If the formation of central galaxies in dark matter haloes traces the assembly history of their host haloes, in haloes of fixed mass, central galaxy clustering may show dependence on properties indicating their formation history. Such a galaxy assembly bias effect has been investigated by Lin et al. 2016, with samples of central galaxies constructed in haloes of similar mass and with mean halo mass verified by galaxy lensing measurements, and no significant evidence of assembly bias is found from the analysis of the projected two-point correlation functions of early- and late-forming central galaxies. In this work, we extend the the investigation of assembly bias effect from real space to redshift (velocity) space, with an extended construction of early- and late-forming galaxies. We carry out halo occupation distribution modelling to constrain the galaxy-halo connection to see whether there is any sign of the effect of assembly bias. We find largely consistent host halo mass for early- and late-forming central galaxies, corroborated by lensing measurements. The central velocity bias parameters, which are supposed to characterise the mutual relaxation between central galaxies and their host haloes, are inferred to overlap between early- and late-forming central galaxies. However, we find a large amplitude of velocity bias for early-forming central galaxies (e.g. with central galaxies moving at more than 50% that of dark matter velocity dispersion inside host haloes), which may signal an assembly bias effect. A large sample with two-point correlation functions and other clustering measurements and improved modelling will help reach a conclusive result.
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