A Robust Determination of the Time Delay in 0957+561A, B and a Measurement of the Global Value of Hubble's Constant

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Abstract
Continued photometric monitoring of the gravitational lens system 0957+561A, B in the g and r bands with the Apache Point Observatory (APO) 3.5 m telescope during 1996 shows a sharp g-band event in the trailing (B) image light curve at the precise time predicted in an earlier paper. The prediction was based on the observation of the event during 1995 in the leading (A) image and on a differential time delay of 415 days. This success confirms the so-called short delay, and the absence of any such feature at a delay near 540 days rejects the "long delay" for this system, thus resolving a long-standing controversy. A series of statistical analyses of our light-curve data yield a best-fit delay of 417 ± 3 days (95% confidence interval) and demonstrate that this result is quite robust against variations in the analysis technique, data subsamples, and assumed parametric relationship of the two light curves. Recent improvements in the modeling of the lens system (consisting of a galaxy plus a galaxy cluster) allow us to derive a value of the global value (at z = 0.36) of Hubble's constant H0 using Refsdal's method, a simple and direct (single-step) distance determination based on experimentally verified and securely understood physics and geometry. The result is H0 = 64 ± 13 km s-1 Mpc-1 (for Ω = 1), where this 95% confidence interval is dominantly due to remaining lens model uncertainties. However, it is reassuring that available observations of the lensing mass distribution overconstrain the model and thus provide an internal consistency check on its validity. We argue that this determination of the extragalactic distance scale (10% accurate at 1 σ) is now of comparable quality, in terms of both statistical and systematic uncertainties, to those based on more conventional techniques. Finally, we briefly discuss the prospects for improved H0 determinations using gravitational lenses, and some other possible implications and uses of the 0957+561A, B light curves.