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.
