Luminosity Functions of Lyman-Break Galaxies at z~4 and 5 in the Subaru Deep Field

We investigate the luminosity functions of Lyman-break galaxies (LBG) at z~4 and 5 based on the optical imaging data obtained in the Subaru Deep Field Project. Three samples of LBGs in a contiguous 875 arcmin^2 area are constructed. One consists of 3,808 LBGs at z~4 down to i'=26.85 selected with the B-R vs R-i' diagram. The other two consist of 539 and 240 LBGs at z~5 down to z'=26.05 selected with two kinds of two-color diagrams: V-i' vs i'-z' and R-i' vs i'-z'. The adopted selection criteria are proved to be fairly reliable by spectroscopic observation. We derive the luminosity functions of the LBGs at rest-frame ultraviolet wavelengths down to M_{UV}=-19.2 at z~4 and M_{UV}=-20.3 at z~5. We find clear evolution of the luminosity function over the redshift range of 0<z<6, which is accounted for by a sole change in the characteristic magnitude, M^*. The cosmic star formation rate (SFR) density at z~4 and z~5 is measured from the luminosity functions. We examine the evolution of the cosmic SFR density and its luminosity dependence over 0<z<6. The SFR density contributed from brighter galaxies is found to change more drastically with cosmic time. The contribution from brighter galaxies has a sharp peak around z=3-4, while that from fainter galaxies evolves relatively mildly with a broad peak at earlier epoch. Combining the observed SFR density with the standard Cold Dark Matter model, we compute the cosmic SFR per unit baryon mass in dark haloes, i.e., the specific SFR. The specific SFR is found to scale with redshift as (1+z)^3 up to z~4, implying that the efficiency of star formation is on average higher at higher redshift in proportion to the cooling rate within dark haloes, while this is not simply the case at z>4.