Contribution of neutral gas to Faraday tomographic data at low frequencies: A first extensive comparison between real and synthetic data
Context. The LOFAR observations of diffuse interstellar polarization at meter wavelengths reveal intricate polarized-intensity structures with an unexpected correlation with neutral H I filaments that cannot be reproduced in simulations with a low cold-neutral-medium abundance. Aims. We aim to investigate whether magneto-hydrodynamic simulations of a thermally bi-stable neutral interstellar medium, with a range of CNM mass fraction, can reproduce the properties of the 3C196 field, which is the high-Galactic-latitude test observational field. Methods. Using 50 pc simulations with varying levels of turbulence and compressibility, we generated synthetic 21 cm and synchrotron observations, including instrumental noise and beam effects, for different line-of-sight orientations relative to the magnetic field. To this end, we developed the code Mock Observation Of Synchrotron Emission (MOOSE) used to generate synthetic synchrotron polarization and Faraday tomography. We also developed a metric, eta, based on the histogram of oriented gradients (HOG) algorithm, to quantify the relative contribution of cold and warm neutral medium structures to the Faraday tomographic data. Results. The synthetic observations show levels of polarization intensity and rotation measure values comparable to those of the 3C196 field, indicating that thermal electrons associated with the neutral H I phase can account for a significant fraction of the synchrotron polarized emission at 100-200 MHz. The simulations consistently reveal a correlation between CNM and Faraday tomographic structures that depends on turbulence level, magnetic-field orientation, and observational noise, but only weakly on CNM mass fraction. We found slightly weaker correlation level between the CNM and polarized-synchrotron emission than that observed in the 3C196 field. Many elements could contribute to this result: the n_e prescription, contribution of the warm ionized medium (not modeled), the longer line of sight in the data compared to the simulations, and the Fourier driving producing CNM structures that are less aligned with B. Conclusions. These results, although based on comparison with the 3C196 field alone, suggest that low-frequency polarimetric observations provide a valuable probe of magnetic-field morphology in the multiphase interstellar medium of the solar neighborhood, while simultaneously underscoring the need for improved modeling of the turbulent, multiphase, and partially ionized interstellar medium. A broader comparative analysis will be essential to more fully clarify how our findings inform the connection between low-frequency polarization data and the structure of partially ionized gas.