Which filaments matter: the relative scalings of anisotropic infall

Abstract

Dark-matter haloes do not form in isolation but within the surrounding cosmic web. By the time a halo begins to collapse, its larger-scale environment has typically collapsed along two axes, forming filaments that channel anisotropic infall toward the halo. In this work, we derive from first principles the characteristic Lagrangian scale ratio at which such an anisotropic tidal field most strongly influences halo formation. Specifically, we identify the inflection point of the conditional probability that the tidal field, smoothed on a scale Rsd, undergoes two-dimensional compression, given the presence of a density peak of rarity nu on a smaller scale Rpk. For a standard LambdaCDM cosmology, we find (Rsd/Rpk)infl = 2.2 + (nu-2.5) for Rpk corresponding to a tophat filter of 8Mpc/h. This result implies that the anisotropic tidal influence on a collapsing halo typically extends to 2-3 times the size of its Lagrangian patch. Recast as a function of formation redshift z, the characteristic filament scale around 2.5 sigma peaks can be approximated by Rsd(z) = 31 /(2+(1+z)**2)Mpc/h. We provide practical scaling laws for selecting dynamically relevant smoothing scales in large-scale surveys and for setting initial patch sizes in high-resolution zoom simulations.

Figures (12)

• Figure 1: Conditional probability (from Equation \ref{['eq:condPDF']}) of identifying a filament-saddle tidal structure at scale $R_{\rm sd}$, given a density peak with ${\nu\ge\nu_{\rm pk}=3}$ at scale $R_{\rm pk}$, for a three-dimensional GRF with a $\Lambda$CDM power spectrum. Solid curves are numerical (Monte-Carlo) results, and filled circles mark the inflection points, tracing the characteristic scale ratio where the halo-filament correlation enhances most significantly. The pink curve corresponds to the tophat filter of $8h^{-1}{\rm Mpc}$, which yields $\sigma_8\approx0.81$ at $z=0$.
• Figure 2: Characteristic scale ratio as a function of peak rarity for a $\Lambda$CDM power spectrum. Dots represent numerical results at the inflection points of conditional PDFs (e.g., Figure \ref{['fig:1']} for $\nu_{\rm pk}=3$), while dashed lines show linear fits. For a rarer peak, halo-filament correlation becomes most sensitive at a larger characteristic scale ratio.
• Figure 3: Characteristic filamentary scale ratio around halos on various scales that collapsed at various redshifts. Halo masses (top $x$-axis) corresponding to the peak scales (bottom $x$-axis) are also marked.
• Figure 4: Characteristic scale of the filamentary tidal environment that most strongly influences density peaks at the time of their collapse, as given by Equation \ref{['eqn:linear']}. Results are shown for peaks with $\nu_{\rm pk} = 3.0$ and $2.5$ (solid lines), together with their corresponding fits (dashed lines from Equation \ref{['eq:Rdcase']} and dash-dotted lines from Equation \ref{['eq:Rdzprecise']}). This relation identifies the characteristic filament scale that governs the formation of the most massive halos at their epoch of formation.
• Figure 5: Similar to Figure \ref{['fig:1']}, but for $\nu_{\rm pk}=2.5$ in a two-dimensional GRF, computed using Equation \ref{['eqn:condPDF2d']}, with a power-law spectrum, $P_m(k)\propto k^{n}$. Solid curves show numerical results, whereas black dashed curves show analytic predictions.