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Faraday tomography of a field centred on the extragalactic point source 3C 196 with the LOw Frequency ARray (LOFAR) revealed an intertwined structure of diffuse polarised emission with straight depolarisation canals and tracers of the magnetized and multi-phase interstellar medium (ISM), such as dust and line emission from atomic hydrogen (HI). This study aims at extending the multi-tracer analysis of LOFAR data to three additional fields in the surroundings of the 3C 196 field. For the first time, we study the three-dimensional structure of the LOFAR emission by determining the distance to the depolarisation canals. We use the Rolling Hough Transform to compare the orientation of the depolarisation canals with that of the filamentary structure seen in HI and, based on starlight and dust polarisation data, with that of the plane-of-the-sky magnetic field. Stellar parallaxes from $Gaia$ complement the starlight polarisation with the corresponding distances. Faraday tomography of the three fields shows a rich network of diffuse polarised emission at Faraday depths between $-10~{\rm rad~m^{-2}}$ and $+15~{\rm rad~m^{-2}}$. A complex system of straight depolarisation canals resembles that of the 3C 196 field. The depolarisation canals align both with the HI filaments and with the magnetic field probed by dust. The observed alignment suggests that an ordered magnetic field organises the multiphase ISM over a large area ($\sim$20$^{\circ}$). In one field, two groups of stars at distances below and above 200 pc, respectively, show distinct magnetic-field orientations. These are both comparable with the orientations of the depolarisation canals in the same field. We conclude that the depolarisation canals likely trace the same change of the magnetic field as probed by the stars, which corresponds to the edge of the Local Bubble., Comment: 14 pages, 11 figures, accepted for publication in A&A

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., Comment: 17 pages, 20 figures, accepted by A&A, in press

Faraday tomography of polarimetric observations at low frequency is a unique tool to study the structure of the magneto-ionic interstellar medium (ISM) based on Faraday depth. LOFAR data below 200 MHz revealed a plethora of features in polarization, whose origin remains unknown. Previous studies highlighted the remarkable association of such features to tracers of the magnetized-neutral ISM, as interstellar dust and atomic hydrogen (HI). However, the physical conditions responsible for the correlation between magneto-ionic and neutral media are yet to be clarified. In this letter we investigate further the correlation between LOFAR data and HI observations at 21cm from the Effelsberg-Bonn HI Survey (EBHIS). We focus on the multiphase properties of the HI gas. We present the first statistical study on the morphological correlation between LOFAR tomographic data and the cold (CNM), luke-warm (LNM), and warm (WNM) HI phases, separately. We use the Regularized Optimization for Hyper-Spectral Analysis (ROHSA) approach to decompose the HI phases based on the Gaussian decomposition of the HI spectra. In at least two fields of view -- Fields 3C196 and A -- out of four -- Fields B and C -- we find a significant correlation between LOFAR and EBHIS data using the Histograms of Oriented Gradients (HOG). The absence of correlation in Fields B and C is caused by low signal-to-noise ratio in polarization. The observed HOG correlation in Fields 3C196 and A is associated with all HI phases and it is surprisingly dominant in the CNM and LNM phases. We discuss possible mechanisms that would explain the correlation between CNM, LNM, and WNM, with polarized emission at Faraday depths up to 10 rad m$^{-2}$. Our results show how the complex structure of the ionic medium seen by LOFAR data is tightly related to phase transition in the diffuse and magnetized neutral ISM traced by HI spectroscopic data., 9 pages, 10 figures, accepted for publication in A&A