Rapid Blue- and Red-shifted Excursions in H$\alpha$ line profiles synthesized from realistic 3D MHD simulations

Rapid blue- and red-shifted events (RBEs/RREs) may have an important role in mass-loading and heating the solar corona, but their nature and origin are still debatable. We aim to model these features to learn more about their properties, formation and origin. A realistic three-dimensional (3D) magneto-hydrodynamic (MHD) model of a solar plage region is created. Synthetic H$\alpha$ spectra are generated and the spectral signatures of these features are identified. The magnetic field lines associated with these events are traced and the underlying dynamic is studied. The model reproduces well many properties of RBEs and RREs, such as spatial distribution, lateral movement, length and lifetimes. Synthetic H$\alpha$ line profiles, similarly to observed ones, show strong blue- or red-shift and asymmetries. These line profiles are caused by the vertical component of velocity with magnitudes larger than $30-40$ km/s that appear mostly in the height range of $2-4$ Mm. By tracing magnetic field lines, we show that the vertical velocity that causes the appearance of RBE/RREs to appear is always associated with the component of velocity perpendicular to the magnetic field line. The study confirms the hypothesis that RBEs and RREs are signs of Alfv{\'e}nic waves with, in some cases, a significant contribution from slow magneto-acoustic mode.