Interpretation of microlensing events in Q2237 + 0305

We point out the uncertainties in the potential models of the foreground galaxy in the gravitational lens Q2237 + 0305. The surface densities and external shears are uncertain by a factor of appproximately less than 2. Very long light curves are calculated for different models using the method developed by Witt (1993) and Lewis et al. (1993). We find that the probability of images being in a quiescent state depends strongly on the potential models and the direction of the source motion relative to the alignment of the (gravitational lens) shear term of the macroimages. For example, the probabilities of finding variations smaller than 0.1 mag and for a period of longer than 0.5 Einstein radii (approximately equals 3-5 yr) in image C and D are approximately 30%. This offers an explanation of why image C and D showed relatively small variations. The quiescent images are more likely to be demagnified, consistent with the observations. Further, the higher the magnification of the macroimages, the weaker are the microlensing events. In addition, we conclude that a simple Gaussian profile has some difficulties in explaining the asymmetric shape and the small amplitude of the observed high-magnification events if they are typical. Source models in which the emission is produced by a brightt compact core and a more extended halo can occur better explain the observed double peak events. More data are needed to clearly distinguish different galaxy potential models.