We have investigated the Cosmic Infrared Background ( CIB ) anisotropies in the framework of the physical evolutionary model for proto-spheroidal galaxies by Granato et al .
( 2004 ) .
After having re-calibrated the cumulative flux function dS / dz at \lambda \geq 850 \mu m using the available determinations of the shot noise amplitude ( the original model already correctly reproduces it at shorter wavelengths ) the CIB power spectra at wavelengths from 250 \mu m to 2 mm measured by Planck , Herschel , SPT and ACT experiments have been fitted using the halo model with only 2 free parameters , the minimum halo mass and the power-law index of the mean occupation function of satellite galaxies .
The best-fit minimum halo mass is \log ( M _ { min } / M _ { \odot } ) = 12.24 \pm 0.06 , higher than , but consistent within the errors , with the estimate by Amblard et al .
( 2011 ) and close to the estimate by Planck Collaboration ( 2011 ) .
The redshift evolution of the volume emissivity of galaxies yielded by the model is found to be consistent with that inferred from the data .
The derived effective halo mass , M _ { eff } \simeq 5 \times 10 ^ { 12 } M _ { \odot } , of z \simeq 2 sub-millimeter galaxies is close to that estimated for the most efficient star-formers at the same redshift .
The effective bias factor and the comoving clustering radius at z \simeq 2 yielded by the model are substantially lower than those found for a model whereby the star formation is fueled by steady gas accretion , but substantially higher than those found for a merging-driven galaxy evolution with a top-heavy initial mass function .