Astronomy and Astrophysics – Astrophysics
Scientific paper
1999-08-26
New Astron. 6 (2001) 249-263
Astronomy and Astrophysics
Astrophysics
18 pages latex, with ps figs included. accepted by New Astronomy (revised to incorporate referees comments)
Scientific paper
10.1016/S1384-1076(01)00047-1
We have selected 42 elliptical galaxies from the literature and estimated their velocity dispersions at the effective radius ($\sigma_{\re}$) 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 $\sigma_{\re}$ 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$^{-1}$. The power law relation we find between the luminosity and the dark matter velocity dispersion measured in this way is $(L/L^{*}) = (\vdm/\vdm^{*})^\gamma$, where $\gamma$ 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$\cdot\log_{10}h \pm 0.30$, $\alpha = 0.15 \pm 0.55$, and the normalization constant $\phi^{*} = (1.34 \pm 0.30) \times 10^{-3} h^{3}$ Mpc$^{-3}$, with the Hubble constant $\hnot$ = 100 $h$ km s$^{-1}$ Mpc$^{-1}$. This normalization implies that morphology type E galaxies make up (10.8 $\pm$ 1.2) per cent of all galaxies.
Cheng Yu-Chung N.
Krauss Lawrence M.
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