A simple approach to the high-redshift sub-millimeter galaxies

We aim at understanding the statistical properties of luminous sub-millimeter (submm) galaxies (SMGs) in the context of cosmological structure formation. By utilizing a cosmological N-body simulation to calculate the distribution of dark halos in the Universe, we consider the dust enrichment in individual halos by Type II supernovae (SNe II). The SN II rate is estimated under a star formation activity which is assumed to occur on a dynamical timescale in the dark matter potential. Our simple framework successfully explains the luminosity function, the typical star formation rate, and the typical dust mass of an observational SMG sample at z～3. We also examine the clustering properties of SMGs, since a positive cross correlation between SMGs and Lyα emitters (LAEs) is indeed observed by a recent observation. In the simulation, we select SMGs by FIR dust luminosity >10¹² L _⊙, while LAEs are chosen such that the age and the virial mass are consistent with the observed LAE properties. The SMGs and LAEs selected in this way show a spatial cross correlation whose strength is consistent with the observation. This confirms that the SMGs really trace the most clustered regions at z～3 and that their luminosities can be explained by the dust accumulation as a result of their star formation activities. We extend our prediction to higher redshifts, finding that a statistical sample of submm galaxies at z≥6 can be obtained by ALMA with a 100 arcmin² survey. With the same survey, a few submm galaxies at z～10 may be detected.