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Clustering of sub-millimeter galaxies in a self-regulated baryon collapse model

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 $λ\ge 850\,μ$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 $250\,μ$m to $2\,$mm measured by {\it Planck}, {\it 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 {\it minimum} halo mass is $\log(M_{\rm min}/M_\odot) = 12.24 \pm 0.06$, 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 {\it effective} halo mass, $M_{\rm eff} \simeq 5\times 10^{12}\,M_\odot$, 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.