We investigate photometric properties of Lyman Break Galaxies (LBGs) at z = 3.5 − 5.2 based on large samples of 2,600 LBGs detected in deep (i ′ 27) and wide-field (1,200 arcmin 2 ) images taken in the Subaru Deep Field (SDF) and the Subaru/XMM Deep Field (SXDF) using broad band B, V , R, i ′ , and z ′ filters. The selection criteria for the LBG samples are examined with 85 spectroscopically identified objects, and the completeness and contamination of the samples are estimated from Monte Carlo simulations based on a photometric-redshift catalog of the Hubble Deep Field-North. We find that these LBG samples are nearly rest-frame UV magnitude-limited samples, missing systematically only 10% of red high-z galaxies (in number) which are a dusty population with E(B − V ) 0.4. We calculate luminosity functions of the LBGs with the estimated completeness and contamination, and find (i) that the number density of bright galaxies (M 1700 < −22 ; corresponding to SFR 100h −2 70 M ⊙ yr −1 with extinction correction) decreases significantly from z = 4 to 5 and (ii) that the faint-end slope of the luminosity functions of LBGs may become steeper towards higher redshifts. We estimate dust extinction of z ≃ 4 LBGs with M < M * (≃ −21) from UV-continuum slopes, and obtain E(B − V ) = 0.15 ± 0.03 as the mean value. The dust extinction remains constant with apparent luminosity, but increases with intrinsic (i.e., extinction-corrected) luminosity. We find no evolution in dust extinction between LBGs at z = 3 and 4. We investigate the evolution of UV-luminosity density by integrating the luminosity functions of LBGs, and find that the UV-luminosity density at 1700Å, ρ UV does not significantly change from z = 3 to z = 5, i.e., ρ UV (z = 4)/ρ UV (z = 3) = 1.0 ± 0.2 and ρ UV (z = 5)/ρ UV (z = 3) = 0.8 ± 0.4, thus the cosmic star-formation rate (SFR) density (with correction for dust extinction) remains constant within the error bars, or possibly a slight decline, from z = 3 to z = 5. We estimate the stellar mass density from the cosmic SFR thus obtained, and find that this stellar mass density is consistent with those derived directly from the stellar mass function at z = 0 − 1, but exceeds those at z ∼ 3 by a factor of 3. We find that the ratio of the UV-luminosity density of Lyman α emitters (LAEs) to that of LBGs is ≃ 60% at z ≃ 5, and thus about a half of star formation probably occurs in LAEs at z ≃ 5. We obtain a constraint on the escape fraction of UV-ionizing photons (i.e., UV continuum in 900Å) produced by LBGs, f esc 0.13. This implies that the escape fraction of LBGs may be larger than that of star-forming galaxies at z = 0.

We report on early results from very deep and wide-field narrow-band imaging on a 543 arcmin 2 area of the Subaru Deep Field. We find 87 Lyman α emitters (LAEs) at z = 4.86 ± 0.03 which are photometrically selected by a combination of two broad bands (R and i ′ ) and one narrow band (N B711; λ c = 7126Å, ∆λ = 73Å). We derive the luminosity functions (LFs) of the LAEs at Lyα luminosity and at UV-continuum (rest-frame 1700Å) luminosity. The LFs show little evolution between z=3.4 and z=4.86 either in Lyα or UV-continuum emission. The amplitude of the LAE LF tends to decline at the bright magnitudes more rapidly than that of the LBG LF at similar redshifts. We calculate the angular correlation function of our LAEs up to ∼ 15 arcmin separations. The angular correlation ω(θ) is found to increase with decreasing angular separations, showing a clear signal of clustering. It is also found that the distribution of LAEs shows a large density gradient with a scale of 15 arcmin, which would indicate the existence of a large-scale structure of LAEs on 20h −1 Mpc scales. We fit the observed correlation function by A ω θ −0.8 to find A ω = 29 arcsec 0.8 . The estimated correlation length is r 0 = 3.5 +0.3 −0.3 h −1 Mpc in comoving units (Ω m = 0.3 and Ω Λ = 0.7), which is slightly larger than the value for z ∼ 4 LBGs with i ′ < 26. We calculate the angular correlation function for two sub-samples of the 87 LAEs divided by Lyα luminosity, UV-continuum luminosity, and Lyα equivalent width (EW ). The Lyα-bright sub-sample shows a larger correlation amplitude than the Lyα-faint sub-sample, while no significant difference is found for the sub-samples divided by UV-continuum luminosity or EW . This may indicate that galaxies with bright Lyα emission are possibly biased against the underlying dark matter halos more strongly than those with bright UV continuum.

We investigate the clustering properties of 2,600 Lyman Break Galaxies (LBGs) at z = 3.5 − 5.2 in two large blank fields, the Subaru Deep Field and the Subaru/XMM Deep Field (600arcmin 2 each). The angular correlation functions of these LBGs show a clear clustering at both z ≃ 4 and 5. The correlation lengths are r 0 = 4.1 +0.2 −0.2 and 5.9 +1.3 −1.7 h −1 100 Mpc (r 0 = 5.1 +1.0 −1.1 and 5.9 +1.3 −1.7 h −1 100 Mpc) for all the detected LBGs (for L L * LBGs) at z ≃ 4 and 5, respectively. These correlation lengths correspond to galaxy-dark matter biases of b g = 2.9 +0.1 −0.1 and 4.6 +0.9 −1.2 (b g = 3.5 +0.6 −0.7 and 4.6 +0.9 −1.2 ), for all the detected LBGs (for L L * LBGs) at z ≃ 4 and 5, respectively. These results, combined with estimates for z ≃ 3 LBGs in the literature, show that the correlation length of L L * LBGs is almost constant, ∼ 5h −1 100Mpc, over z ≃ 3 − 5, while the bias monotonically increases with redshift at z 3. We also find that for LBGs at z ≃ 4 the clustering amplitude increases with UV-continuum luminosity and with the amount of dust extinction. We estimate the mass of dark halos hosting various kinds of high-z galaxies including LBGs with the analytic model given by Sheth & Tormen (1999). We find that the typical mass of dark halos hosting L L * LBGs is about 1 × 10 12 h −1 70 M ⊙ over z ≃ 3 − 5, which is comparable to that of the Milky Way Galaxy. A single dark halo with ∼ 10 12 h −1 70 M ⊙ is found to host 0.1-0.3 LBG on average but host about four K-band selected galaxies.11 Searches of LBGs in targeted fields are also made by, e.g., Bouche & Lowenthal (2003) who find a significant clustering of LBGs around a damped Ly α absorber at z = 3. 12 Spergel et al. (2003) show that the best-fit parameters are n = 0.93 ± 0.03 and σ 8 = 0.84 ± 0.04. However, the differences between these