Multipolar moments of weak lensing signal around clusters. Weighing
  filaments in harmonic space
  Context. Upcoming weak lensing surveys such as Euclid will provide an
unprecedented opportunity to quantify the geometry and topology of the cosmic
web, in particular in the vicinity of lensing clusters. Aims. Understanding the
connectivity of the cosmic web with unbiased mass tracers, such as weak
lensing, is of prime importance to probe the underlying cosmology, seek
dynamical signatures of dark matter, and quantify environmental effects on
galaxy formation. Methods. Mock catalogues of galaxy clusters are extracted
from the N-body PLUS simulation. For each cluster, the aperture multipolar
moments of the convergence are calculated in two annuli (inside and outside the
virial radius). By stacking their modulus, a statistical estimator is built to
characterise the angular mass distribution around clusters. The moments are
compared to predictions from perturbation theory and spherical collapse.
Results. The main weakly chromatic excess of multipolar power on large scales
is understood as arising from the contraction of the primordial cosmic web
driven by the growing potential well of the cluster. Besides this boost, the
quadrupole prevails in the cluster (ellipsoidal) core, while at the outskirts,
harmonic distortions are spread on small angular modes, and trace the
non-linear sharpening of the filamentary structures. Predictions for the signal
amplitude as a function of the cluster-centric distance, mass, and redshift are
presented. The prospects of measuring this signal are estimated for current and
future lensing data sets. Conclusions. The Euclid mission should provide all
the necessary information for studying the cosmic evolution of the connectivity
of the cosmic web around lensing clusters using multipolar moments and probing
unique signatures of, for example, baryons and warm dark matter.
