MUSE observations of the ionized gas in a galaxy group at z = 0.45 with 21-cm HI absorption towards PKS 1610-771

We present results from MUSE observations following up on a 21-cm \ion{H}{i} absorption system detected with the Australian Square Kilometre Array Pathfinder radio telescope at redshift $0.4503$ towards the quasar PKS 1610-771. This \ion{H}{i} absorber has a column density $N_{HI} = 2.7 \pm 0.1 \times 10^{20} \cdot \rm{[T_{s}/100 K]} \cdot \rm{cm}^{-2}$, making it a likely Damped Lyman-$\alpha$ (DLA) system. We identify a galaxy group with four members (A, B, X and Y) at the same redshift as the \ion{H}{i} absorption system, with impact parameters ranging from less than 10\,kpc to almost 200\,kpc from the quasar sightline. \ion{Ca}{ii} and \ion{Na}{i} absorption is also seen in the MUSE spectrum of the background QSO, with velocities coinciding with the initial \ion{H}{i} $21$-cm detection, but tracing less dense and potentially warmer gas. This metal-line component aligns with the rotating ionized disc of galaxy B (impact parameter $18$ kpc from the QSO) and appears to be co-rotating with the galaxy disc, although outflowing gas cannot be directly excluded. In contrast, the $21$-cm \ion{H}{i} absorber is blueshifted relative to the galaxies nearest the absorber and has the opposite sign to the velocity field of galaxy B. Since galaxies A and B are separated by only $17$ kpc on the sky and $70$ km s$^{-1}$ in velocity, it is likely that the $21$-cm detection traces extragalactic clouds of gas formed from their interaction. This system represents a first case study of the cold gas detected in galaxy groups by future large $21$-cm absorption surveys, such as the First Large Absorption Survey in \ion{H}{i}.