An Elliptical Galaxy Luminosity Function and Velocity Dispersion Sample of Relevance for Gravitational Lensing Statistics

We have selected 42 elliptical galaxies from the literature and estimated their velocity dispersions at the effective radius (σRe) and at 0.54 effective radii (σ0.54Re). We find by a dynamical analysis that the normalized velocity dispersion of the dark halo of an elliptical galaxy σDM is roughly σRe multiplied by a constant, which is almost independent of the core radius or the anisotropy parameter of each galaxy. Our sample analysis suggests that σ∗ DM lies in the range 178-198 km s −1. The power law relation we find between the luminosity and the dark matter velocity dispersion measured in this way is (L/L∗) = (σDM/σ∗ DM) γ , where γ is between 2-3. These results are of interest for strong gravitational lensing statistics studies. In order to determine the value of σ∗ DM, we calculate M ∗ BT(0) in the same BT (0) band in which σ∗ DM has been estimated. We select 131 elliptical galaxies as a complete sample set with apparent magnitudes BT (0) between 9.26 and 12.19. We find that the luminosity function is well fitted to the Schechter form, with parameters MBT(0) = -19.66 + 5· log10 h±0.30, α = 0.15±0.55, and the normalization constant φ∗ = (1.34 ± 0.30) × 10−3h3 Mpc−3, with the Hubble constant Ho = 100 h km s−1 Mpc−1. This normalization implies that morphology type E galaxies make up (10.8 ± 1.2) per cent of all galaxies.