The largest Herschel extragalactic surveys, H-ATLAS and HerMES, have
selected a sample of "ultrared" dusty, star-forming galaxies (DSFGs)
with rising SPIRE flux densities ($S_{500} > S_{350} > S_{250}$;
so-called "500 $\mu$m-risers") as an efficient way for identifying DSFGs
at higher redshift ($z > 4$). In this paper, we present a large
Spitzer follow-up program of 300 Herschel ultrared DSFGs. We have
obtained high-resolution ALMA, NOEMA, and SMA data for 63 of them, which
allow us to securely identify the Spitzer/IRAC counterparts and classify
them as gravitationally lensed or unlensed. Within the 63 ultrared
sources with high-resolution data, $\sim$65% appear to be unlensed, and
$\sim$27% are resolved into multiple components. We focus on analyzing
the unlensed sample by directly performing multi-wavelength spectral
energy distribution (SED) modeling to derive their physical properties
and compare with the more numerous $z \sim 2$ DSFG population. The
ultrared sample has a median redshift of 3.3, stellar mass of 3.7
$\times$ 10$^{11}$ $M_{\odot}$, star formation rate (SFR) of 730
$M_{\odot}$yr$^{-1}$, total dust luminosity of 9.0 $\times$ 10$^{12}$
$L_{\odot}$, dust mass of 2.8 $\times$ 10$^9$ $M_{\odot}$, and V-band
extinction of 4.0, which are all higher than those of the ALESS DSFGs.
Based on the space density, SFR density, and stellar mass density
estimates, we conclude that our ultrared sample cannot account for the
majority of the star-forming progenitors of the massive, quiescent
galaxies found in infrared surveys. Our sample contains the rarer,
intrinsically most dusty, luminous and massive galaxies in the early
universe that will help us understand the physical drivers of extreme
star formation.
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