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tokens: evolution is computed by solving the rate equations with one Jacobi iteration with implicit Eulerian time discretization, with a coupling between thermal and chemical states at subcylces in the hydrodynamical time-step (see Bryan et al. 2014 , and references therein for more details). Table 1. Main parameters of the three runs in the Chronos++suite used in the present work. From the left- to right-hand columns define the presence of radiative cooling or star-forming particles, the critical gas number density n * to trigger star formation in the Kravtsov ( 2003 ) model, the time-scale for star formation t * , the thermal feedback efficiency, and the magnetic feedback efficiency ( ε SF and ε SF, b ) from star-forming regions; the efficiency of Bondi accretion α Bondi in the Kim et al. ( 2011 ) model for SMBH; the thermal feedback efficiency and the magnetic feedback efficiency ( ε BH and ε BH, b ) from SMBH; the intensity of the initial magnetic field, B 0 ; the presence of sub-grid dynamo amplification at run time; the ID of the run and some additional descriptive notes. All simulations evolved a volume using 1024 3 cells and DM particles, starting at redshift z = 38. The name convention of all runs is consistent with Vazza et al. ( 2017 ). Table 2. List of observable properties and adopted detection threshold. Note : We associate to each observable a reference instrument, which loosely corresponds to the adopted observational cut. All the runs adopted the Lambda cold dark matter (ΛCDM) cosmology, with density parameters Ω BM = 0.0478 (BM representing the Baryonic Matter), Ω DM = 0.2602 (DM being the dark matter), Ω Λ = 0.692 (Λ, being the cosmological constant), and a Hubble constant H 0 = 67.8 km s −1 Mpc −1 and σ 8 = 0.815 (Planck Collaboration XIII 2016 ). The initial redshift is z = 38, the spatial resolution is (comoving) and the constant mass resolution of for DM particles. Additional details on our sample of simulations can be found in Vazza et al. ( 2017 ) and Gheller Vazza ( 2019 ). An RGB rendering of the projected distribution of different mass components (DM, ionised gas, and neutral Hydrogen) in our CSFBH2 model at z = 0.045 is shown in Fig. 1 . This example shows, at least in a qualitative way, the general difficulty of detecting the diffuse gas in the cosmic via cross-correlation: although on large scales all tracers are well correlated and part of the same web pattern, on scales smaller than a few they present different level of clustering and concentration, making their cross-correlation signal challenging to detect. Figure 1. RGB rendering of the matter distribution in our simulated volume for the CSFBH2 model at z = 0.045: DM density (blue), ionized gas (pink), and neutral hydrogen (green). 2.2 Multiwavelength synthetic observations and halo catalogues We generated emission maps of our simulated volume at different wavelengths, including a number of emission/absorption channels: X-ray emission: we assume for simplicity a