In this paper, we investigate the relationship between 150 MHz luminosity and the star-formation rate – the SFR-L150 MHz relation – using 150 MHz measurements for a near-infrared selected sample of 118 517 z < 1 galaxies. New radio survey data offer compelling advantages over previous generation surveys for studying star formation in galaxies, including huge increases in sensitivity, survey speed, and resolution, while remaining impervious to extinction. The LOFAR Surveys Key Science Project is transforming our understanding of the low-frequency radio sky, with the 150 MHz data over the European Large Area Infrared Space Observatory Survey-North 1 field reaching an rms sensitivity of 20 μJy beam−1 over 10 deg2 at 6 arcsec resolution. All of the galaxies studied have SFR and stellar mass estimates that were derived from energy balance spectral energy distribution fitting using redshifts and aperture-matched forced photometry from the LOFAR Two-metre Sky Survey (LoTSS) Deep Fields data release. The impact of active galactic nuclei (AGN) is minimised by leveraging the deep ancillary data in the LoTSS data release, alongside median-likelihood methods that we demonstrate are resistant to AGN contamination. We find a linear and non-evolving SFR-L150 MHz relation, apparently consistent with expectations based on calorimetric arguments, down to the lowest SFRs < 0.01M⊙ yr−1. However, we also recover compelling evidence for stellar mass dependence in line with previous work on this topic, in the sense that higher mass galaxies have a larger 150 MHz luminosity at a given SFR, suggesting that the overall agreement with calorimetric arguments may be a coincidence. We conclude that, in the absence of AGN, 150 MHz observations can be used to measure accurate galaxy SFRs out to z = 1 at least, but it is necessary to account for stellar mass in the estimation in order to obtain 150 MHz-derived SFRs accurate to better than 0.5 dex. Our best-fit relation is log10(L150 MHz ∕W Hz−1) = (0.90 ± 0.01)log10(ψ∕M⊙ yr−1) + (0.33 ± 0.04)log10(M∕1010M⊙) + 22.22 ± 0.02.

Aims. We provide the most accurate estimate yet of the bright end of the infrared (IR) luminosity functions (LFs) and the abundance of hyperluminous IR galaxies (HLIRGs) with IR luminosities > 10 13 L , thanks to the combination of the high sensitivity, angular resolution, and large area of the LOFAR Deep Fields, which probes an unprecedented dynamic range of luminosity and volume. Methods. We cross-match Herschel sources and LOFAR sources in Boötes (8.63 deg 2), Lockman Hole (10.28 deg 2), and ELAIS-N1 (6.74 deg 2) with rms sensitivities of ∼ 32, 22, and 20 µJy beam −1 , respectively. We divide the matched samples into 'unique' and 'multiple' categories. For the multiple matches, we de-blend the Herschel fluxes using the LOFAR positions and the 150-MHz flux densities as priors. We perform spectral energy distribution (SED) fitting, combined with multi-wavelength counterpart identifications and photometric redshift estimates, to derive IR luminosities. Results. The depth of the LOFAR data allows us to identify highly complete (∼ 92% completeness) samples of bright Herschel sources with a simple selection based on the 250 µm flux density (45, 40, and 35 mJy in Boötes, Lockman Hole, and ELAIS-N1, respectively). Most of the bright Herschel sources fall into the unique category (i.e. a single LOFAR counterpart). For the multiple matches, there is excellent correspondence between the radio emission and the far-IR emission. We find a good agreement in the IR LFs with a previous study out to z ∼ 6 which used de-blended Herschel data. Our sample gives the strongest and cleanest indication to date that the population of HLIRGs has surface densities of ∼ 5 to ∼ 18 / deg 2 (with variations due to a combination of the applied flux limit and cosmic variance) and an uncertainty of a factor of 2. In comparison, the GALFORM semi-analytic model significantly under-predicts the abundance of HLIRGs.

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.

We present a detailed study of the cosmic star formation history over 90 per cent of cosmic time (0 ≲ z ≲ 4), using deep, radio continuum observations that probe star formation activity independent of dust. The Low Frequency Array Two Metre Sky Survey has imaged three well-studied extragalactic fields, Elais-N1, Boötes and the Lockman Hole, reaching $\sim 20\, \mu \rm {Jy/beam}$ rms sensitivity at $150\, \rm {MHz}$. The availability of high-quality ancillary data from ultraviolet to far-infrared wavelengths has enabled accurate photometric redshifts and the robust separation of radio-bright AGN from their star-forming counterparts. We capitalise on this unique combination of deep, wide fields and robustly-selected star-forming galaxies to construct radio luminosity functions and derive the cosmic star formation rate density. We carefully constrain and correct for scatter in the $L_{150\, \rm {MHz}}-\rm {SFR}$ relation, which we find to be $\sim 0.3\, \rm {dex}$. Our derived star formation rate density lies between previous measurements at all redshifts studied. We derive higher star formation rate densities between z ∼ 0 and z ∼ 3 than are typically inferred from short wavelength emission; at earlier times, this discrepancy is reduced. Our measurements are generally in good agreement with far-infrared and radio-based studies, with small offsets resulting from differing star formation rate calibrations.

Feedback from low-excitation radio galaxies (LERGs) plays a key role in the lifecycle of massive galaxies in the local Universe; their evolution, and the impact of these active galactic nuclei on early galaxy evolution, however, remain poorly understood. We use a sample of 10 481 LERGs from the first data release of the LOFAR Two-meter Sky Survey Deep Fields, covering ∼ 25 deg2, to present the first measurement of the evolution of the radio luminosity function (LF) of LERGs out to z ∼ 2.5; this shows relatively mild evolution. We split the LERGs into those hosted by quiescent and star-forming galaxies, finding a new dominant population of LERGs hosted by star-forming galaxies at high redshifts. The incidence of LERGs in quiescent galaxies shows a steep dependence on stellar-mass out to z ∼ 1.5, consistent with local Universe measurements of accretion occurring from cooling of hot gas haloes. The quiescent-LERGs dominate the LFs at z &lt; 1, showing a strong decline in space density with redshift, tracing that of the available host galaxies, while there is an increase in the characteristic luminosity. The star-forming LERG LF increases with redshift, such that this population dominates the space densities at most radio-luminosities by z ∼ 1. The incidence of LERGs in star-forming galaxies shows a much weaker stellar-mass dependence, and increases with redshift, suggesting a different fuelling mechanism compared to their quiescent counterparts, potentially associated with the cold gas supply present in the star-forming galaxies.