The Three Hundred: Gas Properties Outside of Galaxy Cluster with the WHIM Contribution and Detection

We investigate the physical properties and detectability of warm-hot intergalactic medium (WHIM) gas with temperatures in the range $10^5<T<10^7$K around galaxy clusters using simulated galaxy clusters from The Three Hundred project. In simulations with different input physics (GIZMO-SIMBA and Gadget-X), we consistently find that the median gas temperature decreases to the WHIM upper bound, $10^7$K, at $\sim 2 \times R_{200c}$, while the WHIM mass fraction increases with radius until $\sim 3\times R_{200c}$, where it plateaus at $\sim 70$ per cent.By simulating X-ray emission from all gas components, we find that the WHIM contribution to the soft X-ray band (0.2 - 2.3 keV) increases with radius but eventually plateaus at larger distances. The differences between the two simulations become more pronounced at higher redshifts and larger radii. Finally, after accounting for observational effects, primarily by removing (sub)halos, we predict that the signal-to-noise ratio of the X-ray signal obtained by stacking the eRASS1 galaxy cluster catalogue will be $\sim 7$ for GIZMO-SIMBA and $\sim 21$ for Gadget-X.