Nearby galaxies in the LOFAR Two-metre Sky Survey IV. A fundamental plane of the radio-SFR relation
Radio continuum emission has the potential to be an extinction-free tracer of star formation. However, the relation between radio continuum luminosity and star formation rate, the radio-SFR relation, is affected by various effects such as cosmic-ray transport, free-free absorption, and cosmic-ray electron energy losses. We aim to calibrate the radio-SFR relation in a sample of nearby galaxies ranging from dwarf to spiral galaxies covering nearly five orders of magnitude in SFR range. We include, both, global (individual galaxies) and local (kiloparsec sized) measurements. We measured radio continuum luminosities at $144\,\rm MHz$ using observations with the LOw Frequency ARray (LOFAR) and measure radio spectral indices using ancillary $1.4\,\rm GHz$ data. Selecting 70 nearby (distance $d < 30\,\rm Mpc$) galaxies, 15 of which were used for local measurements, with rich ancillary data we present a study of the radio-SFR relation using total infrared, mid-infrared, H$α$, and far-ultraviolet as complementary SFR tracers. About one third of our sample are at least moderately star-forming edge-on galaxies with the remaining ones chosen to be a representative sample of a wide range of morphological types and SFR values. For the first time, we show that the radio luminosity ($L_{144}$), the star-formation rate (SFR), and the radio spectral index ($α$) define a 'fundamental plane' in the [$\log(L_{144})$, $\log(\rm SFR)$, $α$] space. This allows us to define a unified radio-SFR relation that works both for global and local data when using the radio spectral index as a second parameter. A unified radio-SFR relation for, both, global and local data may serve as a litmus test for galaxy simulations that include the effect of cosmic rays and magnetic fields. It also strengthens the case for using the radio-SFR relation as an extinction-free tracer of star formation.