Extended Data Fig. 4: Interferometric microlensing model and constraints on the microlens-source relative motion.
From: Microlensing mass measurement from images of rotating gravitational arcs
Panel a shows the model parameters for a single microlens L (black dot in the center), involving a point-source star (PSPL model) or an extended source (ESPL model). The (unseen) source S is the orange disk, of angular radius ρ in θE units (or the black dot in its center for a point source). The trajectory of the source with respect to the microlens is shown as the black thick arrow. It makes an angle \(\alpha ^{\prime}\) with the East-West horizontal axis, and \({u}_{0}^{\prime}\) (in θE units) is its signed impact parameter relative to the microlens. The major and minor arc-shaped images of the source are in red and blue respectively (or for a point source, the two black dots in their centers). The line joining the center of the two images makes an angle α1 with the East-West axis (with the major image up). For single epochs modelling, u1 is the microlens-source distance in θE units. As the source moves relative to the microlens along the black arrow, the images rotate around the microlens. Panel b displays the source at two consecutive epochs: S1 (orange filled disk) and S2 (orange circle), with corresponding images (major ‘+’ and minor ‘−’) labeled (I1+,I1−) and (I2+,I2−) respectively. Another trajectory is also shown, with the source at consecutive positions \({S}_{1}^{\prime}\) and \({S}_{2}^{\prime}\) and corresponding to images at (\({I}_{1+}^{\prime},{I}_{1-}^{\prime}\)) and (\({I}_{2+}^{\prime},{I}_{2-}^{\prime}\)). The similarity of the arcs for these two scenarii shows that the ratio ρ/u1 is measured by the interferometric squared visibilities, rather than the two parameters individually. Panels c and d show that when the major (red) and minor (blue) images are almost identical (which happens at high magnification), four directions of the microlens-source relative motion are possible (panel c). When three epochs are obtained, only two possibilities only remain (panel d), that can eventually be distinguished by the analysis of closure phases (if the asymmetry between the arcs produces effects above the noise).
