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(abridged) Within nearby galaxies, variations in the radio-FIR correlationhave been observed, mainly because the cosmic ray electrons migrate before theylose their energy via synchrotron emission or escape. The major cosmic rayelectron transport mechanisms within the plane of galactic disks are diffusionand streaming. A predicted radio continuum map can be obtained by convolvingthe map of comic ray electron sources, represented by that of the starformation, with adaptive Gaussian and exponential kernels. The ratio betweenthe smoothing lengthscales at 6cm and 20cm can be used to distinguish betweendiffusion and streaming as the dominant transport mechanism. Star formationmaps of eight rather face-on local and Virgo cluster spiral galaxies wereconstructed from Spitzer and Herschel infrared and GALEX UV observations.Thesemaps were convolved with adaptive Gaussian and exponential smoothing kernels toobtain model radio continuum emission maps. It is found that in asymmetricridges of polarized radio continuum emission the total power emission isenhanced with respect to the star formation rate. The typical lengthscale forthe transport of cosmic ray electrons is l=0.9kpc at 6cm and l=1.8kpc at 20cm.Perturbed spiral galaxies tend to have smaller lengthscales. This is a naturalconsequence of the enhancement of the magnetic field caused by the interaction.The discrimination between the two cosmic ray electron transport mechanisms,diffusion and streaming, is based on (i) the convolution kernel (Gaussian orexponential),(ii) the dependence of the smoothing kernel on the local magneticfield and hence on the local star formation rate, (iii) the ratio between thetwo smoothing lengthscales via the frequency-dependence of the smoothingkernel, and (iv) the dependence of the smoothing kernel on the ratio betweenthe ordered and the turbulent magnetic field.

Deciphering the radio-star formation correlation on kpc-scales I. Adaptive kernel smoothing experiments