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We define a second-order moment of the observational differential microlensing curves that can be used to impose constraints on physical properties of lensed quasars. We show that this quantity is sensitive both to variations in the source size and the deflector mass. We formulize a methodology to recover the source size from the observational measurements when the mass spectrum is fixed. As a case study, we test it with a sample of four quadruple lenses, both in simulated scenarios and with real data from the Chandra X-ray Observatory. In our simulations with a uniform stellar population the method works best to detect sources around 0.1 Einstein radii, giving correct upper/lower limits for much smaller/bigger sizes without requiring a big leap in additional computational effort as compared to a single-epoch approach, yet taking advantage of multi-epoch information. We apply the method to a small sample of X-ray data from four objects assuming a range of star masses, and obtain a degeneracy relation between the source size and deflector mass. Combined with previous estimates for the size of the X-ray corona, the degeneracy relation suggests that X-ray microlensing is mainly induced by planetary mass objects. [ABSTRACT FROM AUTHOR]

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 Chandra X-Ray Observatory. We tentatively detected FeKα emission lines in MG J0414+0534 and Q 0957+561 with over 95% significance, whereas, we did not significantly detect FeKα 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 rest frame 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, (Bayesian), 11.81 ± 3.75 (maximum likelihood), where. However, for MG J0414+0534 and Q 0957+561, the two methods yield substantially 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 RX ∝ MBH with the mass of the central supermassive black hole. Our Bayesian analysis results also indicate that radio-loud quasars tend to have larger unresolved X-ray emission sizes compared to the radio-quiet ones, suggesting a more prominent jet contribution. [ABSTRACT FROM AUTHOR]

We construct a sample of 10 680 wall galaxies and 3064 void galaxies with M R ≲ −20 by cross-referencing a void catalogue from literature with Baryon Oscillation Spectroscopic Survey (BOSS) CMASS and WiggleZ galaxies, where the CMASS survey targets redder galaxies and the WiggleZ survey targets bluer galaxies. Comparing the density profiles of the red and blue galaxies as a function of the void radius, we find that the number ratio of red-to-blue galaxies increases with distances from the void centres, suggesting a deficit of luminous and normal red galaxies in voids. We find a mean (g – r) magnitude colour of 1.298 and 1.210 for the wall and void galaxies, respectively, when considering the combined red and blue samples, which is found to be a significant difference. However, when considering the blue and red samples separately, we find no significant colour difference. We conclude that the constituents galaxies of each population, rather than intrinsic colour difference, is the main driver in the apparent average colour difference of galaxies in voids and walls, indicating a deficit of luminous and normal red galaxies in voids. Our analysis suggests that the primary environmental-dependence effect on galaxy evolution for normal and luminous galaxies between void and wall regions is manifested in the number of red galaxies, which depends on the environmental-dependent merger history. Using a semi-analytic simulation model, we can successfully reproduce the apparent colour difference between the void and wall galaxies. [ABSTRACT FROM AUTHOR]