The evolution of the luminosity functions in the FORS Deep Field from low to high redshift. I. The blue bands

We use the very deep and homogeneous I-band selected dataset of the FORS Deep Field (FDF) to trace the evolution of the luminosity function over the redshift range 0.5 < z < 5.0. We show that the FDF I-band selection down to I sub(AB) = 26.8 misses of the order of 10% of the galaxies that would be detected in a K-band selected survey with magnitude limit K sub(AB) = 26.3 (like FIRES). Photometric redshifts for 5558 galaxies are estimated based on the photometry in 9 filters (U, B, Gunn g, R, I, SDSS z, J, K and a special filter centered at 834 nm). A comparison with 362 spectroscopic redshifts shows that the achieved accuracy of the photometric redshifts is Delta z/(z sub(spec) + 1) less than or equal to 0.03 with only similar to 1% outliers. This allows us to derive luminosity functions with a reliability similar to spectroscopic surveys. In addition, the luminosity functions can be traced to objects of lower luminosity which generally are not accessible to spectroscopy. We investigate the evolution of the luminosity functions evaluated in the restframe UV (1500 AA and 2800 AA), u', B, and g' bands. Comparison with results from the literature shows the reliability of the derived luminosity functions. Out to redshifts of z similar to 2.5 the data are consistent with a slope of the luminosity function approximately constant with redshift, at a value of -1.07 plus or minus 0.04 in the UV (1500 AA, 2800 AA) as well as u', and -1.25 plus or minus 0.03 in the blue (g', B). We do not see evidence for a very steep slope ( alpha less than or equal to -1.6) in the UV at < z > similar to 3.0 and < z > similar to 4.0 favoured by other authors. There may be a tendency for the faint-end slope to become shallower with increasing redshift but the effect is marginal. We find a brightening of M* and a decrease of phi * with redshift for all analyzed wavelengths. The effect is systematic and much stronger than what can be expected to be caused by cosmic variance seen in the FDF. The evolution of M* and phi * from z = 0 to z = 5 is well described by the simple approximations M*(z) = M* sub(0) + a ln (1 + z) and phi *(z) = phi * sub(0)(1 + z) super(b) for M* and phi *. The evolution is very pronounced at shorter wavelengths (a = -2.19, and b = -1.76 for 1500 AA rest wavelength) and decreases systematically with increasing wavelength, but is also clearly visible at the longest wavelength investigated here (a = -1.08, and b = -1.29 for g'). Finally we show a comparison with sem