A continuous parameterization of the cosmic web

TL;DR

The paper tackles the environment–galaxy connection by replacing discrete cosmic web classifications with a continuous description derived from Hessian eigenvalue ratios of the matter density field. Using a DM-only run (smdpl) coupled to the SAG semi-analytic model, it computes the eigenvalues $a\ge b\ge c$ from the tidal field and analyzes environment via $b/a$ and $c/a$ (without relying on a fixed $\lambda_{\rm th}$). The key findings show a continuous distribution of eigenvalue ratios and that $c/a$ provides the strongest environmental signal, correlating with galaxy properties such as color, sSFR, and gas fraction, and revealing transitions around characteristic halo masses. This threshold-free framework is robust to smoothing scales and complements traditional classifications, with clear potential for applying similar analyses to observations once tidal fields can be reconstructed from survey data via DM density and velocity fields.

Abstract

The intrinsic properties of galaxies are influenced by their environments, underscoring the environment's critical role in galaxy formation and evolution. Traditionally, these environments are categorized into four fixed classifications: knots, filaments, walls, and voids, which collectively describe the complex organization of galaxies within large-scale structures. We propose an alternative description that complements the traditional quadripartite categorization by introducing a continuous framework, allowing for a more nuanced examination of the relationship between the intrinsic properties of galaxies and their environments. This complementary description is applied using one of the most prevalent methodologies: categorization using the eigenvalues of the Hessian matrix extracted from the matter density field. We integrated our findings into a semi-analytical model of galaxy formation, combined with cosmological numerical simulations, to analyze how the intrinsic properties of galaxies are influenced by environmental changes. In our study, we find a continuous distribution of eigenvalue ratios, revealing a clear dependence of galaxy properties on their surrounding environments. This method allowed us to identify critical values at which transitions in the behavior of key astrophysical galaxy properties become evident.

Figures (12)

• Figure 1: Relationship between the eigenvalue ratios $b/a$ and $c/a$ for central galaxies, according to conventional classification of the cosmic web, using the threshold $\lambda_{\rm th} = 0$. Each point corresponds to one galaxy, which is color-coded according to the eigenvalues associated with the cell it occupies as indicated by the legend. The size of the magenta points has been arbitrarily increased for visibility, as they are very sparse. The dotted black lines delineate the regions that the eigenvalue ratios may occupy. The horizontal dotted black line at $b/a=1$ indicates that $b/a<1$ whenever $a>0$ and $b/a>1$ only when $a<0$. The positively sloped dotted black line indicates the condition $a>b>c$, which implies $b/a>c/a$ if $a>0$ and $b/a<c/a$ if $a<0$. The area inside (outside) the orange triangle corresponds to $\delta > 0$ ($\delta < 0$).
• Figure 2: Eigenvalue ratios, $b/a$ and $c/a$, as a function of the logarithm of the halo mass ($M_{200}$). Left panel: $b/a$ as a function of $c/a$ in bins of the logarithm of halo mass. This panel shows a zoomed-in view of the region displayed in Fig. \ref{['fig:kfwv_color']}, centered at origin. The dotted black lines delineate the regions that the eigenvalue ratios may occupy. The upper limit of the graph, $b/a=1$, indicates that $b/a<1$ whenever $a>0$. The positively sloped dotted black line indicates the condition $a>b>c$, which implies $b/a>c/a$ if $a>0$ and $b/a<c/a$ if $a<0$. Right panel: Median values of $b/a$ (triangles) and $c/a$ (circles) for equal bins of the logarithm of the halo mass, as a function of the logarithm of the halo mass. In both panels, each color corresponds to each halo mass bin, as indicated by the legend.
• Figure 3: Eigenvalues ratios, $b/a$ and $c/a$, as a function of the logarithm of the stellar mass ($M_{\star}$). Left panel: Eigenvalues ratios, $b/a$ vs. $c/a$, in bins of the logarithm of stellar mass. Right panel: Median values of $b/a$ (triangles) and $c/a$ (circles) for equal bins of the logarithm of the stellar mass, as a function of the logarithm of the stellar mass. In both panels, each color corresponds to each stellar mass bin, as indicated by the legend.
• Figure 4: Spatial distribution of central galaxies, in a slice of $1 \,{\rm Mpc}\,h^{-1}$ in a box of the smdpl simulation. The background shows the logarithm of the density contrast estimated from DM particles, where the colors correspond to the values indicated in the color bar. White filled circles represent galaxies located in environments where the values of their eigenvalue ratios $b/a$ and $c/a$ (corresponding to the cell in which they are located) fall within a circle of radius $0.1 \,{\rm Mpc}\,h^{-1}$ centered on the peaks of three of the contours in the left panel of Fig. \ref{['fig:smass']} marked with crosses. The panels correspond to the blue (left), green (middle), and red crosses (right). Above each panel, the ($c/a$, $b/a$) values are indicated for each cross.
• Figure 5: Galaxy properties as a function of the logarithm of the stellar mass. From top to bottom: Logarithm of DM halo mass, color ( g-r), logarithm of the sSFR, and logarithm of the gas fraction. Each column displays the dependence of these properties on the environment: equal bins in $b/a$ (left panels) and equal bins in $c/a$ (middle panels). Each solid colored line corresponds to one of these bins, as indicated by the legends in each panel. Next to each bin, the number of galaxies contained within that bin is specified. The solid gray line in each panel represents the total sample. For comparison, the right panels show the dependence of these properties on the environment according to the traditional method, categorizing the environment into four types: knots, filaments, walls, and voids. Each main panel is accompanied by a lower panel that shows the difference ($\Delta$) between each colored line and the gray line.