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We study the gas distribution in the Milky Way and Andromeda using aconstrained cosmological simulation of the Local Group (LG) within the contextof the CLUES (Constrained Local UniversE Simulations) project. We analyse theproperties of gas in the simulated galaxies at $z=0$ for three differentphases: `cold', `hot' and HI, and compare our results with observations. Theamount of material in the hot halo ($M_{hot}\approx4-5\times10^{10}\,$M$_{\odot}$), and the cold($M_{cold}(r\lesssim10\,$kpc$)\approx10^{8}\,$M$_{\odot}$) and HI($M_{HI}(r\lesssim50\,$kpc$)\approx 3-4\times10^8\,$M$_{\odot}$) componentsdisplay a reasonable agreement with observations. We also compute theaccretion/ejection rates together with the HI (radial and all-sky) coveringfractions. The integrated HI accretion rate within $r=50\,$kpc gives$\sim$$0.2-0.3\,$M$_{\odot}\,$yr$^{-1}$, i.e. close to that obtained fromhigh-velocity clouds in the Milky Way. We find that the global accretion rateis dominated by hot material, although ionized gas with $T\lesssim10^5\,$K cancontribute significantly too. The $net$ accretion rates of $all$ material atthe virial radii are $6-8\,$M$_{\odot}\,$yr$^{-1}$. At $z=0$, we find asignificant gas excess between the two galaxies, as compared to any otherdirection, resulting from the overlap of their gaseous haloes. In oursimulation, the gas excess first occurs at $z\sim1$, as a consequence of thekinematical evolution of the LG.

The distribution of gas in the Local Group from constrained cosmological simulations: the case for Andromeda and the Milky Way galaxies