An Analysis of ALMA Deep Fields and the Perceived Dearth of High-z Galaxies

Deep, pencil-beam surveys from ALMA at 1.1-1.3mm have uncovered an apparent absence of high-redshift dusty galaxies, with existing redshift distributions peaking around $z\sim1.5-2.5$. This has led to a perceived dearth of dusty systems at $z>4$, and the conclusion, according to some models, that the early Universe was relatively dust-poor. In this paper, we extend the backward evolution galaxy model described by Casey et al. (2018) to the ALMA regime (in depth and area) and determine that the measured number counts and redshift distributions from ALMA deep field surveys are fully consistent with constraints of the infrared luminosity function (IRLF) at $z<2.5$ determined by single-dish submillimeter and millimeter surveys conducted on much larger angular scales ($\sim1-10$deg$^{2}$). We find that measured 1.1-1.3mm number counts are most constraining for the measurement of the faint-end slope of the IRLF at $z4$. Recent studies have suggested that UV-selected galaxies at $z>4$ may be particularly dust-poor, but we find their millimeter-wave emission cannot rule out consistency with the Calzetti dust attenuation law even by assuming relatively typical, cold-dust ($T_{\rm dust}\approx30\,$K) SEDs. Our models suggest that the design of ALMA deep fields requires substantial revision to constrain the prevalence of $z>4$ early Universe obscured starbursts. The most promising avenue for detection and characterization of such early dusty galaxies will come from future ALMA 2mm blank field surveys covering a few hundred arcmin$^{2}$ and the combination of existing and future dual-purpose 3mm datasets.Comment: 21 pages, 12 figures, accepted for publication in Ap