An Estimation of H from Keck Spectroscopy of the Gravitational Lens System 0957 + 561

We present long-slit LRIS/Keck spectroscopic observations of the gravitational lens system 0957 + 561. Averaged over all of our data, the rest-frame velocity dispersion v of the central lens galaxy G1 is v = 279 12 km s ?1. However, there appears to be a signiicant decrease in v as a function of distance from the center of G1. Within 0: 00 2 of the center of G1, we nd the average v = 316 14 km s ?1 , whereas for positions > 0: 00 2 from the center of G1, we nd the average v = 266 12 km s ?1. A plausible explanation is that G1 contains a central massive dark object of mass the central velocity dispersion, and that the outer value of v is the appropriate measure of the depth of the potential well of G1. The determination of a luminosity-weighted estimate of v is essential for a determination of H from Q 0957 + 561; our accurate measurements remove one of the chief uncertainties in the parameterization of this lens system. Thus, with the recent apparent reduction in the uncertainty in the measurement of the time delay for the images A and B of Q 0957 + 561, BA = 417 3 d (Kundi c et al. 1996), we obtain an estimate for the Hubble constant: H = 62 7 km s ?1 Mpc ?1. If for some reason the trend of v with slit position is spurious and we should use the dispersion averaged along the slit, then the estimate of H increases to 67 8 km s ?1 Mpc ?1. These standard errors do not, however, include any contribution from lens model uncertainties. The reduced 2 of model ts to the available position and magniication data for this system is relatively high (4), indicating that the estimate of H may have a signiicant contribution from model errors. Further observations, discussed herein, should allow such errors to be estimated reliably.