FIRcorrelationcoefficients withthe syn-
those regions, I is smaller and α is larger based chrotronemissionareslightlylowerthanthosewith
n n
on the standard method. the free-free emission.
The synchrotronemission is slightly better cor-
related with the 250µm emission (as a proxy for
6. Radio-FIR Correlation
cold dust) than with the 70µm emission (as a
The radio correlations with both monochro- proxyfor warmdust). Onthe contrary,a free-free–
matic and bolometric FIR observations are ob- cold/warm dust differentiation is only hinted, but
tained using three different approaches: classical not yet clear given the errors from the r values.
c
pixel-to-pixel (Pearson correlation), wavelet multi- The free-free emission exhibits an almost linear
scale (Frick et al. 2001), and the q-ratio method correlation with the warmer dust emission at 70
(Helou et al.1985). Although the maingoalof this and 100µm (with a slope of b 0.9). The correla-
paper is to investigate the synchrotron–FIR corre- tion becomes more and more s≃ub-linear with dust
lation,wealsopresentthecorrelationsbetweenthe emission probed at 160 and 250µm.
emissions of the thermal free-free and each of the
The synchrotron emission, on the other hand,
monochromatic FIR bands.
tendstoshowalinearcorrelationwithcolderrather
thanwarmerdust(withasuper-linearcorrelation).
6.1. Classical correlation A similar trend is also seen between the observed
RC and FIR bands.
The pixel-to-pixel correlation is the simplest mea-
Super-linear radio–FIR correlations have been
sureofthecorrelationbetweentwoimages,f (x,y)
1 alsofoundforsamplesofgalaxiesbyPrice & Duric
and f (x,y), with the same angular resolution and
2 (1992) and Niklas (1997a), which were attributed
the same number of pixels using Pearson’s linear
to the non-linearity of the synchrotron–FIR corre-
correlation coefficient, r 5:
c lation and/or to the fact that colder dust may not
Σ(f f )(f f ) benecessarilyheatedbytheyoungmassivestars.A
1i 1 2i 2
r = −h i −h i (7)
c better synchrotron–cold than –warm dust correla-
Σ(f f )2Σ(f i f )2
1i−h 1i 2 −h 2i tion was also found in M31 (Hoernes et al. 1998)
p
When the two images are identical, r = 1. The and in a sample of late-type galaxies (Xu et al.
c
correlation coefficient is r =-1 for images that are 1994).
c
perfectly anti-correlated. The formal error on the One possible issue is that our use of the dust
correlation coefficient depends on the strength of mass to de-redden the Hα emission, and thus the
thecorrelationandthenumberofindependentpix- free-freeemission,issomehowinfluencingthecorre-
els, n, in an image: ∆rc = 1−rc2/√n−2. lations.Totestthis,were-derivethefree-freeemis-
Wecalculatedthecorrelpationsbetweenboththe sionusing theobservedHαemission(notcorrected
radio free-free/synchrotron and the FIR 70, 100, forextinction)andre-visitthethermal/nonthermal
160, and 250µm maps, restricting the intensities correlations with the FIR bands. The results are
to >3 rms noise. We obtained sets of indepen- givenin parenthesis in Table 5. The differences are
×
dent data points (n) i.e. a beam area overlap of less than 4% and within the errors.
< 20%, by choosing pixels spaced by more than
The synchrotron emission based on the stan-
one beamwidth. Since the correlated variables do
dard method also shows a decrease of the slope
notdirectlydependoneachother,wefittedapower
with increasing FIR wavelength (Table 6), similar
law to the bisector in each case (Isobe et al. 1990;
to the TRT based study. However, the expected
Hoernes et al. 1998). The Student’s t-test is also
better linearity of the free-free–warmer dust is not
calculated to indicate the statistical significance
seen using the standard thermal/nonthermal sepa-
of the fit. For a number of independent points of
rationmethod.AsshowninSect.5,inourresolved
n > 100, the fit is significant at the 3σ level if
study, this method results in an excess of the free-
t>3 (e.g. Wall 1979). Errorsin the slope b of the
free diffuse emissioninthe inter-armregionswhere
bisector are standard deviations (1σ).
there is no warm dust and TIR counterparts. This
The results for both radio wavelengths are pre-
ismostprobablycausedby neglectingvariationsof
sented in Table 5. The calculated Student’s t-test
α locallyacrossthegalaxy,sinceinglobalstudies,
n
the standard separation method leads to a linear
5 Please note that using this method it is not possi- thermalradio–FIRcorrelation(e.g. Niklas1997b).
bletoseparate variationsduetoachangeof thephysi- Based on the standard method, the separated RC
cal properties with scale e.g. propagation of CREs(see components are not as tightly correlated with the
Sect. 6.2). FIR bands as the observed RC–FIR correlations.
10