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 $<V/V_{max}>=0.32$. 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 $M^*$ with respect to the real parameters.