Analysis of Time Delays in the Gravitational Lens PG1115+080

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 $\chi^2$ measure of the agreement of this same variation with all of the lightcurves. Our method provides a simpler and more assumption-free alternative to Press et al. (1992a, b), but it has similar advantages: it yields an approximate reconstruction of the source variation and it easily incorporates different assumptions about the relation between the light curves and about measurement errors. We apply this method to the light curves of the quadruple gravitational lens PG1115+080 measured by Schechter et al. (1996). 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 implying a similar $H_0$ for a given lens model). However, the ratio $t_{AC}/t_{BA}$ of the two intermediate delays is poorly determined at $1.13^{+.18}_{-.17}$ (68% confidence), close to the value predicted by lens models ($\sim 1.4$) unlike the Schechter et al. value ($\sim 0.7$). The variation ratios of C with respect to A and of A with respect to B are both different from 1, $1.39^{+.16}_{-.20}$ and $.79^{+.10}_{-.12}$ (95% confidence), respectively. This is an indication of a microlensing gradient, and this type of microlensing may allow us to set both an upper and a lower limit on the size of the quasar optical emission region. (Shortened Abstract)