A detailed study of the radio-FIR correlation in NGC 6946 with Herschel-PACS/SPIRE from KINGFISH

We derive the distribution of the synchrotron spectral index across NGC 6946 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 density. 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 (α_n ~ 1), while it is flat in places of giant Hii regions and in the center of the galaxy (α_n ~ 0.6−0.7). The map of α_n provides observational evidence for aging and energy loss of cosmic ray electrons (CREs) 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 field strength. We find that the synchrotron emission correlates better with cold rather than with warm dust emission, when the diffuse 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. NGC 6946 shows a power-law behavior between the total (turbulent) magnetic field strength B and the star formation rate surface density Σ_(SFR) with an index of 0.14 (0.16) ± 0.01. This indicates an efficient production of the turbulent magnetic field with the increasing gas turbulence expected in actively star forming regions. Moreover, it is suggested that the B-Σ_(SFR) power law index is similar for the turbulent and the total fields in normal galaxies. On the other hand, for galaxies interacting with the cluster environment this index is steeper for turbulent magnetic fields than it is for the total magnetic fields. The scale-by-scale analysis of the synchrotron-FIR correlation indicates that the ISM affects the propagation of old/diffused CREs, resulting in a diffusion coefficient of D_0 = 4.6 × 10^(28) cm^2 s^(-1) for 2.2 GeV CREs.