A Second-Order Moment of Microlensing Variability as a Novel Tool in
  Extragalactic Research
  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
$\textit{Chandra X-ray Observatory}$. 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.
