Modeling parity-violating spectra in Galactic dust polarization with filaments and its applications to cosmic birefringence searches

We extend the dust-filament-based model presented in Herv\'ias-Caimapo & Huffenberger 2022 to produce parity-violating foreground spectra by manipulating the filament orientations relative to the magnetic field. We calibrate our model to observations of the misalignment angle using cross-correlations of Planck and HI 21-cm line data, producing a fiducial model that predicts a $\mathcal{D}_{\ell}^{EB}\sim$few $\mu$K$^2$ dust signal at 353 GHz and where $\sim 56$% of filaments have a positive misalignment angle. The main purpose of this model is to be used as dust with non-zero parity-violating emission in forecasting a measurement of cosmic birefringence by upcoming experiments. Here, we also use our fiducial model to assess the impact of dust in measurements of the isotropic cosmic birefringence angle $\beta$ with Planck data by measuring the misalignment angle as a function of scale, as well as directly using our model's $\mathcal{D}_{\ell}^{EB}$ prediction as a template. In both cases, we measure $\beta$ to be consistent within $0.83\sigma$ of the equivalent measurements with Planck data and its derivatives.