4 Time delay measurement

By sliding the light curves across one another one can derive a rough time delay estimate of $\sim$125 days. As predicted by gravitational lens theory, the brightest quasar image A is the leading component. Using the $\chi^2$ minimization method described in Burud et al. (2001), a time delay value of $128 \pm 3$ (1$\sigma$) days is found from the R-band light curves. The magnitude difference between the A and the B component is $0.692\pm0.003$ mag, corresponding to an A/B flux ratio of $1.892\pm0.002$. The error bar on the time delay is obtained from Monte Carlo simulations of 1000 sets of light curves, assuming that the photometric errors are uncorrelated and follow a Gaussian distribution. The best $\chi^2$-fit is obtained when a linear term, modelling slow microlensing effects, is added to one of the components. The slope of this term is determined by the algorithm. With this external variation, the shifted light curve of the B component plotted in Fig. 4 becomes $B'=B-0.692-0.000067 \times({\rm JD}-2~451~226)$. The linear correction does not remove all the external variations. Faster variations on time scales of 50-100 days are still present. The iterative version of the algorithm (Burud et al. 2001) was also applied in an attempt to correct for these fast variations. This method yields $\Delta t = 130\pm3$ days, slightly higher than the value found with the direct method but still in agreement within the error bars. Even with the iterative method some of the fastest variations are not corrected for (Fig. 4), notably the small peak in the A component at $\sim$JD 2 451 750 (abscissa 850 in Fig. 4).

Figure 4: Time delay shifted light curves of SBS 1520+530. Left: B is shifted by 0.69 mag, no correction for external variations (e.g., as can be induced by microlensing) is applied. Middle: B is shifted by 0.69 mag and a linear correction for the external variations is applied. Right: B is shifted vertically by 0.69 mag and corrected for external variations with the iterative method (cf. Sect. 4).