We have exploited LOFAR deep observations of the Lockman Hole field at 150 MHz to investigate the relation between the radio luminosity of star-forming galaxies (SFGs) and their star-formation rates (SFRs), as well as its dependence on stellar mass and redshift. The adopted source classification, SFRs, and stellar masses are consensus estimates based on a combination of four different spectral energy distribution fitting methods. We note a flattening of the radio spectra of a substantial minority of sources below ∼1.4 GHz. Such sources have thus a lower ‘radio-loudness’ level at 150 MHz than expected from extrapolations from 1.4 GHz using the average spectral index. We found a weak trend towards a lower SFR/ L150 MHz ratio for higher stellar mass, M⋆. We argue that such a trend may account for most of the apparent redshift evolution of the L150 MHz/SFR ratio, in line with previous work. Our data indicate a weaker evolution than found by some previous analyses. We also find a weaker evolution with redshift of the specific SFR than found by several (but not all) previous studies. Our radio selection provides a view of the distribution of galaxies in the SFR- M⋆ plane complementary to that of optical and near-IR selection. It suggests a higher uniformity of the star-formation history of galaxies than implied by some analyses of optical and near-IR data. We have derived luminosity functions at 150 MHz of both SFGs and radio-quiet (RQ) AGN at various redshifts. Our results are in very good agreement with the T-RECS simulations and with literature estimates. We also present explicit estimates of SFR functions of SFGs and RQ AGN at several redshifts derived from our radio survey data.
