  In order to understand the cosmic ray propagation mechanism in galaxies, and
its correlation with the sites of star formation, we compare the spatially
resolved radio spectral index of three spiral galaxies with their IR
distribution. We present new low-frequency radio continuum observations of the
galaxies NGC 0628, NGC 3627, and NGC 7331, taken at 327 MHz with the Very Large
Array. We complemented our data set with sensitive archival observations at 1.4
GHz and we studied the variations of the radio spectral index within the disks
of these spiral galaxies. We also compared the spectral index distribution and
the IR distribution, using 70 $\mu$m Spitzer observations. We found that in
these galaxies the non-thermal spectral index is anticorrelated with the radio
brightness. Bright regions, like the bar in NGC 3627 or the circumnuclear
region in NGC 7331, are characterized by a flatter spectrum with respect to the
underlying disk. Therefore, a systematic steepening of the spectral index with
the increasing distance from the center of these galaxies is observed.
Furthermore, by comparing the radio images with the 70 $\mu$m images of the
Spitzer satellite we found that a similar anticorrelation exists between the
radio spectral index and the infrared brightness, as expected on the basis of
the local correlation between the radio continuum and the infrared emission.
Our results support the idea that in regions of intense star formation the
electron diffusion must be efficient. The observed anticorrelation between
radio brightness and spectral index, may imply that the cosmic ray density and
the magnetic field strength are significantly higher in these regions than in
their surroundings.
