Title: Quasar Microlensing Statistics and Flux-Ratio Anomalies in Lens Models

Abstract: Precise lens modeling is a critical step in time delay studies of multiply imaged quasars, which are key for measuring some important cosmological parameters (specially $H_0$). However, lens models (in particular those semi-automatically generated) often show discrepancies with the observed flux-ratios between the different quasar images. These flux-ratio anomalies are usually explained through differential effects between images (mainly microlensing) that alter the intrinsic magnification ratios predicted by the models. To check this hypothesis, we collect direct measurements of microlensing to obtain the histogram of microlensing magnifications. We compare this histogram with recently published model flux-ratio anomalies and conclude that they cannot be statistically explained by microlensing. The average value of the model anomalies ($0.74\,$magnitudes) significantly exceeds the mean impact of microlensing ($0.33\,$magnitudes). Moreover, the histogram of model anomalies presents a significant tail with high anomalies ($|\Delta m| \ge 0.7$ magnitudes) which is completely unexpected from the statistics of microlensing observations. Microlensing simulations neither predict the high mean nor the fat tail of the histogram of model anomalies. We perform several statistical tests which exclude that microlensing can explain the observed flux-ratio anomalies (although Kolmogorov-Smirnov, which is less sensitive to the tail of the distributions, is not always conclusive). Thus, microlensing cannot statistically explain the bulk of flux-ratio anomalies, and models may explore different alternatives to try to reduce them. In particular, we propose to complement photometric observations with accurate flux ratios of the broad emission lines obtained from integral field spectroscopy to check and, ideally, constrain lens models.