The Radio Spectral Energy Distribution and Star Formation Rate Calibration in Galaxies

We study the spectral energy distribution (SED) of the radio continuum emission from the KINGFISH sample of nearby galaxies to understand the energetics and origin of this emission. Effelsberg multi-wavelength observations at 1.4GHz, 4.8GHz, 8.5GHz, and 10.5GHz combined with archive data allow us, for the first time, to determine the mid-radio continuum (1-10 GHz, MRC) bolometric luminosities and further present calibration relations vs. the monochromatic radio luminosities. The 1-10 GHz radio SED is fitted using a Bayesian Markov Chain Monte Carlo (MCMC) technique leading to measurements for the nonthermal spectral index and the thermal fraction f_th with mean values of alpha_nt=0.97+-0.16 (0.79+-0.15 for the total spectral index) and f_th= 10% +- 9% at 1.4 GHz. The MRC luminosity changes over ~3 orders of magnitude in the sample. The thermal emission is responsible for ~23% of the MRC on average. We also compare the extinction-corrected diagnostics of star formation rate with the thermal and nonthermal radio tracers and derive the first star formation calibration relations using the MRC radio luminosity. The nonthermal spectral index flattens with increasing star formation rate surface density, indicating the effect of the star formation feedback on the cosmic ray electron population in galaxies. Comparing the radio and IR SEDs, we find that the FIR-to-MRC ratio could decrease with star formation rate, due to the amplification of the magnetic fields in star forming regions. This particularly implies a decrease in the ratio at high redshifts, where mostly luminous/star forming galaxies are detected.