Analysis of Time Delays in the Gravitational Lens PG 1115+080

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Abstract
We present a new method for determining time delays among the light curves of various images in a gravitational lens. The method is based on constructing a simple model for the source variation and forming a χ2 measure of the agreement of this same variation with all of the light curves. While inspired by Press, Rybicki, & Hewitt, our approach is different since we do not assume a Gaussian process for the source variation. Our method has a number of desirable properties: first, it yields an approximate reconstruction of the source variation and of other parameters such as relative time delays; second, it easily incorporates different assumptions about the relations among the light curves and about the data measurement errors; finally, it can be applied to more than two light curves by the addition of χ2. We apply this method to the light curves of the quadruple gravitational lens PG 1115+080 measured by Schechter et al. Unlike Schechter et al., we include correlated measurement errors in the analysis, as well as the possibility that microlensing may cause different images to vary by different factors in flux. We find a value of 25.0+ 3.3−3.8 days (95% confidence) for the delay between components B and C (close to the 24-day value of Schechter et al., and so leading to a similar value of the Hubble constant for a given lens model). However, the ratio tAC/tBA of the two intermediate delays is poorly determined at 1.13+ 0.18−0.17 (68% confidence), close to the value predicted by the lens models (~1.4), unlike the Schechter et al. value (~0.7). The variation ratios of C with respect to A and of A with respect to B are both different from 1, 1.39+ 0.16−0.20, and 0.79+ 0.10−0.12 (95% confidence), respectively. This is an indication of a microlensing gradient, and this type of microlensing may allow us to conclude that the size of the quasar optical emission region is about 1000 AU.