  Faraday tomography of radio polarimetric data below 200 MHz from LOFAR are
providing us with a new perspective on the diffuse and magnetized interstellar
medium (ISM). Of particular interest is the discovery of Faraday-rotated
synchrotron polarization associated with neutral gas, as traced by atomic
hydrogen (HI) and dust. Here we present the first in-depth numerical study of
these LOFAR results. We produce and analyze comprehensive synthetic
observations of low-frequency synchrotron polarization from MHD simulations of
colliding super shells in the multiphase ISM. We define five distinct gas
phases over more than four orders of magnitude in gas temperature and density,
ranging from hot, and warm, fully ionized gas to cold neutral medium. We focus
on the contribution of each gas phase to synthetic observations of both
rotation measure and synchrotron polarized intensity below 200 MHz. We also
investigate the link between the latter and synthetic observations of optically
thin HI gas. We find that, not only the fully ionized gas but also the warm
partially ionized and neutral phases strongly contribute to the total rotation
measure and polarized intensity. However, the contribution of each phase to the
observables strongly depends on the choice of integration axis and the
orientation of the mean magnetic field with respect to the shell-collision
axis. Strong correlation between HI synthetic data and synchrotron polarized
intensity, reminiscent of LOFAR results, is obtained with lines of sight
perpendicular to the mean magnetic field direction. Our study suggests that
multiphase modelling of MHD processes is needed in order to interpret
observations of the radio sky at low frequency. This work is a first step
toward understanding the complexity of low-frequency synchrotron emission that
will be soon revolutionized by large-scale surveys with LOFAR and the SKA.
