On the Luminosity Function of Early--Type Galaxies

In a recent paper Loveday et al. (1992) have presented new results on the luminosity function for a sample of galaxies with $b_J\le 17.15$. After having morphologically classified each galaxy (early–type, late–type, merged or uncertain), they have estimated the parameters of a Schechter luminosity function for early-- and late–type galaxies. However, in their sample there is a bias against identifying early–type galaxies at large distances and/or faint magnitudes: in fact, many of the early–type galaxies at faint magnitudes have probably been classified as ``uncertain". As discussed in Loveday et al., the existence of such a bias is indicated by the fact that for these galaxies $<V\mathrm{/}{V}_{max}>=0.32$. In this paper we show, both theoretically and through the use of simulated samples, that this incompleteness strongly biases the derived parameters of the luminosity function for early–type galaxies. If no correction for such incompleteness is applied to the data (as done by Loveday et al.), one obtains a flatter slope $\alpha$ and a brighter $M^{\ast }$ with respect to the real parameters.