Local HI filaments driven by a small-scale dynamo. Unraveling velocities and tangling of dusty magnetized structures

Context. HI filaments are closely related to dusty magnetized structures that are observable in the far infrared (FIR). Recently it was proposed that the coherence of oriented H i structures in velocity traces the line-of-sight magnetic field tangling. Aims. We study the velocity dependent coherence between FIR emission at 857 GHz and HI on angular scales of 18' . Methods. We use HI4PI HI data and Planck FIR data and apply the Hessian operator to extract filaments. For coherence we demand that local orientation angles {\theta} in the FIR at 857 GHz along the filaments are correlated with the HI. Results. We find some correlation for HI column densities at |v_LSR | < 50 km/s but a tight agreement between FIR and HI orientation angles {\theta} exists only in narrow velocity intervals of 1 km/s. Accordingly we assign velocities to FIR filaments. Along the line of sight these HI structures show a high degree of the local alignment with {\theta}, also in velocity space. Interpreting these aligned structures in analogy to the polarization of dust emission defines an HI polarization. We observe polarization fractions up to 80%, with averages of 30%. Orientation angles {\theta} along the filaments, projected perpendicular to the line of sight, are fluctuating systematically and allow to determine a characteristic distribution of filament curvatures. Conclusions. Local HI and FIR filaments identified by the Hessian analysis are coherent structures with well defined radial velocities. HI structures are also organized along the line of sight with a high degree of coherence. The observed bending of these structures in the plane of the sky is consistent with models for magnetic field curvatures induced by a Galactic small-scale turbulent dynamo.