The Resolved Radio--FIR Correlation in Nearby Galaxies with Herschel and Spitzer

We investigate the correlation between the far-infrared (FIR) and radio continuum emission from NGC6946 on spatial scales between 0.9 and 17 kpc. We use the Herschel PACS (70, 100, 160$\mu$m) and SPIRE (250$\mu$m) data from the KINGFISH project. Separating the free-free and synchrotron components of the radio continuum emission, we find that FIR is better correlated with the free-free than the synchrotron emission. Compared to a similar study in M33 and M31, we find that the scale dependence of the synchrotron--FIR correlation in NGC6946 is more similar to M31 than M33. The scale dependence of the synchrotron--FIR correlation can be explained by the turbulent-to-ordered magnetic field ratio or, equivalently, the diffusion length of the cosmic ray electrons in these galaxies.