The Radio Wavelength Time Delay of Gravitational Lens 0957+561

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Abstract
The gravitational lens 0957+561 was monitored with the Very Large Array from 1979 to 1997. The 6 cm light-curve data from 1995 to 1997 and the 4 cm data from 1990 to 1997 are reported here. At 4 cm the intrinsic source variations occur earlier and are twice as large as the corresponding variations at 6 cm. The VLBI core and jet components have different magnification factors, leading to different flux ratios for the varying and nonvarying portions of the VLA light curves. Using both the Press, Rybicki, & Hewitt Q (PRHQ) and dispersion statistical techniques, we determined the time delay, core flux ratio, and excess nonvarying B image flux density. The fits were performed for the 4 and 6 cm light curves, both individually and jointly, and we used Gaussian Monte Carlo data to estimate 68% statistical confidence levels. The delay estimates from each individual wavelength were inconsistent given the formal uncertainties, suggesting that there are unmodeled systematic errors in the analysis. We roughly estimate the systematic uncertainty in the joint result from the difference between the 6 and 4 cm results, giving 409±30 days for the PRHQ statistic and 397±20 days for the dispersion statistic. These results are consistent with the current optical time delay of 417±3 days, reconciling the long-standing difference between the optical and radio light curves and between different statistical analyses. The unmodeled systematic effects may also corrupt light curves for other lenses, and we caution that multiple events at multiple wavelengths may be necessary to determine an accurate delay in any lens system. Now that consensus has been reached regarding the time delay in the 0957+561 system, the most pressing issue remaining for determining H0 is a full understanding of the mass distribution in the lens.
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