A Robust Determination of the Time Delay in 0957+561A,B and a Measurement of the Global Value of Hubble's Constant
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 1 Supported by the Fannie and John Hertz Foundation 2 Currently at the Kitt Peak National Observatory 3 Currently at the Space Telescope Science Institute -- 2 -- 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 Sigma 3 days (95% confidence interval) and demonstrate that this result is quite robust against variations in the analysi...
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ABSTRACT: Several time delay estimates have been reported for the quasar Q0957+561. They come from distinct data sets and published separately. This paper presents a method-ology to estimate a single time delay given several data sets by using multi-objective optimisation. We use General Regression Neural Networks (GRNN) to estimate the time delay, which is one of the most accurate time delay esti-mators – and faster. For the time delay agreement, we use hill-climbing search. We found that the best agreement for the time delay on Q0957+561 is ∆ = 420 days.
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ABSTRACT: We study the problem of estimating the time delay between two signals representing delayed, irregularly sampled and noisy versions of the same underlying pattern. We propose and demonstrate an evolutionary algorithm for the (hyper)parameter estimation of a kernel-based technique in the context of an astronomical problem, namely estimating the time delay between two gravitationally lensed signals from a distant quasar. Mixed types (integer and real) are used to represent variables within the evolutionary algorithm. We test the algorithm on several artificial data sets, and also on real astronomical observations of quasar Q0957+561. By carrying out a statistical analysis of the results we present a detailed comparison of our method with the most popular methods for time delay estimation in astrophysics. Our method yields more accurate and more stable time delay estimates: for Q0957+561, we obtain 419.6 days for the time delay between images A and B. Our methodology can be readily applied to current state-of-the-art optical monitoring data in astronomy, but can also be applied in other disciplines involving similar time series data. Comment: 36 pages, 10 figures, 16 tables, accepted for publication in Pattern Recognition. This is a shortened version of the article: interested readers are urged to refer to the published versionPattern Recognition 08/2009; 43(3):1165-1179. · 2.58 Impact Factor