QSO size ratios from multiband monitoring of a microlensing high-magnification event

We introduce a new scheme to study the nature of the central engine in a lensed QSO. The compact emission regions could have different sizes in different optical wavelengths, and our framework permits to obtain the source size ratios when a microlensing special high-magnification event (e.g., a caustic crossing event, a two-dimensional maximum crossing event and so on) is produced in one of the QSO components. To infer the source size ratios, only cross-correlations between the brightness records in different optical bands are required. While the deconvolution method leads to a richer information (1D intrinsic luminosity profiles), the new approach is free of the technical problems with complex inversion procedures. Using simulations related to recent VR data of Q2237+0305A, we discuss the ability of the scheme in the determination of the visible-to-red ratio q = $R_V/R_R$. We conclude that extremely accurate fluxes (with a few microJy uncertainties, or equivalently, a few milli-magnitudes errors) can lead to ~10% measurements of q. Taking into account the errors in the fluxes of Q2237+0305A from a normal ground-based telescope, ~10 microJy (~10 mmag), it must be possible the achievement of smaller errors from the current superb-telescopes, and thus, an accurate determination of q. Obviously, to measure the visible-to-red ratio, the light curves cannot be contaminated by an intrinsic event or an important high-frequency intrinsic signal, i.e., exceeding the microJy (mmag) level. For an arbitrary lensed QSO, we finally remark that the framework seems to work better with very fast microlensing events.