The role of microlensing in estimates of the relative time delay for the gravitational images of Q0957 + 561

We present a study of the effects of individual stars in the gravitational lens that forms the images A and B of the QSO Q0957 + 561. The main result is evidence that it is very unlikely that microlensing effects dominate the observed fluctuations of the images. Therefore, the measured (but uncertain) correlation between the light curves of the images is likely due to intrinsic luminosity variations at the source, rather than to propagation effects at the lens. It is found, however, that the disagreement between magnification estimates at optical and radio wavelengths is a strong indicator of microlensing. Thus, estimates for the time delay for A and B, $$\Delta\tau_\text {BA}$$, should be obtained for spectral bands that are least affected by microlensing, i.e., the largest emission regions in the QSO. However, recent estimates for $$\Delta\tau_\text {BA}$$ are different for the two available optical data sets, and they depend strongly on the method used to cross-correlate the light curves. From simulated model data, we single out a reliable method for cross-correlation in the present situation. We also propose a method that yields simultaneous estimates for the time delay for an image pair and for their magnification ratio at optical wavelengths.