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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&#39; scalar $α(<4R_{\rm vir})$ 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 $α^{\rm (fil)}(<R)=1/2$ exactly, for any $R$. Also, $α(<4R_{\rm vir,sat})$ 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.