Connecting clustering and the cosmic web:Observational constraints on secondary halo bias

Abstract

Cosmological simulations predict significant secondary dependencies of halo clustering on internal properties and environment. Detecting these subtle signals in observational data remains challenging, with important ramifications for galaxy evolution and cosmology. We probe secondary halo bias in observational survey data, using galaxy groups as dark matter halo proxies. We quantify secondary bias using central galaxy colour and environmental diagnostics. We use an extended, refined galaxy group catalogue from the Sloan Digital Sky Survey. Secondary bias is defined as any deviation in group clustering strength at fixed mass, quantified through the projected two-point correlation function. Our environmental analysis uses DisPerSE to compute distances to critical points of the density field, incorporating local group overdensity measurements on multiple scales. We robustly detect several forms of secondary bias in the clustering of galaxy groups. At fixed mass, groups hosting red central galaxies are more strongly clustered than those with blue centrals, with $b_{\rm relative}$ ranging from $\sim 1.2$ for the 15\% reddest centrals to $\sim 0.8$ for the bluest ones. Environmental dependencies based on cosmic-web distances are also present, though significantly weaker and largely mass-independent. The strongest signal arises from local overdensity: groups in the densest 15\% of environments reach $b_{\rm relative} \sim 1.4$, while those in the least dense regions fall to $b_{\rm relative} \sim 0.7$. These results establish a clear observational hierarchy for secondary halo bias. The colour of central galaxies correlates with the local group overdensity, which, in turn, correlates with the bias at fixed group mass. Assuming that central galaxy colour traces halo assembly history, this three-stage picture offers a conceptual link between our results and halo assembly bias.

Figures (10)

• Figure 1: Main properties of the galaxy groups analysed in this study. The top panel presents the group mass distribution, which exhibits the characteristic decreasing shape. The bottom panel displays the colour ($g-r$) distribution of the central galaxies within these groups. The bimodal nature of this distribution clearly distinguishes between the red and blue galaxy subpopulations.
• Figure 2: Distribution of minimum distances to the cosmic web critical points obtained from DisPerSE. The histograms show the number of central galaxies as a function of their minimum three-dimensional distance to Maxima, Minima, Filament saddles, and Wall saddles.
• Figure 3: Spatial distribution of central galaxies relative to cosmic web topology. The figure visualizes central galaxies within a $-5^{\circ}$-to-$15^{\circ}$ declination slice of the SDSS Legacy North survey. The panels display the spatial positions of central galaxies, characterized by their minimum three-dimensional distance to the four DisPerSE critical point types (Maxima, Minima, Filament saddles, and Wall saddles). Colour-coding represents the scaled distance to the corresponding critical point, given by $\log_{10}(\text{distance}+1)$.
• Figure 4: Distribution of central galaxy colour as a function of cosmic web location and local overdensity. In each panel, a scatter diagram shows the relation between the distance to each critical point of the density field and the local group overdensity ($\log_{10}(\delta)$) on $5$$h^{-1}\, \rm Mpc$ scales for all central galaxies in our sample, colour-coded by their $g-r$ colour. From top to bottom, the panels illustrate the distribution with respect to the distance to: (1) Maxima ($d_{\mathrm{Max}}$), (2) Filament saddles ($d_{\mathrm{Fsadd}}$), (3) Wall saddles ($d_{\mathrm{WSadd}}$), and (4) Minima ($d_{\mathrm{Min}}$). The contour lines (black lines) represent the progressively lower density levels (down to $5\%$ of the peak value). The horizontal dashed lines (green and magenta) mark the 15th ($P_{15}$) and 85th ($P_{85}$) percentiles of the distance distribution, respectively, used to define environment thresholds.
• Figure 5: Secondary bias measurements for subsets of groups split by the colour of their central galaxies (colour bias). Results are shown for both the extreme 15% reddest and bluest centrals (darker colours) and the 50% reddest and bluest centrals (lighter colours). Uncertainties are estimated using jackknife resampling with 50 subsamples for the correlation functions and propagated to the relative bias.