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.