Predictions of the L$_{\rm[CII]}$-SFR and [C$_{\rm II}$] Luminosity Function at the Epoch of Reionization

Abstract: We present the first predictions for the $L_{\rm [CII]}$ - SFR relation and [CII] luminosity function (LF) in the Epoch of Reionization (EoR) based on cosmological hydrodynamics simulations using the SIMBA suite plus radiative transfer calculations via S\'IGAME. The sample consists of 11,137 galaxies covering halo mass $\log M_{\rm halo}\in$[9, 12.4] $M_\odot$, star formation rate SFR$\in$[0.01, 330] $M_\odot$ yr$^{-1}$, and metallicity $<Z_{\rm gas}>{\rm SFR}\in$[0.1, 0.9] $Z\odot$. The simulated $L_{\rm [CII]}$-SFR relation is consistent with the range observed, but with a spread of $\simeq$0.3 dex at the high end of SFR ($>$100 $M_\odot$ yr$^{-1}$) and $\simeq$0.6 dex at the lower end, and there is tension between our predictions and the values of $L_{\rm [CII]}$ above 10$^{8.5}$ $L_\odot$ observed in some galaxies reported in the literature. The scatter in the $L_{\rm [CII]}$-SFR relation is mostly driven by galaxy properties, such that at a given SFR, galaxies with higher molecular gas mass and metallicity have higher $L_{\rm [CII]}$. The [CII] LF predicted by SIMBA is consistent with the upper limits placed by the only existing untargeted flux-limited [CII] survey at the EoR (ASPECS) and those predicted by semi-analytic models. We compare our results with existing models and discuss differences responsible for the discrepant slopes in the $L_{\rm [CII]}$-SFR relatiion.