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Date and Time of the Query: 2019-06-24 T10:14:26 PDT
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For refcode 2001NewA....6..249C:
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2001NewA....6..249C An elliptical galaxy luminosity function and velocity dispersion sample of relevance for gravitational lensing statistics Yu-Chung N. Cheng1 and Lawrence M. Krauss Received 26 August 1999; received in revised form 12 February 2001; accepted 12 February 2001 Abstract We have selected 42 elliptical galaxies from the literature and estimated their 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 that the normalized velocity dispersion of the dark halo of an elliptical galaxy {sigma}_DM_ is roughly {sigma}_R_e__ multiplied by a constant, which is almost independent of the core radius or the anisotropy parameter of each galaxy. Our sample analysis suggests that {sigma}_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^*^)=({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 determine the value of {sigma}_DM_^*^, we calculate M_B_T_(0}^*^ in the same B_T_(0) band in which {sigma}_DM_^*^ has been estimated. We select 131 elliptical galaxies as a complete sample set with apparent magnitudes B_T_(0) between 9.26 and 12.19. We find that the luminosity function is well fitted to the Schechter form, with parameters M_B_T_(0)^*^ = -19.66+5 . log_10_h+/-0.30,{alpha} = 0.15+/-0.55, and the normalization constant {phi}^*^=(1.34+/-0.30)x 10^- 3^h^-3^ Mpc^-3^, with the Hubble constant H_0_=100 h km s^-1^ Mp^-1^. This normalization implies that morphology type E galaxies make up (10.8 +/- 1.2) per cent of all galaxies. Keywords: Gravitational lensing; Galaxies: fundamental parameters; Galaxies: halos; Galaxies: kinematics and dynamics; Galaxies: luminosity function, mass function; Methods: statistical
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