Clustering properties of galaxies at z ∼ 4 in the Subaru/XMM deep survey field

We study the clustering properties of about 1200 z similar to 4 Lyman break galaxy (LBG) candidates with i < 26 that are selected by color from deep BRi' imaging data of a 618 arcmin(2) 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 <theta> = 2"-1000" and find that it is fitted fairly well by a power law, omega(theta) = A(omega)theta (-0.8), with A(omega) = 0.71 +/- 0.26. We then calculate the correlation length r(o) (in comoving units) of the two-point spatial correlation function xi (r) = (r\r(o))(-1.8) from A(omega) using the redshift distribution of LBGs derived from the HDF-N and find that r(o) = 2.7(-0.6)(+0.5) h(-1) Mpc in a Lambda -dominated universe (Omega (m) = 0.3 and Omega (Lambda) = 0.7). This is twice as large as the correlation length of the dark matter at z similar or equal to 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 omega(theta) on small scales (theta less than or similar to 5"), departing from the power-law fit by over 3 sigma significance levels. Interpreting this as being due to galaxy mergers, we estimate the fraction of galaxies undergoing mergers in our LBG sample to be, which is significantly smaller than those of galaxies 3.0% +/- 0.9% at intermediate redshifts.