The circumgalactic medium (CGM) is a crucial component of galaxy evolution, but thus far its physical properties are highly unconstrained. As of yet, no cosmological simulation has reached convergence when it comes to constraining the cold and dense gas fraction of the CGM. Such components are also challenging to observe directly as they require sub-millimetre (sub-mm) instruments with a high sensitivity to extended and mostly diffuse emission. We present a state-of-the-art theoretical effort at modelling the CII CI CI CO(3-2) $867 and OIII line emissions that arise from the interstellar medium (ISM) and CGM of galaxies with the goal of studying the contribution from different cold ($T<10^4$ K) components of galaxy halos. We used the high-resolution cosmological zoom-in simulation gas $ = 883.4 M$_ odot $), which represents a typical star-forming galaxy system at $z = 6.5$, composed of a main disc with stellar mass $M_*=2 odot $ that is undergoing a major merger. We adopted different modelling approaches based on the photoionisation code Our fiducial model uses radiative transfer post-processing with and to create more realistic far-ultraviolet (FUV) radiation fields, which we then compared to other sub-grid modelling approaches adopted in the literature. We find significant differences in the luminosity and in the contribution of different gas phases and galaxy components between the different modelling approaches. CII is the least model-dependant gas tracer, while CI (1-0) and CO(3-2) are very model-sensitive. In all models, we find a significant contribution to the emission of CII (up to sim 10<!PCT!>) and OIII (up to sim 21<!PCT!>) from the CGM. Our fiducial global radiative transfer (RT) model produces a lower density, $T $ K tail of CII emission that is not seen in the other more simplistic models and that resides entirely in the CGM ionised by the FUV background and producing the extended halos observed in CII at high-z .
Notably CII and OIII trace different regions of the CGM: CII arises from an accreting filament and from the tidal tails connecting the main disc and its merging satellites, while OIII traces a puffy halo surrounding the main disc, probably linked to supernova feedback. We discuss our results in the context of sub-mm observations. Using simulated spectra and mock maps, we show that, despite the rather compact angular extent of CGM, deep ALMA observations would not detect this component, even in CII which is the brightest available tracer. Instead, a next generation single-dish observatory such as the Atacama Large Aperture Submillimeter Telescope (AtLAST) could detect CGM in CII at a high signal-to-noise ratio, and possibly even in OIII