Revealing the magnetization of the intracluster medium of Abell 3581 using background Faraday rotation measures from the POSSUM survey

The line-of-sight magnetic field of galaxy clusters can be probed using Faraday rotation measure (RM) data. However, our understanding of cluster magnetism is limited due to the scarcity of polarized background radio sources, with most previous studies being constrained to $\sim 10$ sources per cluster. Leveraging the increased source density of the POlarisation Sky Survey of the Universe's Magnetism (POSSUM), we probe the magnetic field properties of the galaxy cluster Abell 3581 {(A3581)} with 111 RMs. We find that the standard deviation in the RM declines monotonically with increasing radius up to 0.75 Mpc{, agreeing with a radially declining magnetic field and electron density profile modeled as Gaussian and lognormal random fields, respectively. {We compare our observations of the inner 0.75 Mpc of A3581 to various semi-analytic models of the magnetic field and electron density, and obtain several best-fit models.} For the first time, we compare the observed RMs in a cluster to full magnetohydrodynamic simulated clusters from TNG-Cluster and find that the non-monotonic trend in RM standard deviation past 0.75 Mpc in A3581 is likely caused by past or present merger activity. We identify a possible candidate for a merger to be the galaxy group [DZ2015b] 276, which would be the first group detected in RMs that is not strongly emitting in X-rays. We find a possible merger axis of A3581 with this group at a position angle of $θ= 52\pm 4$ deg.