We present a study of the infrared properties for a sample of seven spectroscopically confirmed submillimeter galaxies at $z>$4.0. By combining ground-based near-infrared, Spitzer IRAC and MIPS, Herschel SPIRE, and ground-based submillimeter/millimet
er photometry, we construct their Spectral Energy Distributions (SED) and a composite model to fit the SEDs. The model includes a stellar emission component at $lambda_{rm rest} <$ 3.5$ mu$m; a hot dust component peaking at $lambda_{rest} sim$ 5$,mu$m; and cold dust component which becomes significant for $lambda_{rm rest} >$ 50$,mu$m. Six objects in the sample are detected at 250 and 350$ mu$m. The dust temperatures for the sources in this sample are in the range of 40$-$80 K, and their $L_{rm FIR}$ $sim$ 10$^{13}$ L$_{odot}$ qualifies them as Hyper$-$Luminous Infrared Galaxies (HyperLIRGs). The mean FIR-radio index for this sample is around $< q > = 2.2$ indicating no radio excess in their radio emission. Most sources in the sample have 24$ mu$m detections corresponding to a rest-frame 4.5$ mu$m luminosity of Log$_{10}$(L$_{4.5}$ / L$_{odot}$) = 11 $sim$ 11.5. Their L$_{rm 4.5}$/$L_{rm FIR}$ ratios are very similar to those of starburst dominated submillimeter galaxies at $z sim$ 2. The $L_{rm CO}-L_{rm FIR}$ relation for this sample is consistent with that determined for local ULIRGs and SMGs at $z sim$ 2. We conclude that submillimeter galaxies at $z >$ 4 are hotter and more luminous in the FIR, but otherwise very similar to those at $z sim$ 2. None of these sources show any sign of the strong QSO phase being triggered.
A SST survey in the NOAO Deep-Wide Field in Bootes provides a complete, 8-micron-selected sample of galaxies to a limiting (Vega) magnitude of 13.5. In the 6.88 deg$^2$ field sampled, 79% of the 4867 galaxies have spectroscopic redshifts, allowing an
accurate determination of the local (z<0.3) galaxy luminosity function. Stellar and dust emission can be separated on the basis of observed galaxy colors. Dust emission (mostly PAH) accounts for 80% of the 8 micron luminosity, stellar photospheres account for 19%, and AGN emission accounts for roughly 1 %. A sub-sample of the 8 micron-selected galaxies have blue, early-type colors, but even most of these have significant PAH emission. The luminosity functions for the total 8 micron luminosity and for the dust emission alone are both well fit by Schechter functions. For the 8 micron luminosity function, the characteristic luminosity is u L_{ u}^*(8.0 micron) = 1.8 times 10^{10}$ Lsun while for the dust emission alone it is 1.6 x 10^{10}$ Lsun ull. The average 8 micron luminosity density at z<0.3 is 3.1 x 10^7 Lsun Mpc^{-3}, and the average luminosity density from dust alone is 2.5 x 10^7 Lsun Mpc^{-3}. This luminos ity arises predominantly from galaxies with 8 micron luminosities ($ u L_{ u}$) between $2times 10^9$ and $2 x 10^{10}$ Lsun, i.e., normal galaxies, not LIRGs or ULIRGs.
