AN ESTIMATE OF H-0 FROM KECK SPECTROSCOPY OF THE GRAVITATIONAL LENS SYSTEM-0957+561

We present long-slit LRIS/Keck spectroscopic observations of the gravi tational lens system 0957 + 561. Averaged over all of our data, the re st-frame velocity dispersion a, of the central lens galaxy G1 is sigma (upsilon) = 279 +/- 12 km s(-1). However, there appears to be a signif icant decrease in sigma(upsilon) as a function of distance from the ce nter of G1 that is not typical of the brightest cluster galaxies. With in 0.''2 of the center of G1, we find the average sigma(upsilon) = 316 +/- 14 km s(-1), whereas for positions greater than 0.''2 from the ce nter of G1, we find the average sigma(upsilon) = 266 +/- 12 km s(-1). A plausible explanation is that G1 contains a central massive dark obj ect of mass M-MDO approximate to x 10(9) h(100)(-1) M. (h(100) = H-0/1 00 km s(-1) Mpc(-1)), which contributes to the central velocity disper sion, and that the outer value of sigma(upsilon) is the appropriate me asure of the depth of the potential well of G1. The determination of a luminosity-weighted estimate of sigma(upsilon) is essential for a det ermination of H-0 from Q0957 + 561; our accurate measurements remove o ne of the chief uncertainties in the assumed form of the mass distribu tion of the lens. Thus, with the recent apparent reduction in the unce rtainty in the measurement of the time delay for the images A and B of Q0957 + 561, Delta tau(BA) = 417 +/- 3 days (Kundic et al.), we obtai n an estimate for the Hubble constant: H-0 = 62 +/- 7 km s(-1) Mpc(-1) . If for some reason the trend of sigma(upsilon) with slit position is spurious and we should use the dispersion averaged along the slit, th en the estimate of H-0 increases to 67 +/- 8 km s(-1) Mpc(-1). These s tandard errors, however, do not include any contribution from any erro rs in the assumed form of the mass distribution of the lens. In partic ular, we used the mass model described by Falco, Gorenstein, & Shapiro , as updated by Grogin & Narayan. The reduced chi(2) of model fits to the available position and magnification data for this system is relat ively high (similar to 4), indicating that the estimate of H-0 may hav e a significant contribution from model errors. Further observations, discussed herein, should allow such errors to be estimated reliably.