An Estimate ofH0from Keck Spectroscopy of the Gravitational Lens System 0957+561

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Abstract
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 σv of the central lens galaxy G1 is σv = 279 ± 12 km s-1. However, there appears to be a significant decrease in σv as a function of distance from the center of G1 that is not typical of the brightest cluster galaxies. Within 02 of the center of G1, we find the average σv = 316 ± 14 km s-1, whereas for positions greater than 02 from the center of G1, we find the average σv = 266 ± 12 km s-1. A plausible explanation is that G1 contains a central massive dark object of mass MMDO ≈ 4 × 109 h−1100 M☉ (h100 = H0/100 km s-1 Mpc-1), which contributes to the central velocity dispersion, and that the outer value of σv is the appropriate measure of the depth of the potential well of G1. The determination of a luminosity-weighted estimate of σv is essential for a determination of H0 from Q0957+561; our accurate measurements remove one of the chief uncertainties in the assumed form of the mass distribution of the lens. Thus, with the recent apparent reduction in the uncertainty in the measurement of the time delay for the images A and B of Q0957+561, ΔτBA = 417 ± 3 days (Kundić et al.), we obtain an estimate for the Hubble constant: H0 = 62 ± 7 km s-1 Mpc-1. If for some reason the trend of σv with slit position is spurious and we should use the dispersion averaged along the slit, then the estimate of H0 increases to 67 ± 8 km s-1 Mpc-1. These standard errors, however, do not include any contribution from any errors in the assumed form of the mass distribution of the lens. In particular, we used the mass model described by Falco, Gorenstein, & Shapiro, as updated by Grogin & Narayan. The reduced χ2 of model fits to the available position and magnification data for this system is relatively high (~4), indicating that the estimate of H0 may have a significant contribution from model errors. Further observations, discussed herein, should allow such errors to be estimated reliably.
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