Unveiling large-scale rotational motions in the intragroup medium at

Context. The circumgalactic medium (CGM) is a crucial interface between galaxies and their large-scale environment, regulating gas accretion and feedback processes. Yet its physical and kinematic properties within galaxy groups, where most galaxies reside, remain poorly constrained. Aims. We present the first spatially resolved characterisation of the cool intragroup medium (IGrM) in a spectroscopically confirmed galaxy group at z ≃ 1.167 using absorption-line spectroscopy along multiple sightlines. Methods. Using 30 independent sightlines towards the gravitationally lensed galaxy SGAS J003341.5+024217, we combined background light from an extended gravitational arc and various sources in the field to map the distribution and kinematics of diffuse metal-enriched gas pertaining to this group. Results. We detected prominent Mg <ns0:sc>II</ns0:sc>, Fe <ns0:sc>II</ns0:sc>, Ca <ns0:sc>II</ns0:sc>, and Mg <ns0:sc>I</ns0:sc> absorption extending up to a projected distance of 62 kpc from a massive (log M★ = 11.0 ± 0.1 M⊙) star-forming spiral and its interacting companion. Together with four other members, these form a compact group with a virial radius of 313 kpc. Down-the-barrel, blueshifted absorption indicates outflows. The distribution and two-dimensional kinematics of this gas suggest the influence of both tidal stripping and star formation-driven winds. Intervening absorption across the field partly traces internal galaxy motions. A simple superposition of individual discs cannot reproduce the velocity field at large impact parameters or in counter-rotating regions, while a global IGrM halo with a rotational velocity of ≈130 km s−1 provides a good match. Beyond individual galaxy envelopes, we find the data to be consistent with a group-scale structure that co-rotates in concert with the galaxies. Assuming dynamical equilibrium, we estimated a total (cool+warm+hot) gas mass of 1.3 − 2.5 × 1011 M⊙, with large systematic uncertainties, corresponding to roughly 50% of all baryons within one-quarter of the group’s virial radius. Conclusions. These results point to a multiphase IGrM in which cool (∼104 K) clouds are embedded within a dynamically coherent group-wide halo. The gas appears to be gravitationally bound to the group rather than reaccreting onto individual galaxies. High-redshift strong Mg <ns0:sc>II</ns0:sc> absorbers may thus trace shared metal-enriched halos shaped by galaxy interactions and feedback, with stripped and outflowing gas accumulating in the IGrM over time.