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 analyses that use the 353 GHz channel of Planck to constrain the filamentary misalignment or that use the commander sky model as a template for the dust $\mathcal{D}_{\ell}^{EB}$ spectrum. We attribute this consistency to the extra degrees of freedom introduced by the ad-hoc amplitude parameters for the dust parity-violating spectrum, which are capable of absorbing most of the differences between the model and data as long as a reasonable dust model is provided.