The Radio Continuum-Star Formation Rate Relation in WSRT SINGS Galaxies

We present a study of the spatially resolved radio continuum-star formation rate (RC-SFR) relation using state-of-the-art star formation tracers in a sample of 17 THINGS galaxies. We use SFR surface density (ΣSFR) maps created by a linear combination of GALEX far-UV (FUV) and Spitzer 24 μm maps. We use RC maps at λλ22 and 18 cm from the WSRT SINGS survey and Hα emission maps to correct for thermal RC emission. We compare azimuthally averaged radial profiles of the RC and FUV/mid-IR (MIR) based ΣSFR 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 \mathscr{R}_int = 0.78+/- 0.38, consistent with the relation by Condon. We find a tight correlation between the radial profiles of the radio and FUV/MIR-based ΣSFR for the entire extent of the disk. The ratio \mathscr{R} of the azimuthally averaged radio to FUV/MIR-based ΣSFR agrees with the integrated ratio and has only quasi-random fluctuations with galactocentric radius that are relatively small (25%). Pixel-by-pixel plots show a tight correlation in log-log diagrams of radio to FUV/MIR-based ΣSFR, with a typical standard deviation of a factor of two. Averaged over our sample we find (\Sigma _{SFR})_{RC}\propto (\Sigma _{SFR})_{{hyb}}^{0.63+/- 0.25}, implying that data points with high ΣSFR are relatively radio dim, whereas the reverse is true for low ΣSFR. We interpret this as a result of spectral aging of cosmic-ray electrons (CREs), which are diffusing away from the star formation sites where they are injected into the interstellar medium. This is supported by our finding that the radio spectral index is a second parameter in pixel-by-pixel plots: those data points dominated by young CREs are relatively radio dim, while those dominated by old CREs are slightly more RC bright than what would be expected from a linear extrapolation. We studied the ratio \mathscr{R} of radio to FUV/MIR-based integrated SFR as a function of global galaxy parameters and found no clear correlation. This suggests that we can use RC emission as a universal star formation tracer for galaxies with a similar degree of accuracy as other tracers, if we restrict ourselves to global or azimuthally averaged measurements. We can reconcile our finding of an almost linear RC-SFR relation and sub-linear resolved (on 1 kpc scale) RC-ΣSFR relation by proposing a non-linear magnetic field-SFR relation, B\propto SFR_{{hyb}}^{0.30+/- 0.02}, which holds both globally and locally.