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Modelling galaxy clustering: halo occupation distribution versus subhalo matching

We model the luminosity-dependent projected and redshift-space two-point correlation functions (2PCFs) of the Sloan Digital Sky Survey (SDSS) DR7 Main galaxy sample, using the halo occupation distribution (HOD) model and the subhalo abundance matching (SHAM) model and its extension. All the models are built on the same high-resolution $N$-body simulations. We find that the HOD model generally provides the best performance in reproducing the clustering measurements in both projected and redshift spaces. The SHAM model with the same halo-galaxy relation for central and satellite galaxies (or distinct haloes and subhaloes), when including scatters, has a best-fitting $χ^2/\rm{dof}$ around $2$--$3$. We therefore extend the SHAM model to the subhalo clustering and abundance matching (SCAM) by allowing the central and satellite galaxies to have different galaxy--halo relations. We infer the corresponding halo/subhalo parameters by jointly fitting the galaxy 2PCFs and abundances and consider subhaloes selected based on three properties, the mass $M_{\rm acc}$ at the time of accretion, the maximum circular velocity $V_{\rm acc}$ at the time of accretion, and the peak maximum circular velocity $V_{\rm peak}$ over the history of the subhaloes. The three subhalo models work well for luminous galaxy samples (with luminosity above $L_*$). For low-luminosity samples, the $V_{\rm acc}$ model stands out in reproducing the data, with the $V_{\rm peak}$ model slightly worse, while the $M_{\rm acc}$ model fails to fit the data. We discuss the implications of the modeling results.