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Polarization power spectra and dust cloud morphology

In the framework of studies of the CMB polarization and its Galactic foregrounds, the angular power spectra of thermal dust polarization maps have revealed an intriguing E/B asymmetry and a positive TE correlation. In interpretation studies of these observations, magnetized ISM dust clouds have been treated as filamentary structures only; however, sheet-like shapes are also supported by observational and theoretical evidence. In this work, we study the influence of cloud shape and its connection to the local magnetic field on angular power spectra of thermal dust polarization maps. We simulate realistic filament-like and sheet-like interstellar clouds, and generate synthetic maps of their thermal dust polarized emission using the software $Asterion$. We compute their polarization power spectra in multipole range $\ell \in [100,500]$ and quantify the E/B power asymmetry through the $R_{EB}$ ratio, and the correlation coefficient $r^{TE}$ between T and E modes. We quantify the dependence of $R_{EB}$ and $r^{TE}$ values on the offset angle (between longest cloud axis and magnetic field) and inclination angle (between line-of-sight and magnetic field) for both cloud shapes embedded either in a regular or a turbulent magnetic field. We find that both cloud shapes cover the same regions of the ($R_{EB}$, $r^{TE}$) parameter space. The dependence on inclination and offset angles are similar for both shapes although sheet-like structures generally show larger scatter. In addition to the known dependence on the offset angle, we find a strong dependence of $R_{EB}$ and $r^{TE}$ on the inclination angle. The fact that filament-like and sheet-like structures may lead to polarization power spectra with similar ($R_{EB}$, $r^{TE}$) values complicates their interpretation. In future analyses, this degeneracy should be accounted for as well as the connection to the magnetic field geometry.