Nearby galaxies in the LOFAR Two-metre Sky Survey I. Insights into the non-linearity of the radio-SFR relation

Context. Cosmic rays and magnetic fields are key ingredients in galaxy evolution, regulating both stellar feedback and star formation. Their properties can be studied with low-frequency radio continuum observations that are free from thermal contamination. Aims. We define a sample of 76 nearby (<30 Mpc) galaxies with rich ancillary data in the radio continuum and infrared from the CHANG-ES and KINGFISH surveys, which will be observed with the LOFAR Two-metre Sky Survey (LoTSS) at 144 MHz. Methods. We present maps for 45 of them as part of the LoTSS data release 2 (LoTSS-DR2), where we measure integrated flux densities and study integrated and spatially resolved radio spectral indices. We investigate the radio-star formation rate (SFR) relation using SFRs derived from total infrared and H alpha + 24-mu m emission. Results. The radio-SFR relation at 144 MHz is clearly super-linear with L-144mHz proportional to SFR1,4-1,5. The mean integrated radio spectral index between 144 and approximate to 1400 MHz is <alpha > = -0.56 +/- 0.14, in agreement with the injection spectral index for cosmic ray electrons (CRE5). However, the radio spectral index maps show variation of spectral indices with flatter spectra associated with star-forming regions and steeper spectra in galaxy outskirts and, in particular, in extra-planar regions. We found that galaxies with high SFRs have steeper radio spectra; we find similar correlations with galaxy size, mass, and rotation speed. Conclusions. Galaxies that are larger and more massive are better electron calorimeters, meaning that the CRE lose a higher fraction of their energy within the galaxies. This explains the super-linear radio-SFR relation, with more massive, star-forming galaxies being radio bright. We propose a semi-calorimetric radio-SFR relation that employs the galaxy mass as a proxy for the calorimetric efficiency.