The Spectral Energy Distributionof Galaxies Proceedings IAU Symposium No. 284, 2011 (cid:13)c 2011International AstronomicalUnion R.J. Tuffs & C.C.Popescu, eds. DOI:00.0000/X000000000000000X The Resolved Radio–FIR Correlation in Nearby Galaxies with Herschel and Spitzer Fatemeh S. Tabatabaei1, Eva Schinnerer2, Eric Murphy3, Rainer Beck4, Annie Hughes5, Brent Groves6, and The KINGFISH Team 1Max-Planck-Institutfu¨r Astronomie, K¨onigstuhl 17, 69117-Heidelberg, Germany email: [email protected] 2Max-Planck-Institutfu¨r Astronomie, K¨onigstuhl 17, 69117-Heidelberg, Germany 2 email: [email protected] 1 3The Observatories of the Carnegie Institution for Science, CA 911101, USA 0 email: [email protected] 2 4Max-Planck-Institutfu¨r Radioastronomie, Aufdem Hu¨gel 69, 53121-Bonn, Germany n email: [email protected] a J 5Max-Planck-Institutfu¨r Astronomie, K¨onigstuhl 17, 69117-Heidelberg, Germany email: [email protected] 1 1 6Max-Planck-Institutfu¨r Astronomie, K¨onigstuhl 17, 69117-Heidelberg, Germany email: [email protected] ] O Abstract. We investigate the correlation between the far-infrared (FIR) and radio continuum C emission from NGC6946 on spatial scales between 0.9 and 17kpc. We use the Herschel PACS . (70, 100, 160µm) and SPIRE (250µm) data from the KINGFISH project. Separating the free- h free and synchrotron components of the radio continuum emission, we find that FIR is better p correlatedwiththefree-freethanthesynchrotronemission.ComparedtoasimilarstudyinM33 - o andM31, wefindthat thescale dependenceofthesynchrotron–FIRcorrelation in NGC6946 is r moresimilartoM31thanM33.Thescaledependenceofthesynchrotron–FIRcorrelationcanbe t s explained by the turbulent-to-ordered magnetic field ratio or, equivalently,the diffusion length a of the cosmic ray electrons in these galaxies. [ Keywords. Starformation, ISM,Magnetic field, Cosmic ray electrons. 2 v 2 5 1. Introduction 2 6 The correlation between the radio and far-infrared (FIR) luminosities of galaxies has . been shown to be invariant over more than 4 orders of magnitude and out to a redshift 1 of z ∼ 3 (e.g. Sargent et al. 2010). It is only recently that variations in the radio-FIR 1 1 correlation have become apparent when studying correlations on different scales within 1 galaxies.Detailedmulti-scaleanalysisoftheradioandFIRdatashowedthatthesmallest : scaleonwhichtheradio-FIRcorrelationholdsisnotthesameintheLMC(Hughesetal. v i 2006),M51(Dumasetal.2010),M31andM33(Tabatabaeietal.2007a,submitted);the X reasonisstillunclear.Couldmassivestarformationalonecausesuchvariations?Whatis r the influence of the dust heating sources?Are differences in the magnetic field structure a important? And what is the role of the propagationof cosmic ray electrons (CREs)? One factthat makesthe link betweenstar formationandFIR less obviousis that FIR emission consists of at least two emission components: cold dust and warm dust. The cold dust emission may not be directly linked to the young stellar population, but is rather powered by the interstellar radiation field (ISRF, Xu 1990). Furthermore, it is necessary to distinguish between the two main radio continuum (RC) components, free- freeandsynchrotronemission.Thefree-freeemissionfromelectronsinHIIregionsaround 1 2 Tabatabaei et al. Figure 1. 20cm synchrotron (left) and free-free emission (right) from NGC6946 at 18” resolution. The units are in mJy/beam. Here externalradio sources havebeen blanked. young,massivestars is expected to be closely connectedto the warmdust emission that is heated by those same stars. Although the synchrotron-emitting CREs also originate fromstar forming regions(i.e. supernovaeremnants;the final episodes ofmassive stars), the synchrotron–FIR correlation may not be as tight as the free-free–FIR correlation locally, as a result of diffusion of the cosmic ray electrons from their production sites. 2. Free-free and synchrotron emission from NGC6946 Tabatabaeietal.