The influence of wavelength, flux, and lensing selection effects on the redshift distribution of dusty, star-forming galaxies

We interpret the large variety of redshift distributions of galaxies found by far-infrared and (sub-)millimeter deep surveys depending on their depth and wavelength using the B\'ethermin et al. (2012) phenomenological model of galaxy evolution. This model reproduces without any new parameter tuning the observed redshift distributions from 100 $\mu$m to 1.4 mm, and especially the increase of the median redshift with survey wavelength. This median redshift varies also significantly with the depth of the surveys, and deeper surveys do necessarily not probe higher redshifts. Paradoxically, at fixed wavelength and flux limit, the lensed sources are not always at higher redshift. We found that the higher redshift of 1.4 mm-selected south pole telescope (SPT) sources compared to other SMG surveys is not only caused by the lensing selection, but also by the longer wavelength. This SPT sample is expected to be dominated by a population of lensed main-sequence galaxies and a minor contribution ($\sim$10\%) of unlensed extreme starbursts.