We investigate the luminosity functions of Lyman-break galaxies ( LBG ) at z \sim 4 and 5 based on the optical imaging data obtained in the Subaru Deep Field ( SDF ) Project , a program conducted by Subaru Observatory to carry out a deep and wide survey of distant galaxies .
Three samples of LBGs in a contiguous 875 arcmin ^ { 2 } area are constructed .
One consists of LBGs at z \sim 4 down to i ^ { \prime } = 26.85 selected with the B - R vs R - i ^ { \prime } diagram ( BRi ^ { \prime } -LBGs ) .
The other two consist of LBGs at z \sim 5 down to z ^ { \prime } = 26.05 selected with two kinds of two-color diagrams : V - i ^ { \prime } vs i ^ { \prime } - z ^ { \prime } ( Vi ^ { \prime } z ^ { \prime } -LBGs ) and R - i ^ { \prime } vs i ^ { \prime } - z ^ { \prime } ( Ri ^ { \prime } z ^ { \prime } -LBGs ) .
The number detected is 3 , 808 for BRi ^ { \prime } -LBGs , 539 for Vi ^ { \prime } z ^ { \prime } -LBGs , and 240 for Ri ^ { \prime } z ^ { \prime } -LBGs .
The adopted selection criteria are proved to be fairly reliable by the spectroscopic observation of 63 LBG candidates , among which only 2 are found to be foreground objects .
We estimate the fraction of contamination and the completeness for these three samples by Monte Carlo simulations , and derive the luminosity functions of the LBGs at rest-frame ultraviolet wavelengths down to M _ { \mathrm { UV } } = -19.2 at z \sim 4 and M _ { \mathrm { UV } } = -20.3 at z \sim 5 .
We find clear evolution of the luminosity function over the redshift range of 0 \leq z \leq 6 , which is accounted for by a sole change in the characteristic magnitude , M ^ { \ast } .
The cosmic star formation rate ( SFR ) density at z \sim 4 and z \sim 5 is measured from the luminosity functions .
The measurements of the integrated SFR density at these redshifts are largely improved , since the luminosity functions are derived down to very faint magnitudes .
We examine the evolution of the cosmic SFR density and its luminosity dependence over 0 \leq z \lesssim 6 .
The SFR density contributed from brighter galaxies is found to change more drastically with cosmic time .
The contribution from galaxies brighter than M ^ { \ast } _ { \mathrm { z = 3 } } -0.5 has a sharp peak around z = 3 – 4 , while that from galaxies fainter than M ^ { \ast } _ { \mathrm { z = 3 } } -0.5 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 \sim 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 \gtrsim 4 .