Context. Cosmological simulations predict significant secondary dependences of halo clustering on a variety of internal halo properties, and on environmental factors. Detecting these often subtle signals in observational data remains a significant challenge, with important ramifications for both galaxy evolution and cosmology. Aims. We probed secondary halo bias in observational survey data, employing galaxy groups as proxies for dark matter haloes. We quantified the strength of multiple secondary bias signals defined by the colour of the central galaxy and various environmental diagnostics. Methods. We employed an extended and refined galaxy group catalogue constructed from the Sloan Digital Sky Survey. Secondary bias is defined as any deviation in the clustering strength of groups at fixed mass, quantified through the projected two-point correlation function. Our environmental analysis uses the DisPerSE cosmic-web reconstruction algorithm to compute the distances to the critical points of the density field and incorporates local group overdensity measurements on multiple spatial scales. Results. We robustly detected 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 brelative ranging from ∼1.2 for the 15% reddest centrals to ∼0.8 for the bluest. Environmental dependences 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 brelative ∼ 1.4, while those in the least dense regions fall to brelative ∼ 0.7. These results establish a clear observational hierarchy for secondary halo bias. Conclusions. 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.
Rodríguez et al. (Wed,) studied this question.