Millimetric properties of IRAS galaxies - III. Luminosity functions, sub-mm counts and contributions to the sky background

We exploit observations at 1.25 mm with the ESO-SEST telescope of a southern galaxy sample, selected from the IRAS PSC and complete to S-60 = 2 Jy, to derive the FIR and mm luminosity functions and the conditional probability distributions of FIR and mm luminosity of galaxies. The reliability of these estimates is ensured by the good observed correlation of the far-infrared and mm emissions. This detailed knowledge of the millimetric properties of galaxies is used to simulate the extragalactic sub-mm sky (background intensity, small-scale anisotropy signals and discrete source statistics), which is the target of a variety of ground-based and space observatories. We find, in particular, that a recent tentative detection of a sub-mm background would require, if confirmed, strong evolution with cosmic time of the galaxy long-wavelength emissivity. We finally discuss ways to test such evolution with present and forthcoming facilities: while emphasizing the difficulty of achieving this with large mm telescopes on the ground (because of the poor atmospheric conditions of current sub-mm sites), we mention an interesting opportunity with the long-wavelength camera on ISO. Preliminary results of deep surveys, both from space and from the ground, seem indeed to require excess emission in the past by dusty galaxies with respect to no-evolution predictions.