paper

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

arXiv:astro-ph/9908292 · doi:10.1016/S1384-1076(01)00047-1

Abstract

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 ($\vff$). We find by a dynamical analysis that the normalized velocity dispersion of the dark halo of an elliptical galaxy $\vdm$ 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 $\vdm^{*}$ lies in the range 178-198 km s. The power law relation we find between the luminosity and the dark matter velocity dispersion measured in this way is $(L/L^{*}) = (\vdm/\vdm^{*})^γ$, where is between 2-3. These results are of interest for strong gravitational lensing statistics studies. In order to determine the value of $\vdm^{*}$, we calculate $\mstar$ in the same $\bt$ band in which $\vdm^{*}$ has been estimated. We select 131 elliptical galaxies as a complete sample set with apparent magnitudes $\bt$ between 9.26 and 12.19. We find that the luminosity function is well fitted to the Schechter form, with parameters $\mstar$ = -19.66 + 5, , and the normalization constant Mpc, with the Hubble constant $\hnot$ = 100 km s Mpc. This normalization implies that morphology type E galaxies make up (10.8 1.2) per cent of all galaxies.

18 pages latex, with ps figs included. accepted by New Astronomy (revised to incorporate referees comments)

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