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

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.