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We investigate the alignment of haloes with the filaments of the cosmic webusing an unprecedently large sample of dark matter haloes taken from theP-Millennium $\Lambda$CDM cosmological N-body simulation. We use thestate-of-the-art NEXUS morphological formalism which, due to its multiscalenature, simultaneously identifies structures at all scales. We find strong andhighly significant alignments, with both the major axis of haloes and theirpeculiar velocity tending to orient along the filament. However, the spin -filament alignment displays a more complex trend changing from preferentiallyparallel at low masses to preferentially perpendicular at high masses. This"spin flip" occurs at an average mass of $5\times10^{11}~h^{-1}M_\odot$. Thismass increases with increasing filament diameter, varying by more than an orderof magnitude between the thinnest and thickest filament samples. We also findthat the inner parts of haloes have a spin flip mass that is several timessmaller than that of the halo as a whole. These results confirm that recentaccretion is responsible for the complex behaviour of the halo spin - filamentalignment. Low-mass haloes mainly accrete mass along directions perpendicularto their host filament and thus their spins tend to be oriented along thefilaments. In contrast, high-mass haloes mainly accrete along their hostfilaments and have their spins preferentially perpendicular to them.Furthermore, haloes located in thinner filaments are more likely to accretealong their host filaments than haloes of the same mass located in thickerfilaments.

The Cosmic Ballet: spin and shape alignments of haloes in the cosmic web