2001NewA....6..249C

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 σDM* 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/σDM*)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 σDM*, we calculate MBT0* in the same BT0 band in which σDM* has been estimated. We select 131 elliptical galaxies as a complete sample set with apparent magnitudes BT0 between 9.26 and 12.19. We find that the luminosity function is well fitted to the Schechter form, with parameters MBT0*=-19.66+5.log10h±0.30, α=0.15±0.55, and the normalization constant φ*=(1.34±0.30)x10-3h3 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.