We present new optical spectroscopy of the lens elliptical galaxy in the “ Einstein Cross ” lens system HST 14176 + 5226 , using the Faint Object Camera and Spectrograph ( FOCAS ) of the Subaru telescope .
Our spectroscopic observations are aimed at measuring the stellar velocity dispersion of the lens galaxy , located at high redshift of z _ { L } = 0.81 , as an important component to lens models .
We have measured this dispersion to be 230 \pm 14 km s ^ { -1 } ( 1 \sigma ) inside 0.35 effective radii of the lens , based on the comparison between the observed galaxy spectrum and spectral templates of three G-K giants by means of the Fourier cross-correlation method .
To extract the significance of this information on the geometry of the universe which also affects the lensing of the background image , we attempt to fit three different lens models to the available data of the lens system .
Provided that the lens galaxy has the structural and dynamical properties ( i.e. , its radial density profile , core radius , and velocity anisotropy ) similar to those of local elliptical galaxies , we calculate the likelihood function for the simultaneous reproduction of both the observed image splitting and newly measured velocity dispersion of the lens .
Although the confidence interval depends rather sensitively on the adopted lens models or their parameters , our experiments suggest the larger likelihood for a larger cosmological constant , \Omega _ { \Lambda } : formal 1 \sigma lower limit on \Omega _ { \Lambda } in the flat universe ranges 0.73 to 0.97 , whereas 2 \sigma lower limit is basically unavailable .
This method for determining the world model is thus dependent on lens models but is insensitive to other unavoidable ambiguities , such as the dust absorption or the evolutionary effects of galaxies .
Exploring spectroscopic observations of more lens galaxies at high redshift may minimize the model uncertainties and thus place a much tighter constraint on \Omega _ { \Lambda } .