A population of high-velocity absorption-line systems residing in the Local Group.

Aims. We aim to investigate the ionisation conditions and distances of Galactic high-velocity clouds (HVCs) in the Galactic halo and beyond in the direction of the Local Group (LG) barycentre and anti-barycentre, by studying spectral data of 29 extragalactic background sources obtained with Cosmic Origins Spectropgraph (COS) installed on the Hubble Space Telescope (HST). Methods. We model column-densities of low, intermediate, and high ions, such as Si II, C II, Si III, Si IV, and C IV and use this to construct a set of Cloudy ionisation models. Results. In total, we found 69 high-velocity absorption components along the 29 lines of sight. The ones in the direction of the LG barycentre span the entire range of studied velocities, 100 \lesssim |v_{LSR}|\lesssim 400 km s^-1, while the anti-barycentre sample has velocities up to about 300 km s^-1. For 49 components, we infer the gas densities. In the direction of the LG barycentre, the gas densities exhibit a large range between log n_H=-3.96 to -2.55, while in the anti-barycentre direction the densities are systematically higher, log n_H>-3.25. The barycentre absorbers can be split into two groups based on their density: a high density group with log n_H>-3.54, which can be affected by the Milky Way radiation field, and a low density group (log n_H \leq -3.54). The latter has very low thermal pressures of P/k<7.3 K cm^-3. Conclusions. Our study shows that part of the absorbers in the LG barycentre direction trace gas at very low gas densities and thermal pressures. Such properties indicate that these absorbers are located beyond the virial radius of the Milky Way. Our study also confirms results from earlier, single-sightline studies, suggesting the presence of a metal-enriched intragroup medium filling the LG near its barycentre.