X-ray monitoring of gravitationally lensed radio-loud quasars with Chandra

In this work, we calculated the sizes of unresolved X-ray emission regions in three gravitationally lensed radio-loud quasars, B\,1422+231, MG\,J0414+0534 and Q\,0957+561, using a combination of imaging and spectral analysis on the X-ray data taken from the \textit{Chandra X-Ray Observatory}. We tentatively detected FeK$\alpha$ emission lines in MG\,J0414+0534 and Q\,0957+561 with over 95\% significance, whereas, we did not significantly detect FeK$\alpha$ emission in B\,1422+231. We constructed differential microlensing light curves from absorption corrected count rates. We subsequently performed a microlensing analysis on the X-ray microlensing light curves to measure the X-ray source sizes in soft (0.83--3.6 keV), hard (3.6--21.8 keV), and full (0.83--21.8 keV) bands, based on either Bayesian or maximum likelihood probabilities. For B\,1422+231, sizes from the two methods are consistent with each other, e.g. $R_X^{hard}/R_G = 6.17\pm5.48 \text{ (Bayesian), } 11.81\pm3.75 \text{ (maximum likelihood)}$, where $R_G=GM_{BH}/c^2)$. However, for MG\,J0414+0534 and Q\,0957+561, the two methods yield completely different results suggesting that more frequently sampled data with better signal-to-noise ratio are needed to measure the source size for these two objects. Comparing the acquired size values with the radio-quiet sample in the literature we found that our results are consistent with X-ray source size scaling approximately as $R_X \propto M_{BH}$ with the mass of the central supermassive black hole. Our results also indicate that radio-loud quasars tend to have larger unresolved X-ray emission sizes compared to the radio-quiet ones.