Redshift Horizon for Detecting the First Galaxies in Far-Infared Surveys

We explore the possibility of detecting the first galaxies with the next generation of space-based far infrared (FIR) telescopes by applying an analytical model of primordial dust emission. Our results indicate that FIR/sub-mm sources at $z \gtrsim 7$ will experience a strong negative K-correction. Systems of a given virial mass would exhibit larger dust luminosities at higher $z$, as a consequence of the increase in dust temperature driven by the higher temperature floor set by the cosmic microwave background. In addition, high-$z$ systems are more concentrated, which enhances the heating efficiency associated with stellar radiation. By analysing source densities as a function of $z$, and considering survey areas of 0.1 ${\rm deg}^2$ and 10 ${\rm deg}^2$, we find that the redshift horizon for detecting at least one source would be above $z\sim 7$ for instrument sensitivities $\lesssim 0.1-0.5 \ {\mu}{\rm Jy}$ and $\lesssim 0.5-3.0 \ {\mu}{\rm Jy}$, respectively, with the exact values depending on the nature of primordial dust. However, galaxy populations with higher than typical metallicities, star formation efficiencies and/or dust-to-metal ratios could relax such sensitivity requirements. In addition, the redshift horizon shows a significant dependence on the nature of primordial dust. We conclude that future FIR campaigns could play a crucial role in exploring the nature of dust and star formation in the early universe.