A statistical approach for interpreting polarized dust emission of the filamentary molecular clouds toward the estimate of 3D magnetic field structure

In this study, we perform 3D magnetohydrodynamics (MHD) simulations of filamentary molecular clouds. We then generate synthetic observations based on the simulation results. Using these, we investigate how the new polarization data analysis method recently introduced by Doi et al. (2021) reflects the magnetic field structure in turbulent filamentary molecular clouds. Doi et al. (2021) proposed that the $R_{\mathrm{F}\mathrm{W}\mathrm{H}\mathrm{M}}$, the ratio of the Full Width at Half Maximum (FWHM) of the polarized intensity ($PI$) to that of the total intensity ($I$) can be used to probe the three-dimensional structure of the magnetic field. We calculate the $R_{\mathrm{F}\mathrm{W}\mathrm{H}\mathrm{M}}$ from the density and magnetic field structure obtained in the 3D-MHD simulations. We find that the mean and variance of $R_{\mathrm{F}\mathrm{W}\mathrm{H}\mathrm{M}}$ within a filament are smaller and larger, respectively, with a larger inclination of the magnetic field to the plane-of-sky. We also find that both small-scale ($<0.1\mathrm{p}\mathrm{c}$) and large-scale ($\gtrsim 0.1\mathrm{p}\mathrm{c}$) turbulence affect the polarized intensity of the dust thermal emission. We conclude that future extensive observations of $R_{\mathrm{F}\mathrm{W}\mathrm{H}\mathrm{M}}$ may be able to quantify the inclination of the magnetic field to the plane-of-sky in the filamentary molecular clouds.