| Abstract
| - Context. Hyperluminous infrared galaxies (HLIRGs) are shown to have been more abundant in early epochs. The small samples used in earlier studies are not sufficient to draw robust statistical conclusions regarding the physical properties and the power sources of these extreme infrared (IR) bright galaxies. Aims. We make use of multi-wavelength data of a large HLIRG sample to derive the main physical properties, such as stellar mass, star formation rate (SFR), volume density, and the contribution to the cosmic stellar mass density and the cosmic SFR density. We also study the black hole (BH) growth rate and its relationship with the SFR of the host galaxy. Methods. We selected 526 HLIRGs in three deep fields (Boötes, Lockman-Hole, and ELAIS-N1) and adopted two spectral energy distribution (SED) fitting codes: CIGALE, which assumes energy balance, and CYGNUS, which is based on radiative transfer models and does not adopt an energy balance principle. We used two different active galactic nucleus (AGN) models in CIGALE and three AGN models in CYGNUS to compare results that were estimated using different SED fitting codes and a range of AGN models. Results. The stellar mass, total IR luminosity, and AGN luminosity agree well among different models, with a typical median offset of 0.1 dex. The SFR estimates show the largest dispersions (up to 0.5 dex). This dispersion has an impact on the subsequent analysis, which may suggest that the previous contradictory results could partly have been due to the different choices in methods. HLIRGs are ultra-massive galaxies, with 99% of them having stellar masses larger than 10 11M⊙. Our results reveal a higher space density of ultra-massive galaxies than what was found by previous surveys or predicted via simulations. We find that HLIRGs contribute more to the cosmic SFR density as redshift increases. In terms of BH growth, the two SED fitting methods provide different results. We can see a clear trend in whereby SFR decreases as AGN luminosity increases when using CYGNUS estimates. This may possibly imply quenching by AGN in this case, whereas this trend is much weaker when using CIGALE estimates. This difference is also influenced by the dispersion between SFR estimates obtained by the two codes.
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