Deciphering the radio-star formation correlation on kpc-scales I.
  Adaptive kernel smoothing experiments
  (abridged) Within nearby galaxies, variations in the radio-FIR correlation
have been observed, mainly because the cosmic ray electrons migrate before they
lose their energy via synchrotron emission or escape. The major cosmic ray
electron transport mechanisms within the plane of galactic disks are diffusion
and streaming. A predicted radio continuum map can be obtained by convolving
the map of comic ray electron sources, represented by that of the star
formation, with adaptive Gaussian and exponential kernels. The ratio between
the smoothing lengthscales at 6cm and 20cm can be used to distinguish between
diffusion and streaming as the dominant transport mechanism. Star formation
maps of eight rather face-on local and Virgo cluster spiral galaxies were
constructed from Spitzer and Herschel infrared and GALEX UV observations.These
maps were convolved with adaptive Gaussian and exponential smoothing kernels to
obtain model radio continuum emission maps. It is found that in asymmetric
ridges of polarized radio continuum emission the total power emission is
enhanced with respect to the star formation rate. The typical lengthscale for
the 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 natural
consequence 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 or
exponential),(ii) the dependence of the smoothing kernel on the local magnetic
field and hence on the local star formation rate, (iii) the ratio between the
two smoothing lengthscales via the frequency-dependence of the smoothing
kernel, and (iv) the dependence of the smoothing kernel on the ratio between
the ordered and the turbulent magnetic field.
