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We define a second-order moment of the observational differentialmicrolensing curves that can be used to impose constraints on physicalproperties of lensed quasars. We show that this quantity is sensitive both tovariations in the source size and the deflector mass. We formulize amethodology to recover the source size from the observational measurements whenthe mass spectrum is fixed. As a case study, we test it with a sample of fourquadruple lenses, both in simulated scenarios and with real data from the$\textit{Chandra X-ray Observatory}$. In our simulations with a uniform stellarpopulation the method works best to detect sources around $0.1$ Einstein radii,giving correct upper/lower limits for much smaller/bigger sizes withoutrequiring a big leap in additional computational effort as compared to asingle-epoch approach, yet taking advantage of multi-epoch information. Weapply the method to a small sample of X-ray data from four objects assuming arange of star masses, and obtain a degeneracy relation between the source sizeand deflector mass. Combined with previous estimates for the size of the X-raycorona, the degeneracy relation suggests that X-ray microlensing is mainlyinduced by planetary mass objects.

A Second-Order Moment of Microlensing Variability as a Novel Tool in Extragalactic Research