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Clustering Properties of Galaxies at z ~ 4 in the Subaru/XMM Deep Survey Field

We study the clustering properties of about 1200 z ~ 4 Lyman break galaxy (LBG) candidates with i′ < 26 that are selected by color from deep BRi′ imaging data of a 618 arcmin2 area in the Subaru/XMM-Newton Deep Field taken with Subaru Prime Focus Camera. The contamination and completeness of our LBG sample are evaluated, on the basis of the Hubble Deep Field-North (HDF-N) objects, to be 17% and 45%, respectively. We derive the angular correlation function over θ = 2′′-1000′′ and find that it is fitted fairly well by a power law, ω(θ) = Aωθ-0.8, with Aω = 0.71 ± 0.26. We then calculate the correlation length r0 (in comoving units) of the two-point spatial correlation function ξ(r) = (r/r0)-1.8 from Aω using the redshift distribution of LBGs derived from the HDF-N and find that r0 = 2.7 h-1 Mpc in a Λ-dominated universe (Ωm = 0.3 and ΩΛ = 0.7). This is twice as large as the correlation length of the dark matter at z ≃ 4 predicted from an analytic model by Peacock and Dodds but about twice as small as that of bright galaxies predicted from a semianalytic model by Baugh and coworkers. We find an excess of ω(θ) on small scales (θ ≲ 5′′), departing from the power-law fit by over 3 σ significance levels. Interpreting this as being due to galaxy mergers, we estimate the fraction of galaxies undergoing mergers in our LBG sample to be 3.0% ± 0.9%, which is significantly smaller than those of galaxies at intermediate redshifts.