The bright end of the infrared luminosity functions and the abundance of hyperluminous infrared galaxies

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 >1013L⊙, 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 deg2), Lockman Hole (10.28 deg2), and ELAIS-N1 (6.74 deg2) 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 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/deg2 (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.