The X-Ray Continuum Emission Region in the Lensed Quasar SDSS J133907.23+131038.6 is Much Smaller than the Accretion Disk
We analyze microlensing variability in 15 seasons of optical monitoring data and 4 epochs of new X-ray observations of the doubly-imaged gravitationally lensed quasar SDSS J133907.23+131038.6 to place empirical constraints on the size and structure of that system's X-ray and optical continuum emission regions. Employing a Bayesian Monte Carlo method, we analyzed ground-based optical light curves to constrain the half-light radius of the far-UV source $\log(r_{\rm 1/2, FUV}/{\rm cm})=15.78^{+0.26}_{-0.28}$ at 193 nm, the rest-frame center of the {\it r}-band, assuming a $60^\circ$ inclination angle. This size corresponds to $\sim100\,{\it r}_{\rm g}$ for a $4.0 \times 10^{8} \: {\rm M_{\odot}}$ black hole. We measured the half-light radius of the full band ($0.2-8.0 \: {\rm keV}$) X-ray continuum emission region $\log(r_{\rm 1/2, X_{full}}/{\rm cm})=14.32^{+0.23}_{-0.31}$, a size measurement that is consistent with the radius of the innermost stable circular orbit (ISCO) in the Schwarzschild metric.Two shifted Fe K$\alpha$ lines caused by microlensing are detected in the stacked spectrum of image A at 5.9 and 8.9~keV at $>99\%$ significance.