An elliptical galaxy luminosity function and velocity dispersion sample ofrelevance for gravitational lensing statistics

We have selected 42 elliptical galaxies from the literature and estimated t heir velocity dispersions at the effective radius ( sigma (R) (e)) and at 0 .54 effective radii ( sigma (0.54R e)). We find by a dynamical analysis tha t the normalized velocity dispersion of the dark halo of an elliptical gala xy sigma (DM) is roughly sigma (R) (e) multiplied by a constant, which is a lmost independent of the core radius or the anisotropy parameter of each ga laxy. Our sample analysis suggests that sigma*(DM) lies in the range 178- 1 98 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*) = (sigma (DM )/sigma*(DM))(gamma), where gamma is between 2 and 3. These results are of interest for strong gravitational lensing statistics studies. In order to d etermine the value of sigma*(DM), we calculate M*(B T (O)) in the same B-T( 0) band in which sigma*(DM) has been estimated. We select 131 elliptical ga laxies as a complete sample set with apparent magnitudes B-T(0) between 9.2 6 and 12.19. We find that the luminosity function is well fitted to the Sch echter form, with parameters M*(B T (O)) = =19.66+5.log(10)h +/-0.30, alpha = 0.15 +/-0.55, and the normalization constant phi* = (1.34 +/-0.30)x10(-3 )h(3) Mpc-(3) with the Hubble constant H-o = 100h km s(-1) MPC-(1). This no rmalization implies that morphology type E galaxies make up (10.8 +/- 1.2) per cent of all galaxies. (C) 2001 Published by Elsevier Science B.V.