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Galaxy assembly bias, the correlation between galaxy properties and haloproperties at fixed halo mass, could be an important ingredient in halo-basedmodelling of galaxy clustering. We investigate the central galaxy assembly biasby studying the relation between various galaxy and halo properties in theIllustris hydrodynamic galaxy formation simulation. Galaxy stellar mass$\Mstar$ is found to have a tighter correlation with peak maximum halo circularvelocity $\Vp$ than with halo mass $\Mh$. Once the correlation with $\Vp$ isaccounted for, $\Mstar$ has nearly no dependence on any other halo assemblyvariables. The correlations between galaxy properties related to star formationhistory and halo assembly properties also show a cleaner form as a function of$\Vp$ than as a function of $\Mh$, with the main correlation being with haloformation time and to a less extent halo concentration. Based on thegalaxy-halo relation, we present a simple model to relate the bias factors of acentral galaxy sample and the corresponding halo sample, both selected based onassembly-related properties. It is found that they are connected by thecorrelation coefficient of the galaxy and halo properties used to define thetwo samples, which provides a reasonable description for the samples in thesimulation and suggests a simple prescription to incorporate galaxy assemblybias into the halo model. By applying the model to the local galaxy clusteringmeasurements in Lin et al. (2016), we infer that the correlation between starformation history or specific star formation rate and halo formation time isconsistent with being weak.

Galaxy assembly bias of central galaxies in the Illustris simulation