High redshift JWST predictions from IllustrisTNG: III. Infrared luminosity functions, obscured star formation and dust temperature of high-redshift galaxies

We post-process galaxies in the IllustrisTNG simulations with SKIRT radiative transfer calculations to make predictions for the rest-frame near-infrared (NIR) and far-infrared (FIR) properties of galaxies at $z\geq 4$. The rest-frame $K$- and $z$-band galaxy luminosity functions from TNG are overall consistent with observations, despite a $\sim 0.5\,\mathrm{dex}$ underprediction at $z=4$ for $M_{\rm K}\lesssim -25$ and $M_{\rm z}\lesssim -24$. Predictions for the JWST MIRI observed galaxy luminosity functions and number counts are given. Based on theoretical estimations, we show that the next-generation survey conducted by JWST can detect 500 (30) galaxies in F1000W in a survey area of $500\,{\rm arcmin}^{2}$ at $z=6$ ($z=8$). As opposed to the consistency in the UV, optical and NIR, we find that TNG, combined with our dust modelling choices, significantly underpredicts the abundance of most dust-obscured and thus most luminous FIR galaxies. As a result, the obscured cosmic star formation rate density (SFRD) and the SFRD contributed by optical/NIR dark objects are underpredicted. The discrepancies discovered here could provide new constraints on the sub-grid feedback models, or the dust contents, of simulations. Meanwhile, although the TNG predicted dust temperature and its relations with IR luminosity and redshift are qualitatively consistent with observations, the peak dust temperature of $z\geq 6$ galaxies are overestimated by about $20\,{\rm K}$. This could be related to the limited mass resolution of our simulations to fully resolve the porosity of the interstellar medium (or specifically its dust content) at these redshifts.