Analytical halo models of cosmic tidal fields
  The non-linear cosmic web environment of dark matter haloes plays a major
role in shaping their growth and evolution, and potentially also affects the
galaxies that reside in them. We develop an analytical (halo model) formalism
to describe the tidal field of anisotropic halo-centric density distributions,
as characterised by the halo-centric tidal tensor $\langle T_{ij} \rangle(<R)$
spherically averaged on scale $R\sim4R_{\rm vir}$ for haloes of virial radius
$R_{\rm vir}$. We focus on axisymmetric anisotropies, which allows us to
explore simple and intuitive toy models of (sub)halo configurations that
exemplify some of the most interesting anisotropies in the cosmic web. We build
our models around the spherical Navarro-Frenk-White (NFW) profile after
describing it as a Gaussian mixture, which leads to almost fully analytical
expressions for the `tidal anisotropy' scalar $\alpha(<4R_{\rm vir})$ extracted
from the tidal tensor. Our axisymmetric examples include (i) a spherical halo
at the axis of a cylindrical filament, (ii) an off-centred satellite in a
spherical host halo and (iii) an axisymmetric halo. Using these, we demonstrate
several interesting results. For example, the tidal tensor at the axis of a
pure cylindrical filament gives $\alpha^{\rm (fil)}(<R)=1/2$ exactly, for any
$R$. Also, $\alpha(<4R_{\rm vir,sat})$ for a satellite of radius $R_{\rm
vir,sat}$ as a function of its host-centric distance is a sensitive probe of
dynamical mass loss of the satellite in its host environment. Finally, we
discuss a number of potentially interesting extensions and applications of our
formalism that can deepen our understanding of the multi-scale phenomenology of
the cosmic web.
