22,53,54). This is termed a “flux ratio anomaly” and is most likely due to small scale structure in the mass distribution of the lens (64). The idea is that there is some mass condensation in the smooth dark matter distribution of the lensing galaxy, and this object further perturbs the light from the background quasar through its own gravitational influence. Although the angular deflection due to such an object is undetectable with current telescopes, the change in brightness is detectable, leading to the observed flux ratio anomaly.
One natural explanation for this small scale structure is the population of stars present in the lensing galaxy (this scenario is called microlensing) (98,49,7,111). Another explanation is that some small amount (perhaps 10% or so) of the dark matter could be in clumps of about 106 Msun each (this scenario is called millilensing) (14,9,66).
The degree to which a mass condensation can produce an anomaly is related to the size of its Einstein radius compared to the size of the emitting object. If the emitting object is much larger than the Einstein radius, the anomaly will be smoothed out and average to zero. Emitting objects which are small compared to the Einstein radius can be strongly affected (with the maximum anomaly produced for a point source). The size of the emitting region in a quasar is a function of waveband: the X-rays originate from a small region close to the super-massive black hole; the optical continuum originates from a larger region; broad optical emission lines originate from farther out; and narrow optical emission lines from still farther out. By comparing the flux ratio anomalies (or lack thereof) from these different wavebands, we can get a sense of which scenario -- microlensing or millilensing -- is more likely.
To set the scale, the Einstein radius of a mass in a typical lensing galaxy is 3 microarcseconds, where DL is the angular diameter distance of the lens and m is the mass of the condensation. For the case of millilensing by a 106 Msun dark matter condensation, the Einstein radius would dwarf even the largest emission regions in the lensed quasars, and all wavebands would be affected similarly.
In an analysis of the quadruply lensed quasar 1RXSJ1131-1231, Jeffrey Blackburne, Saul Rappaport, and I reported on optical anomalies on the order of factors of two and X-ray anomalies of factors of three to nine (4). The much more severe anomalies in the X-rays support microlensing rather than millilensing occurring in the lensing galaxy. We were able to estimate the local mass constituency in the lensing galaxy at the location of the images -- about 10% of the mass in stars and 90% in smooth matter -- and to estimate the size of the optical emitting region of the lensed quasar.
Similar findings of wavelength-dependent flux ratio anomalies were reported for RXJ0911+0551 (69) and PG1115+080 (88). Based on these intriguing individual studies, we undertook a systematic study of ten quadruply lensed quasars which had both Chandra X-ray data and HST imaging available (87). We found that almost all systems showed evidence for an anomaly, and, in the systems which showed a pronounced anomaly, the X-rays were generally seen to be more anomalous than the optical. For the reason stated above, this points to microlensing by stellar-mass stars as the primary cause of the flux ratio anomalies.
We quantified the magnitude of the anomalies for the entire sample and found the X-rays to be roughly twice as discrepant as the optical compared to the simple lens models. In the context of microlensing, we are able to estimate the necessary size of the optical emitting region that is required to account for this attenuation of the anomalies in the optical. Based on simulations which explored the effect of source size on the magnitude of microlensing anomalies (70), we concluded that the optical emitting regions of the quasars must have sizes about 1/3 of the Einstein radii of a stellar-mass star in the lensing galaxies. This corresponds to physical sizes on the order of 1000 AU, which is a factor of 3 - 30 larger than expected from a standard thin accretion disk (100). We currently have no good explanation for this disagreement with thin disk models, but, regardless of how this discrepancy is resolved, we have shown how the X-ray and optical observations of flux ratio anomalies can be used as micro-arcsecond probes of the lensed quasars and provide physical measurements of the emitting regions.
Interestingly, these same flux ratio anomalies can be used to provide valuable information on the dark matter content of the lensing galaxies. Dark matter distribution is a very difficult problem to model theoretically, but it is of great importance both in understanding galaxy formation and in determining the nature of the dark matter itself. Schechter & Wambsganns (99) used optical flux ratio anomalies for a sample of eleven quadruply lensed quasars to derive the projected stellar/dark mass ratio at the typical impact parameter of a quasar image in the lensing galaxy. They first assumed that the optical emission region was small compared to the Einstein radii of the stars in the lensing galaxy. The result was very heavily influenced by the inclusion (or exclusion) of the system with the most extreme flux ratio anomaly, SDSS0924+0219. They found less discordant results if they instead assumed that half the optical light came from a pointlike source and half came from a more extended source. But allowing for a fraction of the light to come from a more extended region adds a second parameter to the problem, making determination of the stellar/dark matter ratio more uncertain. If, as we demonstrated in our paper, the X-ray emission comes from a region substantially smaller than the optical emission region, the use of X-ray flux ratio anomalies in the analysis of Schechter & Wambsganss would eliminate that second parameter and more uniquely determine the ratio of stellar matter to dark matter. The same study would also give a better idea of the emission region size required to attenuate microlensing variations. Such an analysis is forthcoming.
In addition to this dark matter study with the existing data, our group is actively pushing this new type of study forward. We have received Chandra observations of four new systems and have an upcoming reobservation of PG1115+080. We are also proposing to obtain broad band optical photometry (ugrizJHKs) with Magellan of the four new systems and seven of the ten systems in our previous study. This coverage from X-rays to near-IR will allow us to observe the evolution of the flux ratio anomalies with wavelength and permit a detailed determination of the accretion disk structure around these supermassive black holes. We expect these very rich data sets to hold many interesting results.