The Structure and Dynamics of Massive High-$z$ Cosmic-Web Filaments: Three Radial Zones in Filament Cross-Sections

We analyze the internal cross-section structure and dynamics of inter-halo cosmic-web filaments that connect to massive high-$z$ galaxies. Our analysis is based on a high-resolution \texttt{AREPO} cosmological simulation zooming in on a volume encompassing three filaments of $\sim 1 \, \Mpc$ length feeding three massive haloes of $\sim 10^{12}\,\msun$ at $z \sim 4$, embedded in a large-scale sheet. Each filament is surrounded by a strong cylindrical accretion shock of radius $r_{\rm shock} \sim 50 \kpc$, within which the gas is in virial equilibrium in the potential well set by an isothermal dark-matter filament. The cross-section of the filament can be divided into three radial zones. In the outer ``thermal'' (\textbf{T}) zone, $r \geq 0.65 \, r_{\rm shock}$, the inward gravity and ram-pressure forces from the inflowing gas are over-balanced by outward thermal pressure forces, causing the inflowing gas to decelerate and the shock to expand outwards. In the intermediate ``vortex'' (\textbf{V}) zone, $0.25 \leq r/ r_{\rm shock} \leq 0.65$, the velocity field is dominated by a quadrupolar vortex structure due to offset inflow along the sheet through the post-shock gas. The outward force is provided mainly by centrifugal forces associated with these vortices and, to a lesser extent, by global rotation and thermal pressure, while shear and turbulent forces that are also associated with the vortex structure add to the force inward. The inner ``stream'' (\textbf{S}) zone, $r < 0.25 \, r_{\rm shock}$, is a dense isothermal core defining the cold streams that feed the galaxies, with $T\sim 3 \times 10^4 \, \Kdegree$ and $n_{\rm H}\sim 0.01 \cmc$. The core is formed by an isobaric cooling flow that results from post-shock cooling on a free-fall time, and is associated with a decrease in the outward forces, though the gas within the core exhibits both inflows and outflows. [abridged]