Flux Ratio Anomalies: Micro- and Milli-lensing

Simple models for lensing potentials that successfully reproduce the positions of quadruple images to high accuracy fail abysmally in reproducing the flux ratios of the multiple images, suggesting the presence of small scale structure within the lensing galaxies. It has been argued that the flux ratio anomalies observed at radio wavelengths signal the presence of CDM mini-halos. We argue that at least some of the anomalies observed at optical wavelengths result from micro-lensing by stars. This model succeeds in explaining observed asymmetry between minima and saddle-points of the light travel time only if a substantial fraction of the projected mass is in a smooth, dark component. 1. Flux Ratio Anomalies? There is a theorem in gravitational lensing that says, under certain circumstances, a close pair of images in a quadruple system will be both bright and of equal brightness (e.g. Gaudi and Petters 2002). The archetype of such systems, PG1115+080 (Weymann et al. 1980), has a pair of bright images separated by 0. 48. But as is often the case, the archetype turns out not to be archetypical. Zhao and Metcalf (2002) have examined a range of “reasonable” models for PG1115 and find that the rms magnitude difference for the A1 and A2 (figure 1) images ought to be roughly 10%. The observed difference appears to have varied with time, having ranged from 5-50% (Vanderriest et al. 1986; Kristian et al. 1993; Courbin et al. 1997; Iwamuro et al 2000), well outside the range allowed by the models. One might argue that the combination of intrinsic variability and gravitational time delay could produce the observed differences, but the predicted differential time delay between A1 and A2 is of order one day and the quasar varies much more slowly (Schechter et al. 1997). Other quads with similar configurations have the same problem, only worse. MG0414+0534 has a I-filter magnitude difference A1 − A2 = 0.9 (Schechter and Moore 1993). By contrast the radio flux ratio (Moore and Hewitt 1977), The separation between images must be small compared to the displacement of the images from the galaxy and the gravitational potential must be smooth on the scale of the image separation. The theorem is then a direct consequence of expanding the light travel time as a power series in the neighborhood of a critical curve, keeping terms up to third order in distance from the critical curve.