The ESO-Sculptor Survey: Luminosity functions of galaxies per spectral type at redshifts 0.1-0.5

[ABRIDGED] We present the first statistical analysis of the complete ESO-Sculptor redshift survey (ESS). The flux-calibrated sample of 617 galaxy spectra with R_c<20.5 is separated into 3 spectral classes (early, intermediate, and late). We report in detail on the spectral classification, the polynomial K-corrections, and all sources of corresponding random and systematic errors. The derived luminosity functions (LF) in the Johnson-Cousins B and Rc bands are in agreement with the results from the comparable CNOC2 survey (Lin et al. 1999), whereas the ESS provides the first estimates of LFs per spectral type in the Johnson V band. A renewed interpretation of the galaxy LFs from a redshift survey are obtained by fitting the ESS LFs with composite functions based on the local LFs per morphological type (Sandage, Binggeli & Tammann 1985; Jerjen & Tammann 1997). As good or better fits than with pure Schechter functions are obtained using: for the early-type LF, a two-wing Gaussian; for the intermediate-type LF, the sum of a Gaussian modeling the Spiral galaxies and a steep Schechter function (alpha=-1.5) representing the dwarf elliptical galaxies; for the late-type LF, a similar composite function with a flat or weaker slope (-0.8<alpha<-0.3) for the Schechter component which represents the dwarf Irregular galaxies. This analysis illustrates how LFs per spectral type may be affected by morphological type mixing, and emphasizes the need for a quantitative morphological classification at z>0.1 which separates the giant and dwarf galaxy populations.Comment: 33 Pages, 13 color figures, A&A Latex macro. Published in A&