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Recent derivations of the galaxy star formation rate density (SFRD) obtainedfrom sub-millimetre (sub-mm) surveys (e.g., SCUBA-2) show a tension withprevious works based on Herschel and multi-wavelength data. Some of these worksclaim that the SFRD derived by pushing the Herschel surveys beyond z~2 areincorrect. However, the current sub-mm surveys obtained from SCUBA-2 data andthe methods used to construct the total infrared (IR) luminosity function (LF)and the SFRD could be affected by some limitations. Here we show how theselimitations (i.e., selection bias and incompleteness effects) might affect thetotal IR LF, making the resulting dusty galaxy evolution of difficultinterpretation. In particular, we find that the assumed spectral energydistribution (SED) plays a crucial role in the total IR LF derivation,moreover, we confirm that the long-wavelength (e.g., 850-micron) surveys can beincomplete against "warm" SED galaxies, and that the use of a wide spectralcoverage of IR wavelengths is crucial to limit the uncertainties and biases.

On the existence of bright IR galaxies at z>2: tension between Herschel and SCUBA-2 results?