Interpreting the Observed Clustering of Red Galaxies atz∼ 3

Daddi et al. have recently reported strong clustering of a population of redgalaxies at z~3 in the Hubble Deep Field-South. Fitting the observed angularclustering with a power law of index -0.8, they infer a comoving correlationlength r_0~8 Mpc/h; for a standard cosmology, this r_0 would imply that the redgalaxies reside in rare, M>10^{13} Msun/h halos, with each halo hosting ~100galaxies to match the number density of the population. Using the framework ofthe halo occupation distribution (HOD) in a $\Lambda$CDM universe, we show thatthe Daddi et al. data can be adequately reproduced by less surprising models,e.g., models with galaxies residing in halos of mass M>M_min=6.3x10^{11} Msun/hand a mean occupation Navg(M)=1.4(M/M_min)^{0.45} above this cutoff. Theresultant correlation functions do not follow a strict power law, showinginstead a clear transition from the 1-halo dominated regime, where the twogalaxies of each pair reside in the same dark matter halo, to the 2-halodominated regime, where the two galaxies of each pair are from different halos.The observed high-amplitude data points lie in the one-halo-dominated regime,so these HOD models are able to explain the observations despite having smallercorrelation lengths, r_0~5 Mpc/h. HOD parameters are only loosely constrainedby the current data because of large sample variance and the lack of clusteringinformation on scales that probe the 2-halo regime. If our explanation of thedata is correct, then future observations covering a larger area should showthat the large scale correlations lie below a \theta^{-1.8} extrapolation ofthe small scale points. Our models of the current data suggest that the redgalaxies are somewhat more strongly clustered than UV-selected Lyman-breakgalaxies and have a greater tendency to reside in small groups.Comment: 16 pages, 2 figures. To appear in ApJ (July 20th, 2004). Minor revisions to match the version in pres