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Clustering of dark matter halos has been shown to depend on halo propertiesbeyond mass such as halo concentration, a phenomenon referred to as haloassembly bias. Standard halo occupation models (HOD) in large scale structurestudies assume that halo mass alone is sufficient in characterizing theconnection between galaxies and halos. Modeling of galaxy clustering can facesystematic effects if the number of galaxies within a halo is correlated withother halo properties. Using the Small MultiDark-Planck high resolution$N$-body simulation and the clustering measurements of the Sloan Digital SkySurvey (SDSS) DR7 main galaxy sample, we investigate the extent to which theconcentration-dependence of halo occupation can be constrained. Furthermore, westudy how allowing for the concentration dependence can improve our modeling ofgalaxy clustering.  Our constraints on HOD with assembly bias suggest that satellite populationis not correlated with halo concentration at fixed halo mass. At fixed halomass, our constraints favor lack of correlation between the occupation ofcentrals and halo concentration in the most luminous samples ($M_{\rmr}<-21.5,-21$), and modest correlation in the $M_{\rm r}<-20.5,-20, -19.5$samples. We show that in comparison with abundance-matching mock catalogs, ourfindings suggest qualitatively similar but modest levels of the impact of haloassembly bias on galaxy clustering. The effect is only present in the centraloccupation and becomes less significant in brighter galaxy samples.Furthermore, by performing model comparison based on information criteria, wefind that in most cases, the standard mass-only HOD model is still favored bythe observations.

How are galaxies assigned to halos? Searching for assembly bias in the SDSS galaxy clustering