The quest for dusty star-forming galaxies at high redshift z ≳ 4

We exploit the continuity equation approach and "main-sequence" star formation timescales to show that the observed high abundance of galaxies with stellar masses greater than or similar to a few 10(10) M-circle dot at redshift z greater than or similar to 4 implies the existence of a galaxy population featuring large star formation rates (SFRs) psi greater than or similar to 10(2) M-circle dot yr(-1) in heavily dust-obscured conditions. These galaxies constitute the high-redshift counterparts of the dusty star-forming population already surveyed for z less than or similar to 3 in the far-IR band by the Herschel Space Observatory. We work out specific predictions for the evolution of the corresponding stellar mass and SFR functions out to z similar to 10, determining that the number density at z less than or similar to 8 for SFRs psi greater than or similar to 30 M-circle dot yr(-1) cannot be estimated relying on the UV luminosity function alone, even when standard corrections for dust extinction based on the UV slope are applied. We compute the number counts and redshift distributions (including galaxy-scale gravitational lensing) of this galaxy population, and show that current data from the AzTEC-LABOCA, SCUBA-2, and ALMA-SPT surveys are already addressing it. We demonstrate how an observational strategy based on color preselection in the far-IR or (sub-)millimeter band with Herschel and SCUBA-2, supplemented by photometric data from on-source observations with ALMA, can allow us to reconstruct the bright end of the SFR functions out to z less than or similar to 8. In parallel, such a challenging task can be managed by exploiting current UV surveys in combination with (sub-) millimeter observations by ALMA and NIKA2 and/or radio observations by SKA and its precursors.