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

We derive the distribution of the synchrotron spectral index across NGC6946 and investigate the correlation between the radio continuum (synchrotron) and far-infrared (FIR) emission using the KINGFISH Herschel PACS and SPIRE data. The radio--FIR correlation is studied as a function of star formation rate, magnetic field strength, radiation field strength, and the total gas surface brightness. The synchrotron emission follows both star-forming regions and the so-called magnetic arms present in the inter-arm regions. The synchrotron spectral index is steepest along the magnetic arms ($\alpha_n \sim 1$), while it is flat in places of giant H{\sc ii} regions and in the center of the galaxy ($\alpha_n \sim 0.6-0.7$). The map of $\alpha_n$ provides an observational evidence for aging and energy loss of cosmic ray electrons propagating in the disk of the galaxy. Variations in the synchrotron--FIR correlation across the galaxy are shown to be a function of both star formation and magnetic fields. We find that the synchrotron emission correlates better with cold rather than with warm dust emission, when the interstellar radiation field is the main heating source of dust. The synchrotron--FIR correlation suggests a coupling between the magnetic field and the gas density. NGC6946 shows a power-law behavior between the total (turbulent) magnetic field strength B and the star formation rate surface density $\Sigma_{\rm SFR}$ with an index of 0.14\,(0.16)$\pm$0.01. This indicates an efficient production of the turbulent magnetic field with the increasing gas turbulence expected in actively star forming regions. The scale-by-scale analysis of the synchrotron--FIR correlation indicates that the ISM affects the propagation of old/diffused cosmic ray electrons, resulting in a diffusion coefficient of $D_0=4.6\times 10^{28}$\,cm$^2$\,s$^{-1}$ for 2.2\,GeV CREs.