(2007b)presentedamethodtoseparatethefree-freeandsynchrotron components of the RC emission from M33, in which a de-reddened Hα map was used as a template for the free-free emission. Using the same method, we derive the free-free emissionfromNGC6946at20cm.Subtractionofthefree-freeemissionfromtheobserved 20cm(VLA +Effelsberg,Beck1991)emissionthenyields the synchrotronmap(Fig.1). Diffusion/propagationof the CREs is evident from the synchrotronmap, which shows a diffuse extended emission as well as strong emission from the galaxy center, giant star forming regions, and spiral arms. The thermal free-free emission has a more clumpy distribution following star forming regions. The thermal fraction is about 8% at 20cm. 3. Wavelet correlation Usinga2Dcontinuouswavelettransformation(’Pet-hat’,Fricketal.2001),wedecom- pose the Herschel PACS/SPIRE FIR and the 20cm maps into 8 spatial scales (a) from 0.9 (∼ twice our linear resolution of 18”) to 17kpc. For each scale of decomposition, we derive cross-correlationcoefficients (rw) between the FIR and RC maps. Figure 2 shows rw(a) betweenthe 70µmandthe free-free/synchrotronemissionin NGC6946,compared with similar correlations in M33 and M31 (Tabatabaei et al. submitted). Radio-FIR correlation in nearby galaxies 3 Figure 2. Multi-scale correlations between 70µm FIR and free-free (left), synchrotron (right) emission from NGC6946, compared to those in M31 and M33. 4. Results The free-free–FIR correlation is stronger than the synchrotron–FIR correlation in NGC6946 as seen in the other two galaxies. Interestingly, the free-free–FIR correlation exhibits a moreorlesssimilar trendinthese galaxies,unlike the synchrotron–FIRcorre- lationwhichshowsmorevariationwithscalea.InNGC6946,thesynchrotron–FIRcorre- lationdecreasestowardssmallerscales.SuchatrendisalsoseeninM31,M51(Dumaset al.2011),andtheLMC(Hughesetal.2006)butnotinM33whichshowsastrongercorre- lationonsmallscalesandweakeronlargerscales(3-5kpc).Whatcausesthesevariations? Assuming that massive stars are the common source of the free-free, FIR (via heating the dust), and synchrotron emission, the synchrotron–FIR variations must be linked to variationsinmagneticfields(structureandstrength)anddiffusion/propagationofCREs. One wouldexpect a better correlationon small scales (∼ 100pc) in galaxieswith higher star formationrate (SFR) due to the strongerturbulent magnetic field and/orhigh con- centrationofyoungCREsneartheirstarformingregions(e.g.Murphyetal.2006).This is evident for M33 which has a 5 times higher SFR surface density, Σ(SFR), than M31 (Tabatabaei & Berkhuijsen 2010). This cannot be investigated in NGC6946, since there is no information for scales < 1kpc. On the other hand, including the LMC and M51 suggests that the smallest scale on which the radio–FIR correlation holds (rw >0.5), is better correlated with the ratio of turbulent-to-ordered magnetic field, which in turn is relatedtothediffusionlengthofCREs(Yan&Lazarian2004),ratherthanwithΣ(SFR) (Tabatabaei et al. submitted). On large scales (a > 1kpc), the synchrotron emission is due to an ordered (uniform) magnetic field and diffused, older CREs. The ordered magnetic field is controlled by variousdynamical,environmentaleffectscausedby,e.g.,galacticrotation,densitywaves, shear and anisotropic compressions in spiral arms (e.g. Fletcher et al. 2011). A good synchrotron–FIRcorrelationonlargescales is expected when enoughdiffuse CREs exist and that they have opportunity to explore the gaseous/dusty components of a galaxy (Hughes et al. 2006). This would require a confinement of the magnetic field to the gas. We plot a schematic view of this condition in Fig.3, showing sources of the FIR and synchrotronemission and factors which control their correlation on small and large scales. 4 Tabatabaei et al. Figure 3. A sketch of various sources of the synchrotron and FIR emission and important factors controlling thesynchrotron-FIRcorrelation on small and large scales in a galaxy. 5. Summary We derived radio–FIR correlations as a function of scale for NGC6946, separately for free-free and synchrotron emission, and for various Herschel FIR bands (70, 100, 160, and 250µm). Our main results are summarized as follows: - We find strong synchrotron emission from the central part and around star-forming regions.ThisisexplainedbythedirectproportionalitybetweenSFRandturbulentmag- netic field/ young CREs. In addition a smooth diffuse emission is present. - The wavelet power spectrum of the synchrotron emission is stronger on scales >1kpc than < 1kpc, possibly due to fast diffusion of CREs in the strong, ordered magnetic field. -TheFIRandfree-freeemissionsarecorrelatedonallscales;abettercorrelationisfound with warmer dust. - The FIR and synchrotronemissionmay not be correlatedon some scales, due to diffu- sion of CREs and/or magnetic field structures. 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