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The continuous flow of gas and dark matter across scales in the cosmic webcan generate correlated dynamical properties of haloes and filaments (and themagnetic fields they contain). With this work, we study the halo spinproperties and orientation with respect to filaments, and the morphology of themagnetic field around these objects, for haloes with masses in the range1e8-1e14 Msun and filaments up to 8 Mpc long. Furthermore, we study how theseproperties vary in presence, or lack thereof, of different (astro)physicalprocesses and with different magnetic initial conditions. We performcosmological magnetohydrodynamical simulations with the Eulerian code Enzo andwe develop a simple and robust algorithm to study the filamentary connectivityof haloes in three dimensions. We investigate the morphological and magneticproperties and focus on the alignment of the magnetic field along filaments:our analysis suggests that the degree of this alignment is partially dependenton the physical processes involved, as well as on magnetic initial conditions.We discuss the contribution of this effect on a potential attempt to detect themagnetic field surrounding these objects: we find that it introduces a bias inthe estimation of the magnetic field from Faraday rotation measure techniques.Specifically, given the strong tendency we find for extragalactic magneticfields to align with the filaments axis, the value of the magnetic field can beunderestimated by a factor 3, because this effect contributes to making theline-of-sight magnetic field (for filaments in the plane of the sky) muchsmaller than the total one.

On the alignment of haloes, filaments and magnetic fields in the simulated cosmic web