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

One of the tightest correlations in astronomy is the relation between the integrated radio continuum and the far-infrared (FIR) emission. 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 cosmic-ray electron sources, represented by that of the star formation, with adaptive Gaussian and exponential kernels. The ratio between the smoothing lengthscales at 6 cm and 20 cm can be used to determine, between diffusion and streaming, which is the dominant transport mechanism. The dependence of the smoothing lengthscale on the star formation rate bears information on the dependence of the magnetic field strength, or the ratio between the ordered and turbulent magnetic field strengths on star formation. 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 was found that in asymmetric ridges of polarized radio continuum emission, the total power emission is enhanced with respect to the star formation rate. At a characteristic star formation rate of $\dot{\Sigma}_*=8 \times 10^{-3}\,M_{\odot}$ yr−1 kpc−2, the typical lengthscale for the transport of cosmic-ray electrons is l = 0.9 ± 0.3 kpc at 6 cm, and l = 1.8 ± 0.5 kpc at 20 cm. 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 thus 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. Based on our empirical results, methods (i) and (ii) cannot be used to determine the cosmic ray transport mechanism. Important asymmetric large-scale residuals and a local dependence of the smoothing length on Bord/Bturb are most probably responsible for the failure of methods (i) and (ii), respectively. On the other hand, the classifications based on l6 cm/l20 cm (method iii) and Bord/Bturb (method iv), are well consistent and complementary. We argue that in the six Virgo spiral galaxies, the turbulent magnetic field is globally enhanced in the disk. Therefore, the regions where the magnetic field is independent of the star formation rate are more common. In addition, Bord/Bturb decreases, leading to a diffusion lengthscale that is smaller than the streaming lengthscale. Therefore, cosmic ray electron streaming dominates in most of the Virgo spiral galaxies