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Recent observations have revealed remarkable insights into the gas reservoirin the circumgalactic medium (CGM) of galaxy haloes. In this paper, wecharacterise the gas in the vicinity of Milky Way and Andromeda analogues inthe HESTIA (High resolution Environmental Simulations of The Immediate Area)suite of constrained Local Group (LG) simulations. The HESTIA suite comprise ofa set of three high-resolution {\sc arepo}-based simulations of the LG, runusing the Auriga galaxy formation model. For this paper, we focus only on the$z = 0$ simulation datasets and generate mock skymaps along with a powerspectrum analysis to show that the distributions of ions tracinglow-temperature gas (HI and SiIII) are more clumpy in comparison to warmer gastracers (OVI, OVII and OVIII). We compare to the spectroscopic CGM observationsof M31 and low-redshift galaxies. HESTIA under-produces the column densities ofthe M31 observations, but the simulations are consistent with the observationsof low-redshift galaxies. A possible explanation for these findings is that thespectroscopic observations of M31 are contaminated by gas residing in the CGMof the Milky Way.

Cold and Hot gas distribution around the Milky-Way-M31 system in the HESTIA simulations