Galaxy counts in the K band , ( J - K ) -colors , and apparent size distributions of faint galaxies in the Subaru Deep Field ( SDF ) down to K \sim 24.5 were studied in detail .
Special attention has been paid to take into account various selection effects including the cosmological dimming of surface brightness , to avoid any systematic bias which may be the origin of controversy in previously published results .
We also tried to be very careful about systematic model uncertainties ; we present a comprehensive surveys of these systematic uncertainties and dependence on various parameters , and we have shown that the dominant factors to determine galaxy counts in this band are cosmology and number evolution .
We found that the pure luminosity evolution ( PLE ) model is well consistent with all the SDF data down to K \sim 22.5 , without any evidence for number or size evolution in a low-density , \Lambda -dominated flat universe which is now favored by various cosmological observations .
On the other hand , a number evolution of galaxies with \eta \sim 2 , when invoked as the luminosity conserving mergers as \phi ^ { * } \propto ( 1 + z ) ^ { \eta } and L ^ { * } \propto ( 1 + z ) ^ { - \eta } for all types of galaxies , is necessary to explain the data in the Einstein-de Sitter universe .
If the popular \Lambda -dominated universe is taken for granted , our result then gives a strong constraint on the number evolution of giant elliptical or early-type galaxies to z \sim 1–2 which must be met by any models in the hierarchically clustering universe , since such galaxies are the dominant population in this magnitude range ( K~ { } \raisebox { -4.3 pt } { $ \stackrel { \textstyle < } { \sim } $ } ~ { } 22.5 ) .
A number evolution with \eta \sim 1 is already difficult to reconcile with the data in this universe .
On the other hand number evolution of late type galaxies and/or dwarf galaxies , which has been suggested by previous studies of optical galaxies , is allowed from the data .
In the fainter magnitude range of K~ { } \raisebox { -4.3 pt } { $ \stackrel { \textstyle > } { \sim } $ } ~ { } 22.5 , we found a slight excess of observed counts over the prediction of the PLE model when elliptical galaxies are treated as a single population .
We suggest that this discrepancy reflects some number evolution of dwarf galaxies and/or the distinct populations of giant and dwarf elliptical galaxies which have been known for local elliptical galaxies .