We investigate the luminosity and colour dependence of clustering of CMASS galaxies in the Sloan Digital Sky Survey-III Baryon Oscillation Spectroscopic Survey Tenth Data Release. The halo occupation distribution framework is adopted to model the projected two-point correlation function measurements on small and intermediate scales (from $0.02$ to $60,h^{-1}{rm {Mpc}}$) and to interpret the observed trends and infer the connection of galaxies to dark matter halos. We find that luminous red galaxies reside in massive halos of mass $M{sim}10^{13}$--$10^{14},h^{-1}{rm M_odot}$ and more luminous galaxies are more clustered and hosted by more massive halos. The strong small-scale clustering requires a fraction of these galaxies to be satellites in massive halos, with the fraction at the level of 5--8 per cent and decreasing with luminosity. The characteristic mass of a halo hosting on average one satellite galaxy above a luminosity threshold is about a factor $8.7$ larger than that of a halo hosting a central galaxy above the same threshold. At a fixed luminosity, progressively redder galaxies are more strongly clustered on small scales, which can be explained by having a larger fraction of these galaxies in the form of satellites in massive halos. Our clustering measurements on scales below $0.4,h^{-1}{rm {Mpc}}$ allow us to study the small-scale spatial distribution of satellites inside halos. While the clustering of luminosity-threshold samples can be well described by a Navarro-Frenk-White (NFW) profile, that of the reddest galaxies prefers a steeper or more concentrated profile. Finally, we also use galaxy samples of constant number density at different redshifts to study the evolution of luminous galaxies, and find the clustering to be consistent with passive evolution in the redshift range of $0.5 lesssim z lesssim 0.6$.
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