The supernova-regulated ISM. IV. A comparison of simulated polarization with Planck observations

The efforts for comparing dust polarization measurements with synthetic observations from MHD models have previously concentrated on the scale of molecular clouds. Here we extend the model comparisons to kiloparsec scales, taking into account hot shocked gas generated by supernovae, and a non-uniform dynamo-generated magnetic field at both large and small scales down to 4 pc spatial resolution. Radiative transfer calculations are used to model dust emission and polarization on the top of MHD simulations. We compute synthetic maps of column density $N_H$, polarization fraction $p$, and polarization angle dispersion $S$, and study their dependencies on the important properties of the MHD simulations. These include the large-scale magnetic field and its orientation, the small-scale magnetic field, and supernova-driven shocks. Similar filament-like structures of $S$ as seen in the Planck all-sky maps are visible in our synthetic results, although the smallest scale structures are absent from our maps. Supernova-driven shock fronts and $S$ do not show significant correlation. Instead, $S$ can clearly be attributed to the distribution of the small-scale magnetic field. We also find that the large-scale magnetic field influences the polarization properties, such that, for a given strength of magnetic fluctuation, a strong plane-of-the-sky mean field weakens the observed $S$, while strengthening $p$. The anticorrelation of $p$ and $S$, and decreasing $p$ as a function of $N_H$ are consistent across all synthetic observations. The magnetic fluctuations follow an exponential distribution, rather than Gaussian, characteristic of flows with intermittent repetitive shocks. The observed polarization properties and column densities are sensitive to the line of sight distance over which the emission is integrated.