Subaru spectroscopy of the gravitational lens HST 14176+5226: Implications for a large cosmological constant

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 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 ± 14 km s^-1 (1 σ) 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 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 the 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 greater likelihood for a larger cosmological constant Ω_λ: the formal 1 σ lower limit on Ω_λ in the flat universe ranges from 0.73 to 0.97, whereas the 2 σ 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 Ω _λ.