Extended X-ray Monitoring of Gravitational Lenses with Chandra and Joint   Constraints on X-ray Emission Regions
  We present an X-ray photometric analysis of six gravitationally lensed quasars, with observation campaigns spanning from 5 to 14 years, measuring the total (0.83 - 21.8 keV restframe), soft (0.83 - 3.6 keV), and hard (3.6 - 21.8 keV) band image flux ratios or each epoch. Using the ratios of the model-predicted macro-magnifications as baselines, we build differential microlensing light curves and obtain joint likelihood functions for the average X-ray emission region sizes. Our analysis yields a Probability Distribution Function for the average half-light radius of the X-Ray emission region in the sample that peaks slightly above 1 gravitational radius and with nearly indistinguishable 68% confidence (one-sided) upper limits of 17.8 and 18.9 gravitational radii for the soft and hard X-ray emitting regions, assuming a mean stellar mass of 0.3 solar masses. We see hints of energy dependent microlensing between the soft and hard bands in two of the objects. In a separate analysis on the root-mean-square of the microlensing variability, we find significant differences between the soft and hard bands but the sign of the difference is not consistent across the sample. This suggests the existence of some kind of spatial structure to the X-ray emission in an otherwise extremely compact source. We also discover a correlation between the RMS microlensing variability and the average microlensing amplitude. 
Eduardo Guerras, Xinyu Dai, Shaun Steele, Ang Liu, Christopher S.   Kochanek, George Chartas, Christopher W. Morgan, Bin Chen
astro-ph.HE astro-ph.GA