  We study the spatially resolved Radio Continuum-Star Formation Rate (RC-SFR)
relation using state-of-the-art star-formation (SF) tracers in a sample of 17
THINGS galaxies. We use hybrid Sigma_SFR maps (GALEX FUV plus Spitzer 24 mu),
RC maps at 22/18 cm from the WSRT SINGS survey, and H-alpha maps to correct for
thermal RC emission. We compare azimuthally averaged radial profiles of the RC
and FUV/MIR-based Sigma_SFR maps and study pixel-by-pixel correlations at fixed
linear scales of 1.2 and 0.7 kpc. The ratio of the integrated SFRs from the RC
emission to that of the FUV/MIR-based SF tracers is R_int = 0.78 +/- 0.38,
consistent with Condon's relation. We find a tight correlation between the
radial profiles of the radio and FUV/MIR-based Sigma_SFR for the entire extent
of the disk. The ratio R of the azimuthally averaged radio to FUV/MIR-based
Sigma_SFR agrees with the integrated ratio with only small quasi-random
fluctuations as function of radius. Pixel-by-pixel plots show a tight
correlation in log-log diagrams of radio to FUV/MIR-based Sigma_SFR, with a
typical standard deviation of a factor of two. Averaged over our sample we find
(Sigma_SFR)_RC ~ (Sigma_SFR)_hyb^{0.63+/-0.25} implying that data points with
high Sigma_SFR are relatively radio dim, whereas the reverse is true for low
Sigma_SFR. We interpret this as a result of spectral ageing of CRe, which is
supported by the radio spectral index: data points dominated by young CRe are
relatively radio dim, those dominated by old CRe are relatively radio bright.
The ratio of radio to FUV/MIR-based integrated SFR is independent of global
galaxy parameters, suggesting that we can use RC emission as a universal SF
tracer for galaxies, if we restrict ourselves to global or azimuthally averaged
measurements. A magnetic field-SFR relation, B ~ SFR_hyb^{0.30+/-0.02}, holding
both globally and locally, can explain our results. (abridged)
