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 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 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 .
NGC 6946 shows a power-law behavior between the total ( turbulent ) magnetic field strength B and the star formation rate surface density \Sigma _ { 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 .
Moreover , it is suggested that the B- \Sigma _ { SFR } power law index is similar for the turbulent and the total fields in normal galaxies , while it is steeper for the turbulent than for the total fields in galaxies interacting with the cluster environment .
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 .