Clustering properties and gravitational lensing of forming spheroidal galaxies

We show that the predictions of the recent physical model by Granato et al. (2001) are fully consistent with the available estimates of the clustering properties of galaxies at (sub)-mm wavelengths. The model is then exploited to compute the expected power spectrum of fluctuations due to clustering at the frequencies of the High Frequency Instrument (HFI) of ESA's {\sc Planck} satellite. The clustering signal is found to be detectable in regions of low interstellar dust emission. A further distinctive prediction of the adopted model is a remarkably high fraction of gravitationally lensed sources at bright mm/sub-mm fluxes. In fact, according to the adopted model, only thanks to gravitational lensing, a significant number of high-$z$ forming spheroidal galaxies will be detectable by large area, shallow surveys at mm/sub-mm wavelengths, such as those carried out by P{\sc lanck}/HFI. Allowing for other source populations, we find that the fraction of gravitationally lensed sources at bright mm/sub-mm fluxes is expected to be up to $\simeq 40%$.