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 (σ_Re) and at 0.54 effective radii (σ_0.54Re). We find by a dynamical analysis that the normalized velocity dispersion of the dark halo of an elliptical galaxy σ_DM is roughly σ_Re 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*)=(σ_DM/σ_DM*) ^γ, where γ is between 2 and 3. These results are of interest for strong gravitational lensing statistics studies. In order to determine the value of σ_DM*, we calculate M_BT0* in the same B_T0 band in which σ_DM* has been estimated. We select 131 elliptical galaxies as a complete sample set with apparent magnitudes B_T0 between 9.26 and 12.19. We find that the luminosity function is well fitted to the Schechter form, with parameters M_BT0*=-19.66+5·log₁₀h±0.30, α=0.15±0.55, and the normalization constant φ*=(1.34±0.30)×10^-3h³ Mpc^-3, with the Hubble constant H_o=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.