Cosmic Ballet III: halo spin evolution in the cosmic web
  We explore the evolution of halo spins in the cosmic web using a very large
sample of dark matter haloes in the $\Lambda$CDM Planck-Millennium N-body
simulation. We use the NEXUS+ multiscale formalism to identify the hierarchy of
filaments and sheets of the cosmic web at several redshifts. We find that at
all times the magnitude of halo spins correlates with the web environment,
being largest in filaments, and, for the first time, we show that it also
correlates with filament thickness as well as the angle between
spin-orientation and the spine of the host filament. For example, massive
haloes in thick filaments spin faster than their counterparts in thin
filaments, while for low-mass haloes the reverse is true. We also have studied
the evolution of alignment between halo spin orientations and the preferential
axes of filaments and sheets. The alignment varies with halo mass, with the
spins of low-mass haloes being predominantly along the filament spine, while
those of high-mass haloes being predominantly perpendicular to the filament
spine. On average, for all halo masses, halo spins become more perpendicular to
the filament spine at later times. At all redshifts, the spin alignment shows a
considerable variation with filament thickness, with the halo mass
corresponding to the transition from parallel to perpendicular alignment
varying by more than one order of magnitude. The environmental dependence of
halo spin magnitude shows little evolution for $z\leq2$ and is likely a
consequence of the correlations in the initial conditions or high redshift
effects